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We prove that the PoA of First Price Auctions is 1 -- 1/e² ≈ 0.8647, closing the gap between the best known bounds [0.7430, 0.8689]. [ABSTRACT FROM AUTHOR]

The security of wireless sensor networks is a hot topic in current research. Game theory can provide the optimal selection strategy for attackers and defenders in the attack-defense confrontation. Aiming at the problem of poor generality of previous game models, we propose a generalized Bayesian game model to analyze the intrusion detection of nodes in wireless sensor networks. Because it is difficult to solve the Nash equilibrium of the Bayesian game by the traditional method, a parallel particle swarm optimization is proposed to solve the Nash equilibrium of the Bayesian game and analyze the optimal action of the defender. The simulation results show the superiority of the parallel particle swarm optimization compared with other heuristic algorithms. This algorithm is proved to be effective in finding optimal defense strategy. The influence of the detection rate and false alarm rate of nodes on the profit of defender is analyzed by simulation experiments. Simulation experiments show that the profit of defender decreases as false alarm rate increases and decreases as detection rate decreases. Using heuristic algorithm to solve Nash equilibrium of Bayesian game provides a new method for the research of attack-defense confrontation. Predicting the actions of attacker and defender through the game model can provide ideas for the defender to take active defense. [ABSTRACT FROM AUTHOR]

This paper considers a non-zero-sum game for linear discrete-time systems involving two players. Based on a quadratic value function, we derive coupled algebraic Riccati equations. Then, we propose both on-policy and off-policy Q-learning algorithms, which operate without prior knowledge of the system dynamics, to achieve Nash equilibrium. These algorithms necessitate the inclusion of probing noise to ensure the persistence of excitation. We show that the on-policy Q-learning algorithm may introduce bias to the Nash equilibrium due to the probing noise, while the off-policy Q-learning algorithm maintains an unbiased property. Finally, we offer a numerical example to validate the effectiveness of the presented on-policy and off-policy Q-learning algorithms. [ABSTRACT FROM AUTHOR]

We study Asynchronous Dynamic games and show that in games with a finite state space and finite action sets, one can obtain the pure strategy Markov perfect equilibrium by using a simple backward induction method when the time period for the game is finite. The equilibrium strategies for games with an infinite horizon are then obtained as the point-wise limit of the equilibrium strategies of a sequence of finite horizon games, where the finite horizon games are truncated versions of the original game with successively longer time periods. We also show that if the game has a fixed K-period cycle, then there is a stationary Markov equilibrium. Using these results, we derive an algorithm to compute the equilibrium strategies. We test the algorithm in three experiments. The first is a two-player asynchronous game with three states and three actions. In the second experiment, we compute the equilibrium of a cybersecurity game in which there are two players, an attacker and a defender. In the third experiment, we compute the stationary equilibrium of a duopoly game with two firms that choose an output in alternate periods. [ABSTRACT FROM AUTHOR]

Uncertainty, time delays, and jumps often coexist in dynamic game problems due to the complexity of the environment. To address such issues, we can utilize uncertain delay differential equations with jumps to depict the dynamic changes in differential game problems that involve uncertain noise, delays, and jumps. In this paper, we first examine a linear quadratic differential game optimistic value problem within an uncertain environment characterized by jumps and delays. By applying the Z (x , y) transform, we convert the infinite-dimensional problem into a finite-dimensional one. We then demonstrate that the condition for the existence of a Nash equilibrium strategy is equivalent to the existence of solutions to two cross-coupled matrix Riccati equations. Furthermore, we explore the saddle point equilibrium strategy of the linear quadratic differential game optimistic value model and derive the corresponding saddle point equilibrium solution. Finally, we apply our results to solve a carbon emission reduction game problem. [ABSTRACT FROM AUTHOR]

Global Nash equilibrium is an optimal solution for each player in a graphical game. This paper proposes an iterative adaptive dynamic programming-based algorithm to solve the global Nash equilibrium solution for optimal containment control problem with robustness analysis to the iterative error. The containment control problem is transferred into the graphical game formulation. Sufficient conditions are given to decouple the Hamilton–Jacobi equations, which guarantee the solvability of the global Nash equilibrium solution. The iterative algorithm is designed to obtain the solution without any knowledge of system dynamics. Conditions of iterative error for global stability are given with rigorous proof. Compared with existing works, the design procedures of control gain and coupling strength are separated, which avoids trivial cases in the design procedure. The robustness analysis exactly quantifies the effect of the iterative error caused by various sources in engineering practice. The theoretical results are validated by two numerical examples with marginally stable and unstable dynamics of the leader. [ABSTRACT FROM AUTHOR]

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We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability, (ii) if a strategy profile is played in two games, it is also played in every convex combination of these games, and (iii) players can shift probability arbitrarily between two indistinguishable actions, and deleting one of these actions has no effect. Our theorem implies that every equilibrium refinement violates at least one of these axioms. Moreover, every solution concept that approximately satisfies these axioms returns approximate Nash equilibria, even in natural subclasses of games, such as two‐player zero‐sum games, potential games, and graphical games. [ABSTRACT FROM AUTHOR]

Copyright of Zhejiang Electric Power is the property of Zhejiang Electric Power Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we first introduced systems of generalized vector quasi-variational equilibrium problems as well as systems of vector quasi-variational equilibrium problems as their special cases in abstract convex spaces. Next, we established some existence theorems of solutions for systems of generalized vector quasi-variational equilibrium problems and systems of vector quasi-variational equilibrium problems in non-compact abstract convex spaces. Furthermore, we applied the obtained existence theorem of solutions for systems of vector quasi-variational equilibrium problems to solve the existence problem of Nash equilibria for noncooperative games. Then, as applications of the existence result of Nash equilibria for noncooperative games, we studied the existence of weighted Nash equilibria and Pareto Nash equilibria for multi-objective games. The results derived in this paper extended and unified the primary findings presented by some authors in the literature. [ABSTRACT FROM AUTHOR]

With the rapid development of autonomous driving technology, the advent of the autonomous driving era has become inevitable. An in-depth study of consumers' willingness to purchase autonomous vehicles is critical to accelerating the adoption and commercialization of autonomous vehicles. By constructing a tripartite evolutionary game model of governments, automobile manufacturers, and consumers, we analyze the stable choice of unilateral strategy and equilibrium strategy of autonomous vehicle purchase intention. The MATLAB2022b tool was used for data simulation analysis to verify the validity of the conclusion and the influence of related factors on the purchase intention toward autonomous vehicles. The results show the following: (1) The combination of government support, active R&D, and consumer purchasing is the evolutionary stability strategy (ESS) of the model. (2) With an increase in government support, the probability of automobile enterprises taking the initiative to participate in R&D also increases. However, the negative impact of risk can significantly reduce the incentive for firms to conduct R&D and reduce the effectiveness of government support. (3) Government subsidies to consumers and purchase incentives offered by automotive companies can significantly increase the likelihood that consumers will purchase an autonomous vehicle. Based on these findings, recommendations are made to strengthen government support, establish risk mitigation mechanisms, and strengthen market promotion efforts to promote the commercialization of autonomous vehicles. The study provides a new perspective for understanding multi-party interactions in the rollout of autonomous vehicles and provides valuable insights for policymakers and industry stakeholders. [ABSTRACT FROM AUTHOR]

State-owned forest farms are key players in managing forestry resources worldwide, playing a pivotal role in advancing the development of the non-timber forest product industry. This paper constructs a tripartite evolutionary game model involving "government–state-owned forest farms–farmer households" to delve into how state-owned forest farms collaborate with governments and farmer households to propel the growth of the non-timber forest product industry. Additionally, it explores the interactive relationships among multiple stakeholders and their asymptotic stability. The findings reveal that (1) under certain conditions, the game model can achieve four stable equilibrium strategies: (0,0,0), (0,1,0), (0,1,1), and (1,1,1). (2) Key factors influencing the tripartite game include the political performance and administrative costs of local governments involved in the industry's development, assessment performance and reduced management and protection expenses of state-owned forest farms, and sales revenue and planting costs of farmers' under-forest products. (3) The market development costs shared by state-owned forest farms and government subsidies for under-forest planting should be within a reasonable range. This ensures effective promotion of farmers' participation in under-forest planting while maintaining the willingness of state-owned forest farms and governments to actively engage. These findings provide concrete guidelines that policymakers can use to spur sustainable growth in the NTFP sector. [ABSTRACT FROM AUTHOR]

Forests are complex ecosystems that require integrated management to balance economic, social, and environmental dimensions. Conflicting objectives among stakeholders make optimal decision-making particularly challenging. This study seeks to balance the economic gains of forest harvesting with the goals of environmental conservation, with a focus on the Shafarood forest in Northern Iran. We applied multi-objective optimization and game theory to maximize the net present value (NPV) of forest harvesting while enhancing carbon sequestration. The research utilized data on stumpage prices, harvesting costs, tree density, volume per ha, growth rates, interest rates, carbon sequestration, and labour costs. Applying the epsilon-constraint method, we derived Pareto optimal solutions for a bi-objective model, and game theory was applied to negotiate between economic and environmental stakeholders. In the fifth round of bargaining, a Nash equilibrium was achieved between the two players. At this equilibrium point, the economic player achieved NPV from forest harvesting of 9001.884 (IRR 10,000/ha) and amount of carbon sequestration of 159.9383 tons/ha. Meanwhile, the environmental player achieved NPV from forest harvesting of 7861.248 (IRR 10,000/ha), along with a carbon sequestration of 159.9731 tons/ha. Results indicate significant trade-offs but reveal potential gains for both economic and environmental goals. These findings provide a robust framework for sustainable forest management and offer practical tools to support informed decision-making for diverse stakeholders. [ABSTRACT FROM AUTHOR]

To stay competitive, firms regularly invest in innovation by supporting internal capital projects (funded and executed in-house) that explore new products and operational improvements. Each year, in a highly competitive process, managers from different functional units of the firm submit proposals (that include estimated costs and benefits) for such projects. Managers, because of their domain knowledge and expertise, are naturally better informed about the costs and benefits of their respective projects and can use this information strategically to secure funding. An example of such behavior is the under-reporting of the cost estimate of a project and subsequently requesting additional funding during the execution phase. Such strategic behavior not only affects the firm's ability to fund the best projects but is also costly. Motivated by this challenge of deciding the funding of such projects at a global agribusiness firm, we seek a mechanism that is both provably near-optimal for the firm and guarantees truthful reporting from managers. Our setting consists of a principal and multiple agents. In each time period, over an infinite horizon, each agent requests funding for a potential project from the principal. Before submitting his proposal, each agent privately estimates the project's cost and its benefit. If funded, each project is executed in one period. The principal's funding decisions are binary; that is, each project is either funded in full or not funded. The actual cost (benefit) of a funded project is realized on its completion and incurred (earned) by the principal. The agents earn utility from the experience and reputation gained in completing projects. In each period, the principal desires to keep the total spend below a budget but can borrow external money at a cost. Our main contribution is a practically appealing dynamic nonmonetary mechanism for internal capital allocation under which, for any ϵ>0 , (a) truth-telling forms an ϵ-Bayesian Nash equilibrium and (b) the principal's expected utility is within ϵ of the expected utility in the first-best setting. This paper was accepted by Karan Girotra, operations management. Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mnsc.2022.01121. [ABSTRACT FROM AUTHOR]

Quantum game theory merges principles from quantum mechanics with game theory, exploring how quantum phenomena such as superposition and entanglement can influence strategic decision making. It offers a novel approach to analyzing and optimizing complex systems where traditional game theory may fall short. Congestion of passengers, if considered as a network, may fall into the categories of optimization cases of quantum games. This paper explores the application of quantum potential games to minimize congestion in common areas at airports. The players/passengers of the airport have identical interests and they share the same utility function. A metric is introduced that considers a passenger's visit to a common area by setting their preferences, in order to avoid congestion. Passengers can decide whether to visit a specific common area or choose an alternative. This study demonstrates that the proposed game is a quantum potential game for tackling congestion, with identical interests, ensuring the existence of a Nash equilibrium. We consider passengers to be players that want to ensure their interests. Quantum entanglement is utilized to validate the concept, and the results highlight the effectiveness of this approach. The objective is to ensure that not all passengers select the same common place of the airport to reduce getting crowded; hence, the airborne disease infection probability increases due to overcrowding. Our findings provide a promising framework for optimizing passenger flow and reducing congestion in airport common areas through quantum game theory. We showed that the proposed system is stable by encapsulating the Lyapunov stability. We compared it to a simulated annealing approach to show the efficacy of the quantum game approach. We acknowledge that this framework can be utilized in other disciplines as well. For our future work, we will research different strategies than binary ones to investigate the efficacy of the approach. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study how the timing of these decisions affects the total profit and the individual profits of the two agents. Design/methodology/approach: This paper study a supply chain for a network good where there is a manufacturer and a retailer. The manufacturer determines its wholesale price and its share in the retailer's advertising cost while the retailer decides the retail price and the advertising cost. Findings: This paper finds that a stronger network externality leads to higher prices and higher advertising efforts. This increases the profits of both manufacturer and retailer, but the manufacturer's share of advertising costs depends on the order in which the supply chain enterprise make their decisions, the strength of network externality and the effect of advertising determines which decision timeline results in a higher price and greater advertising effort. The manufacturer prefers the price decision to be made before the advertising decision, while the retailer prefers these decisions to be made simultaneously. Research limitations/implications: Although this paper studies the price and advertising decision-making order preferences of channel members based on network externalities, this research can also be expanded from the following aspects based on network effects. First, network externality affects advertising cooperation between both parties in the situation such that the pricing power of retail prices is transferred from the retailer to the manufacturer and the retailer relies on revenue sharing (revenue sharing contract, nonwholesale price contract. Second, the manufacturer dominates the issues in the supply chain, but in reality, a retailer can also be the dominator or there are no dominators (Nash equilibrium). Finally, it is possible to consider pricing and advertising decisions in situations where two manufacturers or retailers compete. Practical implications: When the price is reasonable, advertising investment is the main determinant of product sales. The greater the intensity of network externalities the more retailers will be willing to invest in advertising. An increase in the intensity of network externalities may not necessarily enhance manufacturers' motivation or cooperative advertising, but it depends on the decision-making sequence. The strength of network externalities determines the decision-making sequence preferences of supply chain channel members whose preferences vary leading to conflicts of interest. Originality/value: The impact of cooperative advertising or decision sequence on corporate decision-making has not been considered. To fill this gap, the paper integrates network externality and supply chain cooperative advertising models, focusing on the impact of network externality on pricing and advertising decisions, as well as on the sequence of decisions. [ABSTRACT FROM AUTHOR]

A mechanism allocates one unit of an infinitely divisible commodity among agents reporting a number between zero and one. Nash, Pareto optimal Nash, and strong equilibria are analyzed for the case where the agents have single-dipped preferences. One main result is that when the mechanism satisfies anonymity, monotonicity, the zero–one property, and order preservation, then the Pareto optimal Nash and strong equilibria coincide and result in Pareto optimal allocations that are characterized by so-called maximal coalitions: members of a maximal coalition prefer an equal coalition share over obtaining zero, whereas the outside agents prefer zero over obtaining an equal share from joining the coalition. A second main result is an axiomatic characterization of the associated social choice correspondence as the maximal correspondence satisfying minimal envy Pareto optimality, equal division lower bound, and sharing index order preservation. [ABSTRACT FROM AUTHOR]

The scarcity of land drives urban village redevelopment projects, which involve interest redistribution among stakeholders with distinct demands. This paper utilizes evolutionary game theory and simulation methods, constructing a tripartite game model under the institutional arrangement of bottom-up with private developer funding. This study identifies the stable strategies and evolutionary trends of the tripartite interactions under four distinct scenarios and validates these strategies through simulations. The redevelopment of XC village validates the assumptions of the model and theoretical analysis, suggesting that when private developers adopt forced demolition strategies, although villagers ultimately choose to sign the contract of property exchange, it can easily lead to social conflicts. These research findings can enlighten the government to form a tripartite alliance to smooth urban village redevelopment. [ABSTRACT FROM AUTHOR]

This paper makes progress toward learning Nash equilibria in two-player, zero-sum Markov games from offline data. Despite a large number of prior works tackling this problem, the state-of-the-art results suffer from the curse of multiple agents in the sense that their sample complexity bounds scale linearly with the total number of joint actions. The current paper proposes a new model-based algorithm, which provably finds an approximate Nash equilibrium with a sample complexity that scales linearly with the total number of individual actions. This work also develops a matching minimax lower bound, demonstrating the minimax optimality of the proposed algorithm for a broad regime of interest. An appealing feature of the result lies in algorithmic simplicity, which reveals the unnecessity of sophisticated variance reduction and sample splitting in achieving sample optimality. This paper makes progress toward learning Nash equilibria in two-player, zero-sum Markov games from offline data. Specifically, consider a γ-discounted, infinite-horizon Markov game with S states, in which the max-player has A actions and the min-player has B actions. We propose a pessimistic model–based algorithm with Bernstein-style lower confidence bounds—called the value iteration with lower confidence bounds for zero-sum Markov games—that provably finds an ε-approximate Nash equilibrium with a sample complexity no larger than Cclipped⋆S(A+B)(1−γ)3ε2 (up to some log factor). Here, Cclipped⋆ is some unilateral clipped concentrability coefficient that reflects the coverage and distribution shift of the available data (vis-à-vis the target data), and the target accuracy ε can be any value within (0,11−γ]. Our sample complexity bound strengthens prior art by a factor of min{A,B} , achieving minimax optimality for a broad regime of interest. An appealing feature of our result lies in its algorithmic simplicity, which reveals the unnecessity of variance reduction and sample splitting in achieving sample optimality. Funding: Y. Yan is supported in part by the Charlotte Elizabeth Procter Honorific Fellowship from Princeton University and the Norbert Wiener Postdoctoral Fellowship from MIT. Y. Chen is supported in part by the Alfred P. Sloan Research Fellowship, the Google Research Scholar Award, the Air Force Office of Scientific Research [Grant FA9550-22-1-0198], the Office of Naval Research [Grant N00014-22-1-2354], and the National Science Foundation [Grants CCF-2221009, CCF-1907661, IIS-2218713, DMS-2014279, and IIS-2218773]. J. Fan is supported in part by the National Science Foundation [Grants DMS-1712591, DMS-2052926, DMS-2053832, and DMS-2210833] and Office of Naval Research [Grant N00014-22-1-2340]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0342. [ABSTRACT FROM AUTHOR]

The common setting of a queueing-game model consists of a stochastic stream of customers arriving at a queueing system one by one, each customer strategically chooses an action that may depend on information they receive regarding the system state. The aggregate customer decision profile gives rise to a system steady state, and, provided customers arrive at said steady state, if their decision is utility maximizing (ex ante), then this aggregate decision profile constitutes a Nash equilibrium. However, expressing the steady-state distribution for a given decision profile is very often a difficult task, and in such a case, an attempt to find a Nash equilibrium via direct analysis is futile. In the article "Stochastic Approximation of Symmetric Nash Equilibria in Queueing Games," Ravner and Snitkovsky suggest a novel stochastic algorithm that learns the Nash equilibrium in a class of queueing games, based on a single adaptive simulation. The method is robust and is easy to implement, offering a practical solution to queueing-game models that classical queueing-analytic methods prove inadequate. We suggest a novel stochastic-approximation algorithm to compute a symmetric Nash-equilibrium strategy in a general queueing game with a finite action space. The algorithm involves a single simulation of the queueing process with dynamic updating of the strategy at regeneration times. Under mild assumptions on the utility function and on the regenerative structure of the queueing process, the algorithm converges to a symmetric equilibrium strategy almost surely. This yields a powerful tool that can be used to approximate equilibrium strategies in a broad range of strategic queueing models in which direct analysis is impracticable. Funding: This work was supported by Columbia University and the Shenzhen Research Institute for Big Data. [ABSTRACT FROM AUTHOR]

We study the convergence problem for mean field games with common noise and controlled volatility. We adopt the strategy recently put forth by Laurière and the second author, using the maximum principle to recast the convergence problem as a question of "forward-backward propagation of chaos" (i.e., (conditional) propagation of chaos for systems of particles evolving forward and backward in time). Our main results show that displacement monotonicity can be used to obtain this propagation of chaos, which leads to quantitative convergence results for open-loop Nash equilibria for a class of mean field games. Our results seem to be the first (quantitative or qualitative) that apply to games in which the common noise is controlled. The proofs are relatively simple and rely on a well-known technique for proving wellposedness of forward-backward stochastic differential equations, which is combined with displacement monotonicity in a novel way. To demonstrate the flexibility of the approach, we also use the same arguments to obtain convergence results for a class of infinite horizon discounted mean field games. Funding: J. Jackson is supported by the National Science Foundation [Grant DGE1610403]. L. Tangpi is partially supported by the National Science Foundation [Grants DMS-2005832 and DMS-2143861]. [ABSTRACT FROM AUTHOR]

We consider the problem of fairly allocating a set of indivisible goods to a set of strategic agents with additive valuation functions. We assume no monetary transfers, and therefore, a mechanism in our setting is an algorithm that takes as input the reported—rather than the true—values of the agents. Our main goal is to explore whether there exist mechanisms that have pure Nash equilibria for every instance and, at the same time, provide fairness guarantees for the allocations that correspond to these equilibria. We focus on two relaxations of envy-freeness, namely, envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX), and we positively answer the preceding question. In particular, we study two algorithms that are known to produce such allocations in the nonstrategic setting: round-robin (EF1 allocations for any number of agents) and a cut-and-choose algorithm of Plaut and Roughgarden (EFX allocations for two agents). For round-robin, we show that all of its pure Nash equilibria induce allocations that are EF1 with respect to the underlying true values, whereas for the algorithm of Plaut and Roughgarden, we show that the corresponding allocations not only are EFX, but also satisfy maximin share fairness, something that is not true for this algorithm in the nonstrategic setting! Further, we show that a weaker version of the latter result holds for any mechanism for two agents that always has pure Nash equilibria, which all induce EFX allocations. Funding: This work was supported by the Horizon 2020 European Research Council Advanced "Algorithmic and Mechanism Design Research in Online Markets" [Grant 788893], the Ministero dell'Università e della Ricerca Research project of national interest (PRIN) "Algorithms, Games, and Digital Markets," the Future Artificial Intelligence Research project funded by the NextGenerationEU program within the National Recovery and Resilience Plan (PNRR-PE-AI) scheme [M4C2, investment 1.3, line on Artificial Intelligence], the National Recovery and Resilience Plan-Ministero dell'Università e della Ricerca (PNRR-MUR) project IR0000013-SoBigData.it, the Nederlandse Organisatie voor Wetenschappelijk Onderzoek Veni Project [Grant VI.Veni.192.153], and the National Recovery and Resilience Plan Greece 2.0 funded by the European Union under the NextGenerationEU Program [Grant MIS 5154714]. [ABSTRACT FROM AUTHOR]

A major challenge of multiagent reinforcement learning (MARL) is the curse of multiagents, where the size of the joint action space scales exponentially with the number of agents. This remains to be a bottleneck for designing efficient MARL algorithms, even in a basic scenario with finitely many states and actions. This paper resolves this challenge for the model of episodic Markov games. We design a new class of fully decentralized algorithms—V-learning, which provably learns Nash equilibria (in the two-player zero-sum setting), correlated equilibria, and coarse correlated equilibria (in the multiplayer general-sum setting) in a number of samples that only scales with maxi∈[m]Ai , where Ai is the number of actions for the ith player. This is in sharp contrast to the size of the joint action space, which is ∏i=1mAi. V-learning (in its basic form) is a new class of single-agent reinforcement learning (RL) algorithms that convert any adversarial bandit algorithm with suitable regret guarantees into an RL algorithm. Similar to the classical Q-learning algorithm, it performs incremental updates to the value functions. Different from Q-learning, it only maintains the estimates of V-values instead of Q-values. This key difference allows V-learning to achieve the claimed guarantees in the MARL setting by simply letting all agents run V-learning independently. Funding: This work was partially supported by Office of Naval Research Grant N00014-22-1-2253. [ABSTRACT FROM AUTHOR]

Problem definition: Social influenced emotions of pride and guilt have been identified by the environmental psychology (EP) literature as crucial drivers impacting recycling behavior, but they have mostly been overlooked in operations management (OM) research. In contrast, EP studies often ignore firms' operational decisions. We analyze the impacts of both social influence and firms' operational decisions to provide a comprehensive understanding of consumers' recycling behaviors, which is essential for realizing remanufacturing's full potential. Methodology/results: We consider a closed-loop supply chain consisting of a manufacturer selling a single product to a consumer community. Consumers' recycling behavior depends on both the recycling reward offered by the manufacturer, as well as intrinsic and socially influenced pride (guilt) from recycling (not recycling). We develop an evolutionary game to model consumers' recycling behavior and characterize the resulting equilibrium recycling rate, which is then integrated into the manufacturer's decision problem. We characterize the manufacturer's optimal strategy and the equilibrium recycling rate in four distinct regions defined by both the product's overall difficulty of remanufacturing and the underlying strengths of consumers' socially influenced pride and guilt. We show that in settings where the product has a moderately high difficulty of remanufacturing and consumers have stronger socially influenced pride than guilt, the manufacturer optimally induces an interior recycling rate. In such scenarios, there exist win-win pathways in using social influence–based interventions to increase both the manufacturer's profit and the recycling rate. However, misalignment may occur when consumers substantially care for the product's recyclability. Managerial implications: This study bridges sustainable OM and EP literature by analyzing how consumers' socially influenced emotions of pride and guilt affect a manufacturer's optimal decisions, profits, and the resulting recycling rate. We provide important insights for designing effective and efficient social influence–based interventions to improve recycling rates. Funding: W. Chen was supported by the National Natural Science Foundation of China [Grant 71902017], and C.-L. Tseng was supported by the University of New South Wales UNOVA Knowledge Hub. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.0721. [ABSTRACT FROM AUTHOR]

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, with applications in diverse fields such as economics, political science, and biology. However, the Nash equilibrium may not always align with desired outcomes within the broader system. This article introduces a novel game engineering framework that tweaks strategic payoffs within a game to achieve a pre-defined desired Nash equilibrium while averting undesired ones. Leveraging mixed-integer linear programming, this framework identifies intricate combinations of players and strategies and optimal perturbations to their payoffs that enable the shift from undesirable Nash equilibria to more favorable ones. We demonstrate the effectiveness and scalability of our approach on games of varying complexity, ranging from simple prototype games such as the Prisoner's Dilemma and Snowdrift games with two or more players to complex game configurations with up to 10 6 entries in the payoff matrix. These studies showcase the capability of this framework in efficiently identifying the alternative ways of reshaping strategic payoffs to secure desired Nash equilibria and preclude undesired equilibrium states. Our game engineering framework offers a versatile toolkit for precision strategic decision-making with far-reaching implications across diverse domains. [ABSTRACT FROM AUTHOR]

Coordinating with others is part of our everyday experience. Previous studies using sensorimotor coordination games suggest that human dyads develop coordination strategies that can be interpreted as Nash equilibria. However, if the players are uncertain about what their partner is doing, they develop coordination strategies which are robust to the actual partner's actions. This has suggested that humans select their actions based on an explicit prediction of what the partner will be doing—a partner model—which is probabilistic by nature. However, the mechanisms underlying the development of a joint coordination over repeated trials remain unknown. Very much like sensorimotor adaptation of individuals to external perturbations (eg force fields or visual rotations), dynamical models may help to understand how joint coordination develops over repeated trials. Here we present a general computational model—based on game theory and Bayesian estimation—designed to understand the mechanisms underlying the development of a joint coordination over repeated trials. Joint tasks are modeled as quadratic games, where each participant's task is expressed as a quadratic cost function. Each participant predicts their partner's next move (partner model) by optimally combining predictions and sensory observations, and selects their actions through a stochastic optimization of its expected cost, given the partner model. The model parameters include perceptual uncertainty (sensory noise), partner representation (retention rate and internale noise), uncertainty in action selection and its rate of decay (which can be interpreted as the action's learning rate). The model can be used in two ways: (i) to simulate interactive behaviors, thus helping to make specific predictions in the context of a given joint action scenario; and (ii) to analyze the action time series in actual experiments, thus providing quantitative metrics that describe individual behaviors during an actual joint action. We demonstrate the model in a variety of joint action scenarios. In a sensorimotor version of the Stag Hunt game, the model predicts that different representations of the partner lead to different Nash equilibria. In a joint two via-point (2-VP) reaching task, in which the actions consist of complex trajectories, the model captures well the observed temporal evolution of performance. For this task we also estimated the model parameters from experimental observations, which provided a comprehensive characterization of individual dyad participants. Computational models of joint action may help identifying the factors preventing or facilitating the development of coordination. They can be used in clinical settings, to interpret the observed behaviors in individuals with impaired interaction capabilities. They may also provide a theoretical basis to devise artificial agents that establish forms of coordination that facilitate neuromotor recovery. Author summary: Acting together (joint action) is part of everyday experience. But, how do we learn to coordinate with others and collaborate? Using a combination of experiments and computational models we show that through multiple repetitions of the same joint task we select the action which represents the 'best response' to what we believe our opponent will do. Such a belief about our partner (partner model) is developed gradually, by optimally combining prior assumptions (how repeatable or how erratic our opponent behaves) with sensory information about our opponent's past actions. Rooted in game theory and Bayesian estimation, the model accounts for the development of the mutual 'trust' among partners which is essential for establishing a mutually advantageous collaboration, and explains how we combine decisions and movements in complex coordination scenarios. The model can be used as a generative tool, to simulate the development of coordination in a specific joint action scenario, and as an analytic tool to characterize the individual traits or defects in the ability to establish collaborations. [ABSTRACT FROM AUTHOR]

Deep neural networks (DNNs) are fundamental to modern applications like face recognition and autonomous driving. However, their security is a significant concern due to various integrity risks, such as backdoor attacks. In these attacks, compromised training data introduce malicious behaviors into the DNN, which can be exploited during inference or deployment. This paper presents a novel game-theoretic approach to model the interactions between an attacker and a defender in the context of a DNN backdoor attack. The contribution of this approach is multifaceted. First, it models the interaction between the attacker and the defender using a game-theoretic framework. Second, it designs a utility function that captures the objectives of both parties, integrating clean data accuracy and attack success rate. Third, it reduces the game model to a two-player zero-sum game, allowing for the identification of Nash equilibrium points through linear programming and a thorough analysis of equilibrium strategies. Additionally, the framework provides varying levels of flexibility regarding the control afforded to each player, thereby representing a range of real-world scenarios. Through extensive numerical simulations, the paper demonstrates the validity of the proposed framework and identifies insightful equilibrium points that guide both players in following their optimal strategies under different assumptions. The results indicate that fully using attack or defense capabilities is not always the optimal strategy for either party. Instead, attackers must balance inducing errors and minimizing the information conveyed to the defender, while defenders should focus on minimizing attack risks while preserving benign sample performance. These findings underscore the effectiveness and versatility of the proposed approach, showcasing optimal strategies across different game scenarios and highlighting its potential to enhance DNN security against backdoor attacks. [ABSTRACT FROM AUTHOR]

Weapon target assignment is a critical challenge in military contexts. Traditionally, commanding officers manually decide weapon assignments, but the problem's complexity has grown over time. To address this, automated systems have been introduced. These systems fall into two categories, which are static (time-independent) and dynamic (considering changes over time). Static systems solve the problem for a single time step without considering temporal changes. Dynamic systems incorporate time as a variable, adapting to evolving scenarios. Two main approaches exist, which are asset-based and target-based. Asset-based approach maximizes the survival probability of assets, which is our focus in this study. We propose a solution using game theory that spans the entire area and all time frames. We employ game theory, treating continuous functions of time as utility functions for vessels. Continuous probability-to-kill values for weapons are defined across the area. Threat trajectories yield continuous kill probabilities for the weapons, translating to vessel utility. To avoid inefficiencies, we align individual vessel utility with global utility. The Nash Equilibrium provides the optimal weapon assignment strategy. Our study uses a naval environment for analysis. In summary, our research leverages game theory to dynamically assign weapons to naval vessels, aiming to maximize asset survival. [ABSTRACT FROM AUTHOR]

We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in a new light in so far as the incompleteness and undecidability of the concept, as well as the nature of strategies in general, can be seen as the consequences of certain no-go theorems. We show that games of the generic imitation type follow a circularity of idealization that includes the good regulator theorem, generalized synchrony, and undecidability of the Turing test. We discuss Bayesian games in the light of Bell non-locality and establish the basics of quantum games, which we relate to local operations and classical communication protocols. In this light, we also review the rationality of gaming strategies from the players' point of view. [ABSTRACT FROM AUTHOR]

We investigate the equilibrium strategies for customers arriving at overtaking-free queueing networks and receiving partial information about the system's state. In an overtaking-free network, customers cannot be overtaken by others arriving after them. We assume that customer arrivals follow a Poisson process and that service times at any queue are independent and exponentially distributed. Upon arrival, the received partial information is the total number of customers already in the network; however, the distribution of these among the queues is left unknown. Adding rewards for being served and costs for waiting, we analyze the economic behavior of this system, looking for equilibrium threshold strategies. The overtaking-free characteristic allows for coupling of its dynamics with those of corresponding closed Jackson networks, for which an algorithm to compute the expected sojourn times is known. We exploit this feature to compute the profit function and prove the existence of equilibrium threshold strategies. We also illustrate the results by analyzing and comparing two simple network structures. [ABSTRACT FROM AUTHOR]

Under the background of the Energy Internet and the shared economy, it is of great significance to explore the collaborative planning strategies of multi-energy microgrids (MEMGs) and a shared energy storage operator (SESO) supported by shared energy storage resources. In this context, a joint planning method of SESO and MEMG alliances based on a dynamic game with perfect information is proposed in this paper. First, an upper-level model for energy storage capacity configuration and pricing strategy planning of SESO is proposed to maximize the total planning and operational income of SESO. Then, a lower-level model for the optimal configuration of MEMGs' alliance considering SES is proposed to minimize the total planning and operational costs of the MEMG alliance. On this basis, a solving algorithm based on the dynamic game theory with perfect information and the backward induction method is proposed to obtain the Nash equilibrium solution of the proposed bi-level optimization models. Finally, a case study with one SESO and an alliance consisting of five MEMGs is conducted, and the simulation results show that the proposed bi-level optimization method can increase SESO's net income by 1.47%, reduce the average planning costs for each MEMG at least by 1.7%, and reduce model solving time by 62.9% compared with other counterpart planning methods. [ABSTRACT FROM AUTHOR]

We study the Tullock contest model with loss aversion and endogenously formed reference points. In a contest with n possibly heterogeneous players and convex effort costs, we establish sufficient conditions for a unique Nash equilibrium in pure strategies. Subsequently, we analyze the impact of loss aversion on players' spending behavior, probability of winning, and rent dissipation. [ABSTRACT FROM AUTHOR]

In game theory, mechanism design is concerned with the design of incentives so that a desirable outcome will be achieved under the assumption that players act rationally. In this paper, we explore the concept of equilibrium design, where incentives are designed to obtain a desirable equilibrium that satisfies a specific temporal logic property. Our study is based on a framework where system specifications are represented as temporal logic formulae, games as quantitative concurrent game structures, and players' goals as meanpayoff objectives. We consider system specifications given by LTL and GR(1) formulae, and show that designing incentives to ensure that a given temporal logic property is satisfied on some/every Nash equilibrium of the game can be achieved in PSPACE for LTL properties and in NP/SP2 for GR(1) specifications. We also examine the complexity of related decision and optimisation problems, such as optimality and uniqueness of solutions, as well as considering social welfare, and show that the complexities of these problems lie within the polynomial hierarchy. Equilibrium design can be used as an alternative solution to rational synthesis and verification problems for concurrent games with mean-payoff objectives when no solution exists or as a technique to repair concurrent games with undesirable Nash equilibria in an optimal way. [ABSTRACT FROM AUTHOR]

In this article, a game theoretic non‐cooperative dynamic target tracking algorithm that empowers defensive unmanned aerial vehicles (UAVs), with directional sensing capabilities to track and collect information on intrusive UAVs, is proposed. Specifically, defenders aim to maximize the collection of identity information from intruders possessing anti‐tracking and evading capabilities, while simultaneously preventing their entry into protected areas. Game theory is employed to determine the optimal confrontation paths for defenders against the intruders. The probability perception model is utilized for evaluating the dynamic target tracking capability and designing a tracking merit function to assess tracking performance, taking into account both the target's position and the perception relative angle. Furthermore, considering the dynamic interactive behaviors between intruders and defenders, the iterative linear quadratic game (ILQG) algorithm is employed to solve the Nash equilibrium of the non‐cooperative target tracking game. Through simulation experiments, the effectiveness of the proposed algorithm in accomplishing multi‐agent dynamic target tracking tasks is demonstrated and the performance of the algorithm under varying parameters in the intruder's cost function is evaluated, which represent different intrusion intentions. [ABSTRACT FROM AUTHOR]

Traditional jamming technologies have become less effective with the development of anti-jamming technologies, especially with the appearance of intelligent transmitters, which can adaptively adjust their transmission strategies. To deal with intelligent transmitters, in this paper, a game-based intelligent jamming scheme is proposed. Considering that the intelligent transmitter has multiple transmission strategy sets whose prior probabilities are unknown to the jammer, we first model the interaction between the transmitter and the jammer as a dynamic game with incomplete information. Then the perfect Bayesian equilibrium is derived based on assumptions of some prior information. For more practical applications when no prior information about the transmitter is available at the jammer, a Q-learning-based method is proposed to find an intelligent jamming strategy by exploiting the sensing results of the wireless communications. The design of the jammer's reward function is guided by the game utility and the reward is calculated based on the Acknowledgement/Negative Acknowledgement feedback of the receiver. Simulation results show that the proposed scheme has only 0.5 % loss in jamming utility compared to that of the perfect Bayesian equilibrium strategy. Compared to existing jamming schemes, a higher packet error rate can be achieved by the proposed scheme by consuming less jamming power. [ABSTRACT FROM AUTHOR]

This article introduces a class of Nash games among Stackelberg players (NASPs), namely, a class of simultaneous noncooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a Stackelberg game where a leader optimizes a (parametrized) linear objective function subject to linear constraints, whereas its followers solve convex quadratic problems subject to the standard optimistic assumption. Although we prove that deciding if a NASP instance admits a Nash equilibrium is generally a Σ2p -hard decision problem, we devise two exact and computationally efficient algorithms to compute and select Nash equilibria or certify that no equilibrium exists. We use NASPs to model the hierarchical interactions of international energy markets where climate change aware regulators oversee the operations of profit-driven energy producers. By combining real-world data with our models, we find that Nash equilibria provide informative, and often counterintuitive, managerial insights for market regulators. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.03418. [ABSTRACT FROM AUTHOR]

The deepening implementation of the energy and carbon market imposes trading requirements on multiple regional integrated energy system participants, including power generation plants, industrial users, and carbon capture, utilization, and storage (CCUS) facilities. Their diverse roles in different markets strengthen the interconnections among these subsystems. On the other hand, the operation of CCUS, containing carbon capture (CS), power-to-hydrogen (P2H), and power-to-gas (P2G), results in the coupling of regional carbon reduction costs with the operation of electricity and hythane networks. In this paper, we propose a regional economic dispatching model of an integrated energy system. The markets are organized in a centralized form, and their clearing conditions are considered. CCUS is designed to inject hydrogen or natural gas into hythane networks, operating more flexibly. A generalized Nash game is applied to analyze the multiple trading equilibria of different entities. Simulations are carried out to derive a different market equilibrium regarding network scales, seasonal load shifts, and the ownership of CCUS. Simulation results in a 39-bus/20-node coupled network indicate that the regional average carbon prices fluctuate from ¥1078.82 to ¥1519.03, and the organization of independent CCUS is more preferred under the proposed market structure. [ABSTRACT FROM AUTHOR]

Infrastructure networks are critical components of contemporary society, and numerous approaches have been suggested for the selection of strategies to protect these networks. However, for uncertain environments, research on attack and defense game models for infrastructure networks is limited. Therefore, after reviewing the existing approaches, a method based on interval-valued intuitionistic fuzzy set (IVIFS) theory is proposed for attack and defense games in critical infrastructure networks. First, we present the process of constructing the game model proposed in this paper, which mainly includes the formulation of the cost model, the strategies, and the method of generating IVIFS payoffs. Next, the Nash equilibria of the game are identified by a pair of nonlinear programming models based on IVIFS theory. Finally, experiments are conducted on a target scale-free network, and an investigation into the variation patterns of the Nash equilibria under different circumstances is also conducted. We provide explanations for these variation patterns by considering payoffs from the perspective of mathematical programming models. Furthermore, we find that compared to the existing attack and defense game model with crisp payoffs, the model proposed in this paper leads to superior Nash equilibria. Our work is a preliminary attempt to analyse attack and defense games for infrastructure networks based on IVIFS theory, providing a method for assessing payoffs in uncertain environments for the attacker and defender. This topic deserves further study. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of optimism in an e-commerce supply chain where two third-party sellers offer substitutable products through a shared e-commerce platform. In this context, optimism is defined as a cognitive bias in which third-party sellers underestimate the probability of encountering low market potential. We present a game-theoretic model to characterize the equilibrium strategies of both the platform and the sellers. Our analysis reveals that when both sellers exhibit optimism bias, this bias invariably leads to lower expected profits for them. However, seller optimism can benefit both the platform and the whole system. That is, as sellers become more biased, the profits of the platform and the entire supply chain increase. Moreover, when a biased seller competes with a sophisticated one, unilateral optimism can result in a win–lose outcome in which the optimistic seller benefits from her bias at the expense of her sophisticated rival. Indeed, we demonstrate that optimism can confer a competitive advantage in a duopoly, allowing the more biased seller to earn higher profits than its less biased competitor—even if the latter is unbiased or sophisticated. Our work sheds light on the conditions under which optimism bias may have detrimental or beneficial impacts on e-commerce supply chain operations. [ABSTRACT FROM AUTHOR]

With the increasing penetration rate of renewable energy sources over recent years, voltage fluctuations and violations due to the inherent intermittency of renewable energy sources pose a great challenge to the safe and steady operation of distribution networks. To tackle this problem, the voltage regulation problem in distribution networks is formulated as a state-based potential game and then solved in a distributed manner in this paper. Specifically, the power flow model of radial distribution networks is linearized at first. Then, based on the linearized power flow model, a voltage regulation problem in distribution networks is modeled, whose objective function is the sum of voltage profile deviations and reactive power generation costs. Next, the subproblems for each bus is designed based on the state-based potential game theory, in the solving of which only its local and neighbor information are required, facilitating the design of the distributed voltage regulation algorithm. Further, the proposed algorithm is improved by freezing the states of isolated buses during each iteration, increasing its resilience against random link failures. Simulation results show that the proposed distributed voltage regulation algorithm can achieve fast and effective voltage profile regulation in distribution networks while preserving the privacy of distributed generators, even in the presence of random communication link failures. In addition, compared to other distributed voltage regulation algorithms, the proposed algorithm exhibits a faster convergence rate and better voltage regulation performance.

The Internet of Things (IoT) has permeated various fields relevant to our lives. In these applications, countless IoT devices transmit vast amounts of data, which often carry important and private information. To prevent malicious users from spoofing these information, the first critical step is effective authentication. Physical Layer Authentication (PLA) employs unique characteristics inherent to wireless signals and physical devices and is promising in the IoT due to its flexibility, low complexity, and transparency to higher layer protocols. In this paper, the focus is on the interaction between multiple malicious spoofers and legitimate receivers in the PLA process. First, the interaction is formulated as a static spoof detection game by including the spoofers and receivers as players. The best authentication threshold of the receiver and the attack rate of the spoofers are consideblack as Nash Equilibrium (NE). Then, closed-form expressions are derived for all NEs in the static environment in three cases: multiplayer games, zero-sum games with collisions, and zero-sum games without collisions. Considering the dynamic environment, a Multi-Agent Deep Deterministic Policy Gradient (MADDPG) algorithm is proposed to analyze the interactions of receiver and spoofers. Last, comprehensive simulation experiments are conducted and demonstrate the impact of environmental parameters on the NEs, which provides guidance to design effective PLA schemes.

In this paper, we first introduced systems of generalized vector quasi-variational equilibrium problems as well as systems of vector quasi-variational equilibrium problems as their special cases in abstract convex spaces. Next, we established some existence theorems of solutions for systems of generalized vector quasi-variational equilibrium problems and systems of vector quasi-variational equilibrium problems in non-compact abstract convex spaces. Furthermore, we applied the obtained existence theorem of solutions for systems of vector quasi-variational equilibrium problems to solve the existence problem of Nash equilibria for noncooperative games. Then, as applications of the existence result of Nash equilibria for noncooperative games, we studied the existence of weighted Nash equilibria and Pareto Nash equilibria for multi-objective games. The results derived in this paper extended and unified the primary findings presented by some authors in the literature.

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Abstract The security of wireless sensor networks is a hot topic in current research. Game theory can provide the optimal selection strategy for attackers and defenders in the attack-defense confrontation. Aiming at the problem of poor generality of previous game models, we propose a generalized Bayesian game model to analyze the intrusion detection of nodes in wireless sensor networks. Because it is difficult to solve the Nash equilibrium of the Bayesian game by the traditional method, a parallel particle swarm optimization is proposed to solve the Nash equilibrium of the Bayesian game and analyze the optimal action of the defender. The simulation results show the superiority of the parallel particle swarm optimization compared with other heuristic algorithms. This algorithm is proved to be effective in finding optimal defense strategy. The influence of the detection rate and false alarm rate of nodes on the profit of defender is analyzed by simulation experiments. Simulation experiments show that the profit of defender decreases as false alarm rate increases and decreases as detection rate decreases. Using heuristic algorithm to solve Nash equilibrium of Bayesian game provides a new method for the research of attack-defense confrontation. Predicting the actions of attacker and defender through the game model can provide ideas for the defender to take active defense.

In the context of China’s vigorous promotion of inter-provincial electricity market construction， there exists a competitive dynamic among multiple purchasing provinces participating in the inter-provincial electricity spot market. To devise a rational bidding strategy for these purchasing provinces， a game bidding model for electricity purchasing tailored to the inter-provincial electricity spot market is proposed. Firstly， the marginal inter-provincial electricity purchase quantity-price curve is calculated based on the operational conditions of the electricity market within each province， serving as the bidding curve for its participation in the inter-provincial electricity spot market. Subsequently， a model for market clearance and pricing in the inter-provincial electricity spot market is proposed under the scenario of variable flow directions of tie-lines. A non-cooperative game bidding model for the inter-provincial market， involving multiple purchasing provinces， is established， where the bidding curve obtained under Nash equilibrium represents the optimal electricity purchase bid for the purchasing provinces. Finally， a simulation calculation is conducted on a case study system comprising two selling provinces and three purchasing provinces to validate the effectiveness of the proposed model and obtain the Nash equilibrium solution of the bidding model for electricity purchase.

With the rapid development of technologies and applications, extending from trusted environments to untrusted environments is the development trend of Internet of Things (IoT) applications. Due to the limited resources of nodes and the rise of edge computing, more and more IoT applications are required to have task delegation functions. Delegating IoT tasks in untrusted environments has to solve two problems: First, how to evaluate the trustworthiness of nodes so that requesters can delegate tasks to trusted providers; the second is how to ensure the successful implementation of the task delegation between the requester and the provider. While trust models are often used to solve the first problem, the lack of ability to describe transactions between the requester and the provider makes them unsuitable for solving the second problem. In recent years, game theory has been more applied to task delegation. By setting appropriate utility functions, game theory can ensure the successful implementation of task delegation. However, since it is unable to evaluate the trustworthiness of nodes, game theory cannot solve the first problem. This paper combines the advantages of trust models and game theory to construct a game of three-party task delegation based on trust to explore a solution to problems of IoT task delegation in an untrusted environment. Finally, aiming at the problem that setting essential parameter values of trust models is empirical and experimental, this paper theoretically discusses how to set these values in an untrusted environment. [ABSTRACT FROM AUTHOR]

To alleviate the pressure of economic development on the marine environment, the Marine Ecological Compensation (MEC) has become a major policy tool for the Chinese government to reconcile the contradiction between economic development and the marine environment. In this paper, we propose a novel two-stage bargaining game data envelopment analysis (DEA) model to evaluate the performance of MEC under the cooperative structure. The proposed model considers the link between marine economic development (MED) and marine environmental protection (MEP). Meanwhile, the equivalent form, Nash equilibrium solution, sensitivity and stability of the model are as well documented to further analyze MED and MEP. Eventually, a case study of 30 coastal cities in China serves to verify the practicable effectiveness of the foregoing model combined with numerical simulation and support key insights as below: (i) According to the results evaluated by the decentralized DEA model, we find that if one party of MED and MEP takes priority, the efficiency score of the other party will be severely affected; (ii) the evaluation results of sensitivity and stability demonstrate that inputs and outputs have different impact degrees on the efficiency scores of MED and MEP, which provide directions for improving the efficiency of both systems; (iii) The proposed model addresses the limitation of the conventional two-stage DEA model that cannot handle uncertain variables, thus revealing the influence of uncertainty on MEC efficiency. The compelling evidence presented in the case study solidifies the effectiveness of the proposed model, establishing its promising prospects for application in evaluating the performance of DMUs with a two-stage structure. [ABSTRACT FROM AUTHOR]

This study presents a novel Buyback Rail Freight Option (BRFO), leveraging Stackelberg game theory to enhance the strategic management of rail freight transactions. By integrating traditional buyback theory with a multi-phase trigeminal tree pricing model and parameter identification through a nonparametric Ito stochastic method, the research addresses key challenges of information asymmetry and market uncertainty. The proposed methodology emphasizes dynamic pricing strategies and market adaptation, constructing a Nash equilibrium framework within railway freight pricing. The findings suggest significant strategic benefits for railway enterprises, positioning BRFO as a crucial tool for improving competitiveness in the face of alternative transport options. [ABSTRACT FROM AUTHOR]

The proposed study introduces a novel anti-jamming approach for cognitive radio networks (CRNs) by integrating the Stackelberg game model with direct sequence spread spectrum (DSSS) techniques. This innovative combination enhances the security and performance of CRNs by optimizing resource allocation and fortifying network resilience against jamming attacks. The Stackelberg game model provides a strategic framework where the Defender and Adversary dynamically adjust their strategies to achieve Nash equilibrium, ensuring strategic stability. The application of DSSS further improves signal robustness, mitigating interference from jamming attempts. Simulation results demonstrate significant improvements in network security, resource utilization, and overall performance, validating the efficacy and advantages of the proposed scheme in maintaining reliable communication in the presence of adversarial threats. [ABSTRACT FROM AUTHOR]

Thanks to reinforcement learning (RL), decision‐making is more convenient and more economical in different situations with high uncertainty. In line with the same fact, it is proposed that prosumers can apply RL to earn more profit in the transactive energy market (TEM). In this article, an environment that represents a novel framework of TEM is designed, where all participants send their bids to this framework and receive their profit from it. Also, new state‐action spaces are designed for sellers and buyers so that they can apply the Soft Actor‐Critic (SAC) algorithm to converge to the best policy. A brief of this algorithm, which is for continuous state‐action space, is described. First, this algorithm is implemented for a single agent (a seller and a buyer). Then we consider all players including sellers and buyers who can apply this algorithm as Multi‐Agent. In this situation, there is a comprehensive game between participants that is investigated, and it is analyzed whether the players converge to the Nash equilibrium (NE) in this game. Finally, numerical results for the IEEE 33‐bus distribution power system illustrate the effectiveness of the new framework for TEM, increasing sellers' and buyers' profits by applying SAC with the new state‐action spaces. SAC is implemented as a Multi‐Agent, demonstrating that players converge to a singular or one of the multiple NEs in this game. The results demonstrate that buyers converge to their optimal policies within 80 days, while sellers achieve optimality after 150 days in the games created between all participants. [ABSTRACT FROM AUTHOR]