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We investigate a robust equilibrium investment-reinsurance problem for n ambiguity-averse competitive insurers, n ≥ 2 . Each insurer is allowed to purchase proportional reinsurance and invest in a risk-free asset and a risky asset. Each insurer aims to maximize the expected utility of a weighted relative terminal wealth with respect to the other competitors. In this article, the risky asset is assumed to follow a general and flexible model: the square root factor process. Following the game theory approach, we derive the closed solutions of the robust equilibrium investment-reinsurance strategies. Moreover, the verification theorem is provided in this article. Finally, we demonstrate some numerical analyses and give the economic explanations as well. [ABSTRACT FROM AUTHOR]

Welfare and other properties of Berge equilibria are investigated. In particular, we address the questions to what extent Berge equilibrium can select from multiple Nash equilibria; can serve as a substitute for Nash equilibria; can Pareto improve upon Nash equilibrium. Furthermore, some of the recent results on the relation between Berge equilibria and Kantian equilibria are summarized. [ABSTRACT FROM AUTHOR]

The research is devoted to the study of the functional role structure of the interaction of the company's top management. The subject area of the study includes projects of digital transformation of business processes. The functional role status of IT directors for such positions as CIO, CDO, CDTO, CTO, CA was investigated. The analysis of the most frequently used models of interaction of IT directors was carried out and the optimal model was determined. The study was conducted using the Delphi expert assessment and the hierarchy analysis method. For the established optimal model related to the integration type of management, the organisational features of its application are described. Solutions are proposed to improve the quality of functional-role interaction of IT directors, which consider personal effectiveness, interaction style, ability to adopt technologies. The results of the study inform scientists about new data in the field of organisational behaviour for companies implementing digital initiatives. Practitioners can use the results of our research to adapt their organisational structure in such a way as to reduce the risks of the human factor during the implementation of the digital transformation strategy. [ABSTRACT FROM AUTHOR]

An outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), epi-centred in Hubei Province of the People's Republic of China, quickly spread worldwide and caused COVID-19 pandemic. It infected hundreds of millions of people and caused millions of deaths. In this paper, we develop a compartmental ODE model of COVID-19 transmission. We consider a possibility of breakthrough infections after the vaccination and account for both symptomatic and asymptomatic infections and transmissions. We also incorporate game theory to study the optimal vaccination decisions from the individuals' perspective. We show that vaccination alone is unlikely to eliminate COVID-19. To achieve herd immunity, the individuals would have to receive a dose of a vaccine more frequently than once every 3 months. It is therefore crucial to adhere to various guidelines, such as quarantine, isolate and wear a mask if tested positive for COVID-19. [ABSTRACT FROM AUTHOR]

To address the conflict of inconsistent driving intentions between the driver and driving assistance system in cooperative steering, a human–machine cooperative steering control framework based on non-cooperative Nash game is proposed. The competitive relationship between the driver and driving assistance system with different control objectives is modeled as a non-cooperative Nash game. The cooperative steering under human–machine Nash game condition is transformed into a model predictive control optimization problem to achieve coordination through Nash equilibrium. A flexible driving authority allocation strategy based on time-to-collision is then proposed for vehicle lateral control, with dynamic driving authority weights fed into the human–machine cooperative steering model in real time. The effectiveness of the non-cooperative Nash game human–machine cooperative steering strategy and flexible driving authority allocation strategy is validated through simulations and hardware-in-the-loop experiments. Results show the proposed strategy can improve vehicle safety while retaining certain driver freedom when human–machine control targets conflict, by flexibly transferring authority from the driver to the assistance system as collision risk increases. [ABSTRACT FROM AUTHOR]

In this paper, the open-loop and closed-loop local and remote stochastic nonzero-sum game (LRSNG) problem is investigated. Different from previous works, the stochastic nonzero-sum game problem under consideration is essentially a special class of two-person nonzero-sum game problem, in which the information sets accessed by the two players are inconsistent. More specifically, both the local player and the remote player are involved in the system dynamics, and the information sets obtained by the two players are different, and each player is designed to minimise its own cost function. For the considered LRSNG problem, both the open-loop and closed-loop Nash equilibrium are derived. The contributions of this paper are given as follows. Firstly, the open-loop optimal Nash equilibrium is derived, which is determined in terms of the solution to the forward and backward stochastic difference equations (FBSDEs). Furthermore, by using the orthogonal decomposition method and the completing square method, the feedback representation of the optimal Nash equilibrium is derived for the first time. Finally, the effectiveness of our results is verified by a numerical example. [ABSTRACT FROM AUTHOR]

In order to deal with the aging problem, the pension system is actively transformed into the funded scheme. However, the funded scheme does not completely replace PAYGO (Pay as You Go) scheme and there exist heterogeneous mixes among PAYGO, EET (Exempt, Exempt, Taxed) and individual savings in different countries. In this paper, we establish the optimal mix by solving a Nash equilibrium between the pension participants and the government. Given the obligatory PAYGO and EET contribution rates, the participants choose the optimal asset allocation of the individual savings and the consumption policies to achieve the objective. The results extend the 'Samuelson-Aaron' criterion to age-dependent preference orderings. Under the baseline model, we identify three critical ages to distinguish the multiple outcomes of preference orderings based on heterogeneous characteristic parameters. The government is fully aware of the optimal feedback of the participants. It chooses the optimal PAYGO and EET contribution rates to maximize the overall utility of the participants weighted by each cohort's population. As such, the negative population growth rate leads to the decline of the PAYGO attractiveness as well as the increase of the older cohorts' weight in the government's decision-making. The optimal mix is the comprehensive result of the two effects. [ABSTRACT FROM AUTHOR]

In this paper we study Nash equilibria in auctions from the kinetic theory of active particles point of view. We propose a simple learning rule for agents to update their bidding strategies based on their previous successes and failures, in first-price auctions with two bidders. Then, we formally derive the corresponding kinetic equations which describe the evolution over time of the distribution of agents on the bidding strategies. We show that the stationary solution of the equation corresponds to the symmetric Nash equilibrium of the auction, and we prove the convergence to this stationary solution when time goes to infinity. We also introduce a more general learning rule that only depends on the income of agents, and we apply to both first- and second-price auctions. We show that agents learn the Nash equilibrium in first- and second-price auctions with these rules. We present agent-based simulations of the models, and we discuss several open problems. [ABSTRACT FROM AUTHOR]

Carbon emission reduction (CER) in the construction industry can aid in achieving the international community's carbon neutrality target. However, the low motivation of construction enterprises to reduce carbon emissions and the unsatisfactory effect of CER are still unresolved issues. This study aims to address these issues by constructing a building supply chain (BSC) consisting of a developer and a contractor using government subsidies and cost-sharing contracts. The optimal government subsidy and feedback equilibrium strategies of the BSC are examined using a combination of differential game theory and numerical simulations. The findings demonstrate that (1) cost-sharing contracts may enhance developer and contractor profits and building CER, goodwill, and demand without relying on government subsidies; (2) when subsidized by the government, each equilibrium strategy meets or exceeds the performance of the centralized model, with the cost-sharing contract having a negligible effect on the enhancement of each equilibrium strategy; and (3) both the game structure and the positioning of construction enterprises in the BSC are connected to the number of government subsidies. The city of Shenzhen, one of China's first low-carbon pilot cities, provides a realistic environment for the simulation analysis, with the Block K residential building in Nanshan District serving as a case study. Furthermore, this work contributes to the body of knowledge by proposing a novel CER model for the BSC using differential game theory. The research provides new insights into the role of government subsidies in shaping profit distribution, game structure, and enterprise positioning. Findings demonstrate the value of cost-sharing contracts in improving CER, goodwill, demand, and profits when implemented collaboratively. This advances the theoretical understanding of incentives and strategies for promoting CER in construction. This research highlights the importance of collaborative efforts between the government and the building supply chain (BSC) to promote sustainable construction and carbon emission reduction (CER). The study found that government subsidies can be an effective tool to encourage developers and contractors to adopt CER practices. However, relying solely on subsidies is insufficient—collaboration through mechanisms such as cost-sharing contracts can further enhance sustainability outcomes when enterprises work together. To facilitate low-carbon construction, the government could provide subsidies for developers' promotional and marketing activities as well as funding for contractors' research and development of sustainable materials and technologies. Financial incentives such as tax breaks and preferential lending for potential homebuyers can also accelerate consumer demand. Ultimately, creating a supportive environment where enterprises proactively pursue CER creates a win–win situation where the BSC becomes more sustainable while firms improve their branding and profitability. The insights from this research highlight the need for a multipronged approach. Governments play a key role through policy and financial support. Realizing the full potential of sustainable construction also requires active participation from developers, contractors, and consumers. By outlining optimal strategies and incentives, this study provides valuable guidance to construction industry stakeholders seeking to implement CER collaboratively. [ABSTRACT FROM AUTHOR]

We consider the problem of approximating Nash equilibria of N functions f 1 , ... , f N of N variables. In particular, we show systems of the form u ̇ j (t) = − ∇ x j f j (u (t)) (j = 1 , ... , N) are well-posed and the large time limits of their solutions u (t) = (u 1 (t) , ... , u N (t)) are Nash equilibria for f 1 , ... , f N provided that these functions satisfy an appropriate monotonicity condition. To this end, we will invoke the theory of maximal monotone operators on a Hilbert space. We will also identify an application of these ideas in game theory and show how to approximate equilibria in some game theoretic problems in function spaces. [ABSTRACT FROM AUTHOR]

We consider finite graphical n-person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in stationary mixed strategies, we introduce probability distributions in all non-terminal positions. The corresponding probability distributions on the set of plays can be defined in two different ways called the Markov and a-priori realizations. The former one guarantees existence of a uniform best response for each player in every situation. Nevertheless, Nash equilibrium may fail to exist even in stationary mixed strategies. The classical Nash's theorem is not applicable, because in this case limit distributions and expected payoffs may be discontinuous. Although a-priori realizations do not share many nice properties of the Markov ones (for example, the existence of uniform best responses) but in return, Nash's theorem is applicable. We illustrate both realizations in details by two examples with 2 and 3 players. We also survey some general results related to Nash-solvability, in pure and mixed stationary strategies, of stochastic n-person games with perfect information and n-person graphical games among them. [ABSTRACT FROM AUTHOR]

The generation maintenance scheduling deals with a time sequence of preventive maintenance outages for a given set of generation units in an electricity market subject to power system restrictions. Incorporating a leader–follower structure in generation maintenance scheduling models is essential because of the inherent conflict between the interests of an independent system operator (ISO) and generation companies (GENCOs). The present paper proposes a new preventive maintenance scheduling model for generation companies facing the risk of involving generation units' disruption and demand variations while ensuring the reliability of the power system. Each GENCO proposes the maintenance schedule of its generation units to the ISO in a non-cooperative manner intending to maximize its net profit. Then ISO reacts to the aggregated schedule according to the power system's reliability index. Thus, a new formula is developed to consider all the interactions between the power system's stakeholders. In this regard, a stochastic multi-leader one-follower approach is applied. The GENCOs are considered independent leaders at the upper-level and the ISO is considered a follower at the lower-level. Then an equivalent single-level counterpart model is presented for each leader. So, the whole problem is converted into multiple individual stochastic single-level models, and then the Nash Equilibrium concept is used to determine GENCO equilibrium strategies. The proposed methodology is evaluated using some modified IEEE reliability test systems. The numerical analysis confirms that the proposed model is more effective in cases with higher uncertainties. Moreover, the performed analysis demonstrated the importance of applying a bi-level approach to the problem. Finally, the superiority of the proposed approach compared to the existing one is confirmed. [ABSTRACT FROM AUTHOR]

The study on how equilibria behave when perturbations occur in the data of a game is a fundamental theme, since actions and payoffs of the players may be affected by uncertainty or trembles. In this paper, we investigate the asymptotic behavior and the variational stability of the subgame perfect Nash equilibrium (SPNE) in one-leader one-follower Stackelberg games under perturbations both of the action sets and of the payoff functions. To pursue this aim, we consider a general sequence of perturbed Stackelberg games and a set of assumptions that fit the usual types of perturbations. We study if the limit of SPNEs of the perturbed games is an SPNE of the original game and if the limit of SPNE-outcomes of perturbed games is an SPNE-outcome of the original game. We fully positively answer when the follower's best reply correspondence is single-valued. When the follower's best reply correspondence is not single-valued, the answer is positive only for the SPNE-outcomes; whereas the answer for SPNEs may be negative, even if the perturbation does not affect the sets and affects only one payoff function. However, we show that under suitable non-restrictive assumptions it is possible to obtain an SPNE starting from the limit of SPNEs of perturbed games, possibly modifying the limit at just one point. [ABSTRACT FROM AUTHOR]

We consider a queueing system which opens at a given point in time and serves a finite number of users according to the last-come first-served discipline with preemptive-resume (LCFS-PR). Each user must decide individually when to join the queue. We allow for general classes of user preferences and service time distributions and show existence and uniqueness of a symmetric Nash equilibrium. Furthermore, we show that no continuous asymmetric equilibrium exists, if the population consists of only two users, or if arrival strategies satisfy a mild regularity condition. For an illustrative example, we implement a numerical procedure for computing the symmetric equilibrium strategy based on our constructive existence proof for the symmetric equilibrium. We then compare its social efficiency to that obtained if users are instead served on a first-come first-served (FCFS) basis. [ABSTRACT FROM AUTHOR]

We investigate the RFID adoption and chain structure (i.e., integrated or decentralized) decisions in two supply chains under two competition modes (i.e., Bertrand or Cournot competition). Each chain consists of a manufacturer and an exclusive retailer, who suffers from inventory misplacement problem. Two supply chains first simultaneously choose chain structure and then decide whether to invest in RFID technology. We develop an analytical model to derive the equilibrium outcomes, then further analyze the interactions between RFID adoption and chain structure under two competition modes. We find that in equilibrium, both chains prefer to choose integration under Cournot competition, while they might be better off from decentralization under Bertrand competition. Moreover, there may exist a prisoner's dilemma for the equilibrium strategies on RFID adoption and chain structure. Specifically, when both chains adopt RFID, the prisoner's dilemma occurs if the competition is fierce; when only one chain adopts RFID, the chain who forgoes RFID adoption is easier to trap into the prisoner's dilemma; when no chain adopts RFID, a high misplacement rate may aggravate the prisoner's dilemma if the competition is weak, and the supply chain members under Cournot competition may escape such dilemma if the competition is fierce. In addition, competition mode doesn't affect the optimal strategies for RFID adoption and chain structure. Further, in the case where the manufacturer affords a higher production cost, Cournot competition is more conducive to coordinate chains when competition is weak or relatively fierce, whereas Bertrand competition will be more effective when competition is moderate or very fierce. [ABSTRACT FROM AUTHOR]

A probabilistic approach to the epidemic evolution on realistic social-contact networks allows for characteristic differences among subjects, including the individual number and structure of social contacts, and the heterogeneity of the infection and recovery rates according to age or medical preconditions. Within our probabilistic Susceptible-Infectious-Removed (SIR) model on social-contact networks, we evaluate the infection load or activation margin of various control scenarios; by confinement, by vaccination, and by their combination. We compare the epidemic burden for subpopulations that apply competing or cooperative control strategies. The simulation experiments are conducted on randomized social-contact graphs that are designed to exhibit realistic person–person contact characteristics and which follow near homogeneous or block-localized subpopulation spreading. The scalarization method is used for the multi-objective optimization problem in which both the infection load is minimized and the extent to which each subpopulation's control strategy preference ranking is adhered to is maximized. We obtain the compounded payoff matrices for two subpopulations that impose contrasting control strategies, each according to their proper ranked control strategy preferences. The Nash equilibria, according to each subpopulation's compounded objective, and according to their proper ranking intensity, are discussed. Finally, the interaction effects of the control strategies are discussed and related to the type of spreading of the two subpopulations. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach to routing architecture based on the Session–Cookie protocol. The proposed architecture performs service discovery by integrating IoTs geographic clustering technique and polymorphism mechanism. Prioritizing requests is done in cookies and the load balancing on sessions. The efficiency of the proxy server's distributed cache and service discovery is improved. Smart devices, vehicles, and people inaugurate a p2p connection to receive the service, exchange data, and share files in applications such as parking systems, navigation, and vehicle insurance companies. According to the results, the average response time and the bandwidth consumption have decreased, and the cache hit rate has reached 86%. Based on the principles of game theory, the proposed architecture in the extensive game model with imperfect information in the conditions ((mtcp, mudp), (Y, Y); λ = 1, µ = 0)) has a weak sequential equilibrium and Nash equilibrium. [ABSTRACT FROM AUTHOR]

In the realm of evolutionary game theory, the majority of scenarios involve players with incomplete knowledge, specially regarding their opponents' actions and payoffs compounded by the ever‐shifting landscape of players' interactions. These dynamics present formidable challenges in both the analysis and optimization of game evolution. To address this, a novel model named the networked evolutionary game (NEG) is proposed based on incomplete information with switched topologies. This model captures situations where players possess limited insight into their opponents' benefits, yet make decisions based on their own payoffs while adapting to different networks and new players. To bridge the gap between incomplete and complete information games, R. Selten's transformation method is leveraged, a renowned approach that converts an incomplete information game into an interim agent game, thereby establishing the equivalence of pure Nash equilibria (NE) in both scenarios. Employing the semi‐tensor product (STP) of matrices, a powerful tool in logistic system, the evolution of the model is articulated through algebraic relationships. This enables to unravel the patterns of game evolution and identify the corresponding pure Nash equilibria. By introducing control players, strategically positioned within the game, optimized control is facilitated over the evolutionary trajectory, ultimately leading to convergence towards an optimal outcome. Finally, these concepts are illustrated with a practical example within the paper. [ABSTRACT FROM AUTHOR]

Given the complexity of issuing, verifying, and trading green power certificates in China, along with the challenges posed by policy changes, ensuring that China's green certificate market trading system receives proper mechanisms and technical support is crucial. This study presents a green power certificate trading (GC-TS) architecture based on an equilibrium strategy, which enhances the quoting efficiency and multi-party collaboration capability of green certificate trading by introducing Q-learning, smart contracts, and effectively integrating a multi-agent trading Nash strategy. Firstly, we integrate green certificate trading with electricity and carbon asset trading, constructing pricing strategies for the green certificate, carbon, and electricity trading markets; secondly, we design a certificate-electricity-carbon efficiency model based on ensuring the consistency of green certificates, green electricity, and carbon markets; then, to achieve diversified green certificate trading, we establish a multi-agent reinforcement learning game equilibrium model. Additionally, we propose an integrated Nash Q-learning offer with a smart contract dynamic trading joint clearing mechanism. Experiments show that trading prices have increased by 20%, and the transaction success rate by 30 times, with an analysis of trading performance from groups of 3, 5, 7, and 9 trading agents exhibiting high consistency and redundancy. Compared with models integrating smart contracts, it possesses a higher convergence efficiency of trading quotes. [ABSTRACT FROM AUTHOR]

Recently a framework was developed for aggregative variational inequalities by means of the Selten–Szidarovszky technique. By referring to this framework, a powerful Nash equilibrium uniqueness theorem for sum-aggregative games is derived. Payoff functions are strictly quasi-concave in own strategies but may be discontinuous at the origin. Its power is illustrated by reproducing and generalising in a few lines an equilibrium uniqueness result in Corchón and Torregrosa (2020) for Cournot oligopolies with the Bulow–Pfleiderer price function. Another illustration addresses an asymmetric contest with endogenous valuations in Hirai and Szidarovszky (2013). • Selten–Szidarovszky technique. • Aggregative games. • Nash equilibrium uniqueness. • Generalised convexity. [ABSTRACT FROM AUTHOR]

In 1971, Wilson (1971) proved that "almost all" finite games have an odd number of mixed Nash equilibria. Since then, several other proofs have been given, but always for mixed extensions of finite games. In this paper, we present a new oddness theorem for large classes of polynomial payoff functions and semi-algebraic sets of strategies. Additionally, we provide some applications to recent models of games on networks such that Patacchini-Zenou's model about juvenile delinquency and conformism (Patacchini and Zenou, 2012), Calvó-Armengol-Patacchini-Zenou's model about social networks in education (Calvó-Armengol et al., 2009), Konig-Liu-Zenou's model about R&D networks (König et al., 2019), Helsley-Zenou's model about social networks and interactions in cities (Helsley and Zenou, 2014). [ABSTRACT FROM AUTHOR]

This paper examines capacity-constrained oligopoly pricing with sellers who seek myopic improvements. We employ the Myopic Stable Set solution concept and establish the existence of a unique pure-strategy price solution for any given level of capacity. This solution is shown to coincide with the set of pure-strategy Nash equilibria when capacities are large or small. For an intermediate range of capacities, it predicts a price interval that includes the mixed-strategy support. This stability concept thus encompasses all Nash equilibria and offers a pure-strategy solution when there is none in Nash terms. It particularly provides a behavioral rationale for different pricing patterns, including Edgeworth price cycles and states of hyper-competition with supply shortages. We also analyze the impact of a change in firm size distribution. A merger among the biggest firms may lead to more price dispersion as it increases the maximum and decreases the minimum myopically stable price. [ABSTRACT FROM AUTHOR]

We consider finite two-player normal form games with random payoffs. Player A's payoffs are i.i.d. from a uniform distribution. Given p ∈ [ 0 , 1 ] , for any action profile, player B's payoff coincides with player A's payoff with probability p and is i.i.d. from the same uniform distribution with probability 1 − p. This model interpolates the model of i.i.d. random payoff used in most of the literature and the model of random potential games. First we study the number of pure Nash equilibria in the above class of games. Then we show that, for any positive p , asymptotically in the number of available actions, best response dynamics reaches a pure Nash equilibrium with high probability. [ABSTRACT FROM AUTHOR]

We present a model of firm entry in an industry that operates under an aggregate production quota or cap-and-trade (CAT) regulation. Firms are heterogeneous in their own productivity; each knows its costs of production but is uncertain about where its costs rank among an entrant population. We show the existence of a unique, symmetric, dominance solvable, Bayesian Nash equilibrium in switching strategies in a parameterized game with a continuum of players. Our main result is that uncertainty over one's productivity rank is sufficient to cause socially inefficient over-entry when the average cost in the population of potential entrants is low. We find socially inefficient under-entry when the opposite conditions hold. Within both the class of models on global games with strategic substitutes and the class of models on firm entry, our model offers innovative insights into inefficient over-entry, under-entry, and introduces a novel underlying mechanism that drives entry bias. [ABSTRACT FROM AUTHOR]

We consider an energy system with n consumers who are linked by a Demand Side Management (DSM) contract, i.e. they agreed to diminish, at random times, their aggregated power consumption by a predefined volume during a predefined duration. Their failure to deliver the service is penalised via the difference between the sum of the n power consumptions and the contracted target. We are led to analyse a non-zero sum stochastic game with n players, where the interaction takes place through a cost which involves a delay induced by the duration included in the DSM contract. When n → ∞ , we obtain a Mean-Field Game (MFG) with random jump time penalty and interaction on the control. We prove a stochastic maximum principle in this context, which allows to compare the MFG solution to the optimal strategy of a central planner. In a linear quadratic setting we obtain a semi-explicit solution through a system of decoupled forward-backward stochastic differential equations with jumps, involving a Riccati Backward SDE with jumps. We show that it provides an approximate Nash equilibrium for the original n-player game for n large. Finally, we propose a numerical algorithm to compute the MFG equilibrium and present several numerical experiments. [ABSTRACT FROM AUTHOR]

We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied and Zhang (2019) and Luo and Schied (2020), who considered the single asset case, we prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We then focus our attention on the conditions on the model parameters making the trading profile of the agents at equilibrium, and as a consequence the price trajectory, wildly oscillating and the market unstable. While Schied and Zhang (2019) and Luo and Schied (2020) highlighted the importance of the value of transaction cost in determining the transition between a stable and an unstable phase, we show that also the scaling of market impact with the number of agents J and the number of assets M determines the asymptotic stability (in J and M) of markets. [ABSTRACT FROM AUTHOR]

Ensuring source location privacy is crucial for the security of underwater acoustic sensor networks amid the growing use of marine environmental monitoring. However, the traditional source location privacy scheme overlooks multi-attacker cooperation strategies and also has the problem of high communication overhead. This paper addresses the aforementioned limitations by proposing an underwater source location privacy protection scheme based on game theory under the scenario of multiple cooperating attackers (SLP-MACGT). First, a transformation method of a virtual coordinate system is proposed to conceal the real position of nodes to a certain extent. Second, through using the relay node selection strategy, the diversity of transmission paths is increased, passive attacks by adversaries are resisted, and the privacy of source nodes is protected. Additionally, a secure data transmission technique utilizing fountain codes is employed to resist active attacks by adversaries, ensuring data integrity and enhancing data transmission stability. Finally, Nash equilibrium could be achieved after the multi-round evolutionary game theory of source node and multiple attackers adopting their respective strategies. Simulation experiments and performance evaluation verify the effectiveness and reliability of SLP-MACGT regarding aspects of the packet forwarding success rate, security time, delay and energy consumption: the packet delivery rate average increases by 30%, security time is extended by at least 85%, and the delay is reduced by at least 90% compared with SSLP, PP-LSPP, and MRGSLP. [ABSTRACT FROM AUTHOR]

Population games are games with a finite set of available strategies and an infinite number of players, in which the reward for choosing a given strategy is a function of the distribution of players over strategies. The paper shows that, in a certain class of maxmin optimization problems, it is possible to associate a population game to a given maxmin problem in such a way that solutions to the optimization problem are found from Nash equilibria of the associated game. Iterative solution methods for maxmin optimization problems can then be derived from systems of differential equations whose trajectories are known to converge to Nash equilibria. In particular, we use a discrete-time version of the celebrated replicator equation of evolutionary game theory, also known in machine learning as the exponential multiplicative weights algorithm. The resulting algorithm can be viewed as a generalization of the Iteratively Reweighted Least Squares (IRLS) method, which is well known in numerical analysis as a useful technique for solving Chebyshev function approximation problems on a finite grid. Examples are provided to show the use of the generalized IRLS method in collective investment and in decision making under model uncertainty. [ABSTRACT FROM AUTHOR]

Abstract.Inspired by the idea of game learning, this paper studies the Cournot game model of the multi-oligopoly market and studies the realization of the Nash equilibrium by using adaptive differential evolution algorithm based on relaxation strategies. The realization path of Nash equilibrium is attained through an adaptive differential evolution based on a relaxation strategy procedure applied to an objective function with best response dynamics. Among them, the objective function is derived from the sum of the payoff changes of each oligopoly under best response decisions. And theoretically proved that the Nash equilibrium is the optimal solution of the objective function. [ABSTRACT FROM AUTHOR]

Natural ecological communities exhibit complex mixtures of interspecific biological interactions, which makes finding optimal yet sustainable exploitation rates challenging. Most fisheries management advice is at present based on applying the Maximum Sustainable Yield (MSY) target to each species in a community by modelling it as if it was a monoculture. Such application of single‐species MSY policies to strongly interacting populations can result in tragic overexploitation. However, the idea of 'maximising the yield from each species separately' can be extended to take into account species interactions. This leads to a form of Nash Equilibrium, where the yields of each species are simultaneously maximised. Here we present 'nash', an R package that streamlines the computation of Nash equilibrium reference points for fisheries and other systems represented by a user‐defined multispecies or ecosystem model. We present two real‐world fisheries management applications alongside performance benchmarks. Satisfactory search results are shown across models with an approximate factor 7 increase in performance when compared to the expensive round‐robbing sequential optimisation algorithms used by other authors in the literature. We believe that the nash package can play an instrumental role in fully implementing ecosystem‐based management policies worldwide. [ABSTRACT FROM AUTHOR]

In a typical traffic scenario, automated vehicles are required to interact with surrounding traffic participants, e.g. human-driven vehicles, pedestrians, etc. In this paper, a novel adaptive authority allocation strategy considering the social behaviours of surrounding vehicles is proposed for the shared steering control (SSC) of automated vehicles. First, a Koopman-based potential-field-driven distributed model predictive control (K-PF-DMPC) method is proposed for the modelling of vehicle interaction to describe surrounding vehicle's social behaviour. This method effectively deals with the nonlinearity embedded in the non-cooperative game-based vehicle interaction model, so that the analytical form of Nash equilibrium can be derived for a fast online solution. Then, the SSC system of the automated vehicle is implemented by a weighted summation method. To balance the driving performance and intervention degree while considering the surrounding vehicles' social behaviours, a hybrid fuzzy strategy (HFS) is proposed for allocating the control authority between the driver and automation. The value of authority allocation coefficient is calculated by fusing the outputs from two shared fuzzy controllers, i.e. the enhanced and weakened shared fuzzy controllers, in accordance to the belief of the surrounding vehicle's type. Several numerical simulations and driver-in-the-loop simulator experiments are conducted for validation. Results show that the proposed strategy can provide appropriate steering intervention to the driver owing to the consideration of the surrounding vehicle's social behaviour and obtains the best driver-automation collaboration performance compared with the comparative groups. [ABSTRACT FROM AUTHOR]

Considering overshoot and chatter caused by the unknown interference, this article studies the adaptive robust optimal controls of continuous‐time (CT) multi‐input systems with an approximate dynamic programming (ADP) based Q‐function scheme. An adaptive integral reinforcement learning (IRL) scheme is proposed to study the optimal solutions of Q‐functions. First, multi‐input value functions are presented, and Nash equilibrium is analyzed. A complex Hamilton–Jacobi–Issacs (HJI) equation is constructed with the multi‐input system and the zero‐sum‐game‐based value function. It is a challenging task to solve the HJI equation for nonlinear system. Thus, A transformation of the HJI equation is constructed as a Q‐function. The neural network (NN) is applied to learn the solution of the transformed Q‐functions based on the adaptive IRL scheme. Moreover, an error information is added to the Q‐function for the issue of insufficient initial incentives to relax the persistent excitation (PE) condition. Simultaneously, an IRL signal of the critic networks is introduced to study the saddle‐point intractable solution, such that the system drift and NN derivatives in the HJI equation are relaxed. The convergence of weight parameters is proved, and the closed‐loop stability of the multi‐system with the proposed IRL Q‐function scheme is analyzed. Finally, a two‐engine driven F‐16 aircraft plant and a nonlinear system are presented to verify the effectiveness of the proposed adaptive IRL Q‐function scheme. [ABSTRACT FROM AUTHOR]

This article develops distributed optimal control policies via Q‐learning for multi‐agent systems (MASs) by solving dual games. According to game theory, first, the distributed consensus problem is formulated as a multi‐player non‐zero‐sum game, where each agent is viewed as a player focusing only on its local performance and the whole MAS achieves Nash equilibrium. Second, for each agent, the anti‐disturbance problem is formulated as a two‐player zero‐sum game, in which the control input and external disturbance are a pair of opponents. Specifically, (1) an offline data‐driven off‐policy for distributed tracking algorithm based on momentum policy gradient (MPG) is developed, which can effectively achieve consensus of MASs with guaranteed l2$$ {l}_2 $$‐bounded synchronization error. (2) An actor‐critic‐disturbance neural network is employed to implement the MPG algorithm and obtain optimal policies. Finally, numerical and practical simulation results are conducted to verify the effectiveness of the developed tracking policies via MPG algorithm. [ABSTRACT FROM AUTHOR]

In the digital innovation ecosystem, the symbiosis mode formed between ecosystem members not only relates to their survival and development but also affects the ecosystem's symbiosis evolution mechanism. Based on symbiosis theory, this study first explores the evolutionary equilibrium strategy and its stability for three types of populations—core enterprises, digital platforms, and university research institutes—and then uses numerical simulation and a case study to explore the symbiotic evolution mechanism of the digital innovation ecosystem. The results show that: First, the digital innovation ecosystem is a complex adaptive system in which the three types of populations form different symbiotic relationships under different symbiotic modes and conduct symbiotic activities, such as value co-creation, to characterize the unique symbiotic evolutionary structure. Second, in this ecosystem, the symbiotic relationship formed by the combined values of different symbiotic coefficients between populations determines the outcome of symbiotic evolution. Third, the ideal direction of the evolution of the digital innovation ecosystem is a mutually beneficial symbiotic relationship. Thus, the symbiotic relationship between populations should be transformed into a mutually beneficial symbiotic relationships as much as possible. This study makes theoretical contributions by shedding light on the symbiotic evolution mechanism of the digital innovation ecosystem. It also offers countermeasures for the digital innovation cooperation of various stakeholders in China's digital innovation ecosystem. [ABSTRACT FROM AUTHOR]

In this article, a distributed charging strategy problem for plug-in electric vehicles (PEVs) with feeder constraints based on generalized Nash equilibria (GNE) in a novel smart charging station (SCS) is investigated. The purpose is to coordinate the charging strategies of all PEVs in SCS to minimize the energy cost of SCS. Therefore, we build a non-cooperative game framework and propose a new price-driven charging control game by considering the overload constraint of the assigned feeder, where each PEV minimizes the fees it pays to satisfy its optimal charging strategy. On this basis, the existence of GNE is given. Furthermore, we employ a distributed algorithm based on forward–backward operator splitting methods to find the GNE. The effectiveness of the employed algorithm is verified by the final simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we examine the class of congestion games with player-specific payoff functions introduced by Milchtaich, I. (1996). Focusing on the special case of two resources, we give a short and simple method for identifying all Nash equilibria in pure strategies. We also provide a computation algorithm based on our theoretical analysis. [ABSTRACT FROM AUTHOR]

We investigate the role and performance of imitative behavior in a class of quantity-setting, Cournot games. Within a framework of evolutionary competition between rational, myopic best-response and imitation heuristics with differential heuristics' costs, we found that the equilibrium stability depends on the sign of the cost differential between the unstable heuristic (Cournot best-response) and the stable one (imitation) and on the intensity of the evolutionary pressure. When this cost differential is positive (i.e., imitation is relatively cheaper vis a vis Cournot), most firms use this heuristic and the Cournot equilibrium is stabilized for market sizes for which it was unstable under Cournot homogeneous learning. However, as the number of firms increases (n = 7) , instability eventually sets in. When the cost differential is negative (imitation is more expensive than Cournot), complicated quantity fluctuations, along with the co-existence of heuristics, arise already for the triopoly game. [ABSTRACT FROM AUTHOR]

This study presents a bioeconomic model of prey-predator interactions incorporating the presence of refuges for prey species to mitigate predation. The main objective is to assess the impact of prey refuges on prey biomass, predator biomass, catches, fishing effort, and profits for fishermen exploiting these marine species. The model analyzes system positivity and boundedness, examines equilibrium points and their stability, and conducts numerical simulations by varying the refuge availability parameter (m) to interpret the effects on fishing effort, catches, and profits across different scenarios. The findings shed light on the dynamics of the ecosystem and highlight the importance of refuge availability in sustainable fisheries management, supporting the conservation of marine resources and the well-being of fishermen. [ABSTRACT FROM AUTHOR]

The rapid growth of edge devices and mobile applications has driven the adoption of edge computing to handle computing tasks closer to end-users. However, the heterogeneity of edge devices and their limited computing resources raise challenges in the efficient allocation of computing resources to complete services with different characteristics and preferences. In this paper, we delve into an edge scenario comprising multiple Edge Computing Servers (ECSs), multiple Device-to-Device (D2D) Edge Nodes (ENs), and multiple edge devices. In order to address the resource allocation challenge among ECSs, ENs, and edge devices in high-workload environments, as well as the pricing of edge resources within the resource market framework, we propose a Risk Assessment Contract Algorithm (RACA) based on risk assessment theory. The RACA enables ECSs to assess risks associated with local users by estimating their future revenue potential and updating the contract autonomously at present and in the future. ENs acquire additional resources from ECSs to efficiently complete local users' tasks. Simultaneously, ENs can also negotiate reasonable resource requests and pricing with ECSs by a Stackelberg game algorithm. Furthermore, we prove the unique existence of Nash equilibrium in the established game, implying that equilibrium solutions can stably converge through computational methods in heterogeneous environments. Finally, through simulation experiments on the dataset, we demonstrate that risk assessment can better enhance the overall profit capability of the system. Moreover, through multiple experiments, we showcase the stability of the contract's autonomous update capability. The RACA exhibits better utility in terms of system profit capabilities, stability in high-workload environments, and energy consumption. This work provides a more dynamic and effective solution to the resource allocation problem in edge systems under high-workload environments. [ABSTRACT FROM AUTHOR]

In most wireless networks, users/peers are connected to backbone networks using access links. The access link capacity is divided into upload and download capacity, and these capacities are used for upload and download of data, respectively. A peer can modify this division of link capacity between upload and download. A peer will allocate its entire link capacity for download to maximize utility. But incentive mechanism forces them to allocate some portion of capacity for upload. This paper investigates how to optimally divide link capacity so that peers receive maximum utility in a P2P network. We model this scenario as a game and determine capacity partitioning of peers during the Nash equilibrium NE. We also prove the social optimality of NE. As this portioning maximizes individual as well as social benefit, so NE is an optimal state of capacity partition. Using simulation, we verify that NE is an optimal state. BitTorrent network and a distributed algorithm for dividing access capacities are simulated, and partition providing maximum utility is compared with NE. This work provides a generalized expression and the mathematical proof for capacity partitioning at which peers receive maximum utility. [ABSTRACT FROM AUTHOR]

To reduce the learning time and space occupation, this study presents a novel model‐free algorithm for obtaining the Nash equilibrium solution of continuous‐time nonlinear non‐zero‐sum games. Based on the integral reinforcement learning method, a new integral HJ equation that can quickly and cooperatively determine the Nash equilibrium strategies of all players is proposed. By leveraging the neural network approximation and gradient descent method, simultaneous continuous‐time adaptive tuning laws are provided for both critic and actor neural network weights. These laws facilitate the estimation of the optimal value function and optimal policy without requiring knowledge or identification of the system's dynamics. The closed‐loop system stability and convergence of weights are guaranteed through the Lyapunov analysis. Additionally, the algorithm is enhanced to reduce the number of auxiliary NNs used in the critic. The simulation results for a two‐player non‐zero‐sum game validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we design a competition framework for two insurers with ambiguity aversion under the utility framework and investigate the resulting stochastic reinsurance game problem. Each insurer does not have perfect confidence in the drift terms of the insurance risk and chooses to purchase per-loss reinsurance to reduce her claim risk, and the reinsurance premium is determined via the mean-variance premium principle. The objective of each insurer is to find the optimal reinsurance strategy so as to maximize the ratio of expected utility of her terminal payoff to her competitor's under the worst-case scenario. By the dynamic programming principle and corresponding Hamilton–Jacobi–Bellman–Isaacs equation, we derive the solutions for both the equilibrium reinsurance strategy and value function under the exponential utility function. In particular, we examine the existence and uniqueness of equilibrium strategy. Finally, several numerical examples are presented to illustrate the effects of competitive relationship, ambiguity aversion and some important model parameters on the equilibrium strategy, which provide useful insights for reinsurance in reality. [ABSTRACT FROM AUTHOR]

This paper studies discrete-time nonzero-sum stochastic games under the risk-sensitive first passage discounted cost criterion. The state space is a countable set and the costs are allowed to be unbounded. Under the suitable optimality conditions, we prove that the risk-sensitive first passage discounted optimal value function of each player is a unique solution to the risk-sensitive first passage optimality equation via an approximation method. Moreover, by the risk-sensitive first passage discounted optimality equation, we show the existence of a randomized Markov Nash equilibrium. Finally, three examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

Mutually beneficial cooperation is a common part of economic systems as firms in partial cooperation with others can often make a higher sustainable profit. Though cooperative games were popular in 1950s, recent interest in noncooperative games is prevalent despite the fact that cooperative bargaining seems to be more useful in economic and political applications. In this paper we assume that the strategy space and time are inseparable with respect to a contract. Furthermore, it is assumed that each firm's strategy polygon is a geodesic polygon which changes its shape every point of time with the stubbornness strategy surface of firm's executive board follow a Gaussian free field. This gives us more flexibility to deal with generalized geodesic cooperative games which is the main contribution of this paper. Under this environment we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry fails to give a proper feedback Nash equilibrium. Cooperation occurs when two firms' strategies fall into each other's influence curvature in this strategy spacetime. Small firms in an economy dominated by large firms are subject to the influence of large firms. We determine an optimal feedback semicooperation of the small firm in this case using a Liouville-Feynman path integral method. [ABSTRACT FROM AUTHOR]

This work is devoted to Markovian-switching systems. In particular, backward stochastic differential equations (BSDEs), forward-backward stochastic differential equations (FBSDEs), such equations with mean-field interactions, and related nonzero-sum stochastic mean-field games. First, BSDEs with Markovian switching, FBSDEs with Markovian-switching, and FBSDEs with both mean-field interactions and regime-switching are examined. Unique solvability of the underlying equations is obtained under monotonicity conditions without assuming non-degeneracy condition for the forward equation. Then the existence of open-loop Nash equilibrium points for nonzero-sum linear-quadratic stochastic differential games with random coefficients is investigated. [ABSTRACT FROM AUTHOR]

We consider a nonzero-sum N-player Markov game on an abstract measurable state space with compact metric action spaces. The payoff functions are bounded Carathéodory functions and the transitions of the system are assumed to have a density function satisfying some continuity conditions. The optimality criterion of the players is given by a total expected payoff on an infinite discrete-time horizon. Under the condition that the game model is absorbing, we establish the existence of Markov strategies that are a noncooperative equilibrium in the family of all history-dependent strategies of the players for both the constrained and the unconstrained problems. We obtain, as a particular case of our results, the existence of Nash equilibria for discounted constrained and unconstrained game models. [ABSTRACT FROM AUTHOR]

Motivated by the self-pursuit of controlled objects, we consider the exact controllability of a linear mean-field type game-based control system (MF-GBCS, for short) generated by a linear-quadratic (LQ, for short) Nash game. A Gram-type criterion for the general time-varying coefficients case and a Kalman-type criterion for the special time-invariant coefficients case are obtained. At the same time, the equivalence between the exact controllability of this MF-GBCS and the exact observability of a dual system is established. Moreover, an admissible control that can steer the state from any initial vector to any terminal random variable is constructed in closed form. [ABSTRACT FROM AUTHOR]

This paper is concerned with the investment and reinsurance problem between two insurance companies and a reinsurance company by constructing a two‐layer stochastic differential game. Insurance companies invest in a risk‐free asset, a defaultable bond, and a risky asset under the bi‐fractional Brownian motion environment; reinsurance companies invest in a risk‐free asset and a risky asset under the bi‐fractional Brownian motion environment. In order to maximize the expected utility of the insurance companies' relative wealth and the expected utility of the reinsurance company's wealth at the terminal time, we solve the Hamilton–Jacobi–Bellman (HJB) equations by using the differential game theory and stochastic optimal control theory and obtain the equilibrium investment–reinsurance and reinsurance premium strategies. Finally, we investigate the influence of the parameters on the equilibrium strategy through numerical examples and analyze its economic implications. [ABSTRACT FROM AUTHOR]