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This paper investigates the N-coalition game, which covers the generalized Nash equilibrium problems (GNEPs) and distributed optimization problems. To seek the Nash equilibrium of the N-coalition games, we firstly exploit a centralized algorithm. Under the full information, the algorithm can exponentially converge to the Nash equilibrium of the N-coalition games. Then, based on the extremum seeking (ES) approach, we extend the centralized algorithm to distributed counterpart. Different from the centralized algorithm, the explicit cost functions are not available in the distributed algorithm. The players not only can converge to a small neighborhood of the Nash equilibrium, but do not communicate with the other coalitions. Furthermore, in order to reduce the communication burden in intra-coalition, an event-triggered based distributed algorithm is proposed. By the algorithm, the players only communicate with their neighbors in intra-coalition at event-triggered time constants, and also can converge to a neighborhood of the Nash equilibrium of the N-coalition games. Finally, an example about Nash-Cournot game is given to illustrate the effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider the distributed generalized Nash equilibrium (GNE) seeking problem in strongly monotone games. The transmission among players is implemented through a digital communication network with limited bandwidth. For improving communication efficiency or/and security, an event-triggered coding-decoding-based communication is first proposed, where the data (decision variable) are first mapped to a series of finite-level codewords and, only when an event condition is satisfied, then sent to the neighboring agents. Moreover, a distributed communication-efficient GNE seeking algorithm is constructed accordingly, and the overrelaxation scheme is further taken into consideration. Through primal-dual analysis, the proposed algorithm is proven to converge to a variational GNE with fixed step-sizes by recasting it as an inexact forward-backward iteration. Finally, numerical simulations illustrate the benefit of the proposed algorithms in terms of saving communication resources. [ABSTRACT FROM AUTHOR]

There are two recognized classes of strategic-form symmetric games, both of which can be conveniently defined through the corresponding player symmetry groups. We investigate the basic properties of these groups and several related concepts. We generalize the notion of coveringness and adapt their results to characterize these player symmetry groups. We study the relationships between the coveringnesses of various symmetry groups. Our results demonstrate that these symmetry groups have rich mathematical structures that are of game theoretical and economic interests.

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]

The Lowest Unique Positive Integer game, a.k.a. Limbo, is among the simplest games that can be played by any number of players and has a nontrivial strategic component. Players independently pick positive integers, and the winner is the player that picks the smallest number nobody else picks. The Nash equilibrium for this game is a mixed strategy, (p (1) , p (2) , ...) , where p(k) is the probability you pick k. A recursion for the Nash equilibrium has been previously worked out in the case where the number of players is Poisson distributed, an assumption that can be justified when there is a large pool of potential players. Here, we summarize previous results and prove that as the (expected) number of players, n, goes to infinity, a properly scaled version of the Nash equilibrium random variable converges in distribution to a Unif(0, 1) random variable. The result implies that for large n, players should choose a number uniformly between 1 and ϕ n ∼ O (n / ln (n)) . Convergence to the uniform is rather slow, so we also investigate a continuous analog of the Nash equilibrium using a differential equation derived from the recursion. The resulting approximation is unexpectedly accurate and is interesting in its own right. Studying the differential equation yields some useful analytical results, including a precise expression for ϕ n , and efficient ways to sample from the continuous approximation. [ABSTRACT FROM AUTHOR]

Charactering Cournot equilibria in settings with asymmetric firms is a challenging problem. In their technical note "Multimarket Cournot Equilibria with Heterogeneous Resource-Constrained Firms," R. Caldentey and M. Haugh consider competition in a multimarket setting where firms are subject to varying budget or capacity constraints. They explicitly characterize the unique equilibrium in this environment by introducing the concepts of augmented and cutoff budgets for firms and markets. In particular, they show that a firm operates in a particular market if only if its augmented budget surpasses the market's cutoff budget. They also investigate how the equilibrium properties change as the number of firms N varies while maintaining a fixed aggregate budget. They show via a numerical study that increasing N leads to a higher total output across all markets but that this monotonicity need not hold individual at the level of an individual market level. They also show that, although the firms' cumulative payoff decreases in N, the consumer surplus and social surplus increase in N. We study Cournot competition among firms in a multimarket framework where each of the firms face different budget/capacity constraints. We assume independent linear inverse demand functions for each market and completely characterize the resulting unique equilibrium. Specifically, we introduce the notions of augmented and cutoff budgets for firms and markets, respectively. We show, for example, that firm i operates in market j if and only if firm i's augmented budget is greater than market j's cutoff budget. We also study the properties of the equilibrium as a function of the number of firms N while keeping the aggregate budget fixed. In a numerical study, we show that increasing N increases the total output across all markets although this monotonicity can fail to hold at the individual market level. Similarly, we show that that, although the firms' cumulative payoff decreases in N, the consumer surplus and social surplus increase in N. Funding: R. Caldentey thanks the University of Chicago Booth School of Business for financial support. [ABSTRACT FROM AUTHOR]

In this article, we manage the energy consumption of numerous intelligent homes and charging stations including several electric vehicles in real-time using a computationally efficient predictive controller. The studied scenario is made up of a couple of primary layers. At the low level of the hierarchical framework, users are clustered into different groups based on their vehicles' departure times. Meanwhile, the energy consumption of subordinate users is controlled by multiple aggregators, interaction among which is modeled as an aggregative game. The high-level interactive and distributed control problem can be solved by a predictive controller, wherein the terminal constraints related to the reference energy of each cluster's storage capacity are transferred to the end of the prediction horizon. Additionally, each aggregator can only exchange local data with some neighboring aggregators through an untrustable communication network. As a result of denial of service attacks on the aggregators' network, the strong connectivity of the communication graph may be directly destroyed, leading to performance degradation. To address such an issue, each aggregator reconstructs the attacked information of its neighbors using a linear combination of received data in the last two iterations. Furthermore, a time-ofuse pricing tariff whose value is small for faithful households is investigated so that convergence time remains unaltered. Practical examples are simulated to assess the usefulness of the proposed iterative algorithm. [ABSTRACT FROM AUTHOR]

The work gives a review on the distributed Nash equilibrium seeking of noncooperative games in multi-agent networks, which emerges as one of the frontier research topics in the area of systems and control community. Firstly, we give the basic formulation and analysis of noncooperative games with continuous action spaces, and provide the motivation and basic setting for distributed Nash equilibrium seeking. Then we introduce both the gradient-based algorithms and best-response based algorithms for various type of games, including zero-sum games, aggregative games, potential games, monotone games, and multi-cluster games. In addition, we provide some applications of noncooperative games.

In this article, a distributed nonmodel based generalized Nash equilibrium (GNE) seeking algorithm is proposed for a class of constrained noncooperative games with unknown cost functions. In the game, the strategy of each agent is restricted by both the coupled equality constraint and local inequality constraints. By virtue of the exact penalty method, an auxiliary cost function is constructed with the cost function and the local constraints. The main feature of the proposed algorithm depends on the capability to estimate the gradient information of auxiliary cost functions with only the values of costs. This is obtained by the extremum seeking control (ESC). To deal with the coupled constraints, only the Lagrange multiplier is transmitted among agents with some prior information about the coupled constraints. Moreover, a diminishing dither signal is introduced in the seeking algorithm to remove undesirable steady‐state oscillations occurred in the classical ESC. As a result, the nonlocal convergence of the designed seeking algorithm to the GNE of the game is obtained by the singular perturbation theory, averaging analysis and Lyapunov stability theory. Numerical examples are given to verify the effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

When imposing traffic congestion pricing around downtown commercial centers, there is a concern that commercial activities will have to consider relocating due to reduced demand, at a cost to merchants. Concerns like these were important in the debates before the introductions of congestion charges in both London and Stockholm and influenced the final policy design choices. This study introduces a sequential experimental game to study reactions to congestion pricing in the commercial sector. In the game, merchants first make location choices. Consumers, who drive to do their shopping, subsequently choose where to shop. Initial responses to the introduction of congestion pricing and equilibrium selection adjustments over time are observed. These observations are compared to responses and adjustments in a condition where congestion pricing is reduced from an initially high level. Payoffs are non-linear and non-transparent, making it less than obvious that the efficient equilibrium will be selected, and introducing possibilities that participants need to discover their preferences and anchor on past experiences. We find that initial responses reflect standard inverse price–demand relations, and that adjustments over time rely on signaling by consumers leading to the efficient equilibrium. There is also evidence that priming from initial experiences influence play somewhat. We confirm that commercial activities relocate following the introduction of congestion pricing and that the adjustment process is costly to merchants. [ABSTRACT FROM AUTHOR]

Noncooperative game-theoretic methods have been widely utilized in system-level engineering applications as they are capable of aggregating interests, information, and behaviors of many independent, self-interested entities with conflicting objectives via payoffs. Another major advantage is the existence of adaptive learning dynamics that involve realistic, constrained decision making, and converge to Nash equilibrium. If players are not fully rational (e.g., constrained or regulated), such convergence is generally not guaranteed except in some special games, such as potential games (PGs). Within each PG, there exists a potential function that connects the global objective with players’ payoffs and actions such as optimizers of the global objective align with Nash equilibrium. Therefore, PGs have been widely utilized in many engineering domains and recently to power grids. This article summarizes the state-of-the-art existing literature on applying various PG models in power grids and provides an overlook of potential models and algorithms that have not received sufficient attention but possess unique capabilities to solve existing challenges in power grids. [ABSTRACT FROM AUTHOR]

Game theory-based models are widely used to solve multiple competitive problems such as oligopolistic competitions, marketing of new products, promotion of existing products competitions, and election presage. The payoffs of these competitive models have been conventionally considered as deterministic. However, these payoffs have ambiguity due to the uncertainty in the data sets. Interval analysis-based approaches are found to be efficient to tackle such uncertainty in data sets. In these approaches, the payoffs of the game model lie in some closed interval, which are estimated by previous information. The present paper considers a multiple player game model in which payoffs are uncertain and varies in a closed intervals. The necessary and sufficient conditions are explained to discuss the existence of Nash equilibrium point of such game models. Moreover, Nash equilibrium point of the model is obtained by solving a crisp bi-linear optimization problem. The developed methodology is further applied for obtaining the possible optimal strategy to win the parliament election presage problem. [ABSTRACT FROM AUTHOR]

To drive competitive advantage in today's fast-paced and disruptive business environment, firms are increasingly investing in the modularization of their technology infrastructure. In a rapidly changing and interconnected business environment where flexibility is key, modularity is often hailed as a foundational pillar of information technology systems of the future. For networked firms, modularity has been traditionally viewed as unambiguously beneficial because it allows for closer alignment with partner firms and also mitigates risk by lowering partner switching costs. However, we find that in interfirm networks undergoing technology transitions in the form of adoption of new interorganizational systems such as blockchains, modularity can also engender additional risks. Specifically, the early stages of IOS adoption are characterized by information asymmetries, and we find that high levels of technological modularity can render firms more susceptible to opportunistic information withholding by network partners. Our findings run counter to the traditional view of modularity as a capability that can improve the efficiency of IOS adoption, or as a governance mechanism that reduces risks associated with IOS adoption. As optimism and investments toward modularity grow, by identifying associated risks, our work cautions managers to adopt a more qualified view of this capability during technological transitions. The successful adoption of interorganizational systems (IOSs), such as blockchains or electronic data interchanges, in interfirm networks requires timely and accurate sharing of information about these roll-outs. In reality, however, the early stages of IOS adoption are characterized by information asymmetries that can arise due to a separation between firms that select and develop the IOS, and firms that implement it. This often results in staggered and asymmetric flows of information that can engender strategic information withholding behaviors. Drawing upon resource and network-based views, we study how the technological modularity of networked firms can affect these behaviors. Interestingly, we find that high levels of technological modularity can render firms more susceptible to opportunistic information withholding by network partners. Our findings run counter to the traditional view of modularity as a capability that can improve the efficiency of IOS adoption, or as a governance mechanism that reduces risks associated with IOS adoption. We find that network density and embeddedness can mitigate the opportunistic risks of technological modularity, whereas network topology can have diverging effects. In a rapidly changing and interconnected business environment where flexibility is key, modularity is often hailed as a foundational pillar of information technology systems of the future. As optimism and investments toward modularity grow, by identifying associated risks, our work cautions managers to adopt a more qualified view of this capability during technological transitions. [ABSTRACT FROM AUTHOR]

We study strategic games on weighted directed graphs, where each player's payoff is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed nonnegative integer bonus for picking a given strategy. These games capture the idea of coordination in the absence of globally common strategies. We identify natural classes of graphs for which finite improvement or coalition-improvement paths of polynomial length always exist, and consequently a (pure) Nash equilibrium or a strong equilibrium can be found in polynomial time. The considered classes of graphs are typical in network topologies: simple cycles correspond to the token ring local area networks, whereas open chains of simple cycles correspond to multiple independent rings topology from the recommendation G.8032v2 on Ethernet ring protection switching. For simple cycles, these results are optimal in the sense that without the imposed conditions on the weights and bonuses, a Nash equilibrium may not even exist. Finally, we prove that determining the existence of a Nash equilibrium or of a strong equilibrium is NP-complete already for unweighted graphs, with no bonuses assumed. This implies that the same problems for polymatrix games are strongly NP-hard. [ABSTRACT FROM AUTHOR]

This paper reconsiders Joseph Farrell׳s (1987) and Matthew Rabin׳s (1994) analyses of coordination via preplay communication, focusing on Farrell׳s analysis of Battle of the Sexes. Replacing their equilibrium and rationalizability assumptions with a structural non-equilibrium model based on level-k thinking, I reevaluate FR׳s assumptions on how players use language and their conclusions on the limits of communication in bringing about coordination. The analysis partly supports their assumptions about how players use language, but suggests that their “agreements” do not reflect a full meeting of the minds. A level-k analysis also yields very different conclusions about the effectiveness of communication.

This paper proposes a distributed Nash equilibrium seeking strategy for noncooperative games over strongly connected topologies, where the players suffer from unmodeled nonlinearities and external disturbances. By using the neural network (NN) universal approximation theorem, a neuro‐adaptive seeking controller is proposed. Besides, the event‐triggered mechanism is introduced to reduce communication costs of the players. Furthermore, by developing a Lyapunov function, it is shown that the states of the players asymptotically converge to the Nash equilibrium. Finally, a simulation is conducted to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

A linear-quadratic positional differential game of three persons is considered. Coefficient criteria are established under which there is no Nash equilibrium situation in the game but at the same time there exists an equilibrium of objections and counterobjections. [ABSTRACT FROM AUTHOR]

We develop a model of Cournot competition between capacity-constrained firms that sell a single good to multiple regions. We provide a novel characterization for the unique equilibrium allocation of the good across regions and design an algorithm to compute it. We show that a reduction in transportation costs by a firm may negatively impact the profit of all firms and reduce aggregate consumer surplus if such a firm is capacity constrained. Our results imply that policies promoting free trade may have unintended consequences and reduce aggregate welfare in capacity-constrained industries. This paper was accepted by David Simchi-Levi, revenue management and market analytics. [ABSTRACT FROM AUTHOR]

Manufacturers utilize dual-channel supply-chain to cope with customer preferences. This structure allows manufacturer's online facility and conventional retailer to deliver their products more efficiently. However, this mechanism also brings up anew internal competition between manufacturers and retailers. To observe the price effect within this system, response surface methodology is used to model the customer preference. The independent variables are online and retailer prices, while the dependent variables are price and cross-price sensitivities. To simulate proposed model into real-practice, game theory is employed. The strategies are the priority of each channel price and cross-price sensitivities. Based on this game model, a Nash equilibrium is obtained. This research proposes anovelty by means of the usage of response surface results as game theory payoffs to represent the uncertainty in a competitive environment. The integration of response surface model and game matrix can be used as managerial implication in predicting competitors' behaviour. [ABSTRACT FROM AUTHOR]

We consider selfish colorful bin packing games in which a set of items, each one controlled by a selfish player, are to be packed into a minimum number of unit capacity bins. Each item has one of m ≥ 2 colors and no items of the same color may be adjacent in a bin. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions, i.e., the egalitarian and the proportional ones. Although, under both cost functions, these games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when m ≥ 3 , while they are equal to 3 when m = 2 . We finally focus on the subcase of games with uniform sizes (i.e., all items have the same size). We show a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance. All of our bounds on the price of anarchy and stability hold with respect to both their absolute and asymptotic version. [ABSTRACT FROM AUTHOR]

We study strong Nash equilibria in mixed strategies in finite games. A Nash equilibrium is strong if no coalition of players can jointly deviate so that all players in the coalition get strictly better payoffs. Our main result concerns games with two players and states that if a game admits a strong Nash equilibrium, then the payoff pairs in the support of the equilibrium lie on a straight line in the players' utility space. As a consequence, the set of games that have a strong Nash equilibrium in which at least one player plays a mixed strategy has measure zero. We show that the same property holds for games with more than two players, already when no coalition of two players can profitably deviate. Furthermore, we show that, in contrast to games with two players, in a strong Nash equilibrium an outcome that is strictly Pareto dominated may occur with positive probability. [ABSTRACT FROM AUTHOR]

We investigate pure Nash equilibria in generalized graphk-coloring games where we are given an edge-weighted undirected graph together with a set of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player consists of k colors. The utility of a player v in a given state or coloring is given by the sum of the weights of edges {v, u} incident to v such that the color chosen by v is different than the one chosen by u, plus the profit gained by using the chosen color. Such games form some of the basic payoff structures in game theory, model lots of real-world scenarios with selfish players and extend or are related to several fundamental class of games. We first show that generalized graph k-coloring games are potential games. In particular, they are convergent and thus Nash Equilibria always exist. We then evaluate their performance by means of the widely used notions of price of anarchy and price of stability and provide tight bounds for two natural and widely used social welfare, i.e., utilitarian and egalitarian social welfare. [ABSTRACT FROM AUTHOR]

Generalizing certain network interdiction games communicated to us by Andrew Liu and his collaborators, this paper studies a bilevel, non-cooperative game wherein the objective function of each player's optimization problem contains a value function of a second-level linear program parameterized by the first-level variables in a non-convex manner. In the applied network interdiction games, this parameterization is through a piecewise linear function that upper bounds the second-level decision variable. In order to give a unified treatment to the overall two-level game where the second-level problems may be minimization or maximization, we formulate it as a one-level game of a particular kind. Namely, each player's objective function is the sum of a first-level objective function ± a value function of a second-level maximization problem whose objective function involves a difference-of-convex (dc), specifically piecewise affine, parameterization by the first-level variables. This non-convex parameterization is a major difference from the family of games with min-max objectives discussed in Facchinei et al. (Comput Optim Appl 59(1):85–112, 2014) wherein the convexity of the overall games is preserved. In contrast, the piecewise affine (dc) parameterization of the second-level objective functions to be maximized renders the players' combined first-level objective functions non-convex and non-differentiable. We investigate the existence of a first-order stationary solution of such a game, which we call a quasi-Nash equilibrium, and study the computation of such a solution in the linear-quadratic case by Lemke's method using a linear complementarity formulation. [ABSTRACT FROM AUTHOR]

In this paper, we consider a stochastic Nash game in which each player minimizes a parameterized expectation-valued convex objective function. In deterministic regimes, proximal best-response (BR) schemes have been shown to be convergent under a suitable spectral property associated with the proximal BR map. However, a direct application of this scheme to stochastic settings requires obtaining exact solutions to stochastic optimization problems at each iteration. Instead, we propose an inexact generalization of this scheme in which an inexact solution to the BR problem is computed in an expected-value sense via a stochastic approximation (SA) scheme. On the basis of this framework, we present three inexact BR schemes: (i) First, we propose a synchronous inexact BR scheme where all players simultaneously update their strategies. (ii) Second, we extend this to a randomized setting where a subset of players is randomly chosen to update their strategies while the other players keep their strategies invariant. (iii) Third, we propose an asynchronous scheme, where each player chooses its update frequency while using outdated rival-specific data in updating its strategy. Under a suitable contractive property on the proximal BR map, we proceed to derive almost sure convergence of the iterates to the Nash equilibrium (NE) for (i) and (ii) and mean convergence for (i)–(iii). In addition, we show that for (i)–(iii), the generated iterates converge to the unique equilibrium in mean at a linear rate with a prescribed constant rather than a sublinear rate. Finally, we establish the overall iteration complexity of the scheme in terms of projected stochastic gradient (SG) steps for computing an ɛ -NE2 (or ɛ -NE∞) and note that in all settings, the iteration complexity is O (1 / ɛ 2 (1 + c) + δ) , where c = 0 in the context of (i), and c > 0 represents the positive cost of randomization in (ii) and asynchronicity and delay in (iii). Notably, in the synchronous regime, we achieve a near-optimal rate from the standpoint of solving stochastic convex optimization problems by SA schemes. The schemes are further extended to settings where players solve two-stage stochastic Nash games with linear and quadratic recourse. Finally, preliminary numerics developed on a multiportfolio investment problem and a two-stage capacity expansion game support the rate and complexity statements. [ABSTRACT FROM AUTHOR]

The literature suggests that mangers are overly competitive and overemphasize competitors' payoffs in making decisions. The authors demonstrate how two seemingly innocuous but common decision inputs that mid- and entry-level managers use–(1) advice from colleagues and (2) training–could propagate this bias. The authors conduct an experiment in which one generation of participants plays a noncooperative game and then passes on advice on how to play the same game to the second generation. The authors find that the second generation is more likely to accept decisions that negatively impact the competitor's profits, even when those decisions result in lower payoffs. The results suggest that the advice of the first generation causes the second generation to be more sensitive to relative performance. In a second experiment, the authors show that training films that create negative feelings toward competitors can have adverse effects on managers' decisions. The training increases the willingness of managers to sacrifice own profits to reduce competitor profitability. These findings have important implications for managers in competitive markets. This research suggests that standard training materials that emphasize beating competitors should be carefully assessed for their unintentional but potentially damaging effects. In particular, training designed to evoke affective responses toward competitors must be used judiciously. Firms that give junior managers more autonomy and responsibility should also be cognizant that the advice these managers get and the information they share may propagate a competitive bias. To mitigate this problem, an option is to devote resources to better understand the content and nature of advice that managers share with one another. [ABSTRACT FROM AUTHOR]

Starting from Hendricks and McAfee's (2000) example of the Allies' decision to feint at Calais and attack at Normandy on D-Day, this paper models misrepresentation of intentions to competitors or enemies. Allowing for the possibility of bounded strategic rationality and rational players' responses to it yields a sensible account of lying via costless, noiseless messages. In many cases the model has generically unique pure-strategy sequential equilibria, in which rational players exploit boundedly rational players, but are not themselves fooled. In others, the model has generically essentially unique mixed-strategy sequential equilibria, in which rational players' strategies protect all players from exploitation.

This paper reports experiments designed to study strategic sophistication, the extent to which behavior in games reflects attempts to predict others' decisions, taking their incentives into account. We studied subjects' initial responses to normal-form games with various patterns of iterated dominance and unique pure-strategy equilibria without dominance, using a computer interface that allowed them to search for hidden payoff information, while recording their searches. Monitoring subjects' information searches along with their decisions allows us to better understand how their decisions are determined, and subjects' deviations from the search patterns suggested by equilibrium analysis help to predict their deviations from equilibrium decisions.

Facility location games have been a topic of major interest in economics, operations research, and computer science, starting from the seminal work by Hotelling [Hotelling H (1929) Stability in competition. Econom. J. 39(153):41–57]. In the classical pure location Hotelling game, businesses compete for maximizing customer attraction by strategically locating their facilities, assuming no price competition, and customers are attracted to their closest facilities. Surprisingly, very little rigorous work has been presented on multiunit facility location games, where the classical pure location Hotelling games are extended to contexts where each player is to locate several facilities. In this paper, we present two major contributions to the study of multiunit pure location Hotelling games. In the first part of this paper, we deal with the two-player multiunit setting and fully characterize its equilibria. In the second part of this paper, we deal with multiunit facility location games, with N ≥ 3 players; our main result in this part is the full characterization of the settings where pure strategy equilibria exist. Our results also extend classical results on necessary and sufficient conditions for a strategy profile to be in equilibrium in a pure location (single-unit) Hotelling game to multiunit pure location games. [ABSTRACT FROM AUTHOR]

The paper considers a model of competition among firms that produce a homogeneous good in a networked environment. A bipartite graph determines which subset of markets a firm can supply to. Firms compete à la Cournot and decide how to allocate their production output to the markets they are directly connected to. We provide a characterization of the production quantities at the unique equilibrium of the resulting game for any given network. Our results identify a novel connection between the equilibrium outcome and supply paths in the underlying network structure. We then proceed to study the impact of changes in the competition structure, for example, due to a firm expanding into a new market or two firms merging, on firms' profits and consumer surplus. The modeling framework we propose can be used in assessing whether expanding in a new market is profitable for a firm, identifying opportunities for collaboration, for example, a joint venture between competing firms, and guiding regulatory action in the context of market design and antitrust analysis. The online appendix is available at https://doi.org/10.1287/mnsc.2018.3061. This paper was accepted by Gad Allon, operations management. [ABSTRACT FROM AUTHOR]

Collaborative fundraising mechanisms—known as joint fundraising appeals—have received increasing attention as innovative ways to reduce fundraising competition between aid agencies. While some aid agencies participate in joint fundraising activities, others consider that the disadvantages outweigh the benefits. Based on the analysis of two‐stage sequential game theory models, the article identifies key factors that affect aid agencies' decisions about participation in a joint fundraising mode. Our analysis indicates that expected effects of the joint fundraising mode depend on aid agencies' efficiency levels. For efficient aid agencies, the joint mode functions as a buffer to prevent them from fierce competition. In the case of inefficient aid agencies, the competitive mode saves aid agencies from underinvestment in fundraising activities. We classify representative allocation rules currently applied in the humanitarian context into three types. Our analysis shows that these allocation rules only lead to beneficial allocations for limited circumstances. Following the analysis of the three representative allocation rules, the present work also analyzes aid agencies' negotiation‐based allocation without predetermined allocation rules, using generalized Nash bargaining. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their opponents and the communication graph is not necessarily the same as the players' cost dependency graph. We develop a relatively fast algorithm within the framework of inexact-ADMM, based on local information exchange between the players. We prove its convergence to Nash equilibrium for fixed step-sizes and analyse its convergence rate. Numerical simulations illustrate its benefits when compared to a consensus-based gradient type algorithm with diminishing step-sizes. [ABSTRACT FROM AUTHOR]

We explore the conditions under which behavior in a strategic setting can be rationalized as the best response to some belief about other players' behavior. We show that a restriction on preferences, which we term quasi-monotonicity, provides such a test for a family of ultimatum games. Preferences are quasi-monotone if an agent prefers an allocation that improves her payoff at least as much as that of others. In an experiment, we find that 94% of the proposers make choices that are arbitrarily close to quasi-monotone preferences and beliefs. We also find that 90% of the responders make inconsistent choices in no more than 5% of the decision problems. Subjects whose choices are consistent as proposers are also more likely to make consistent choices as responders and to believe that others act consistently. Finally, we find little support for the convexity of preferences. [ABSTRACT FROM AUTHOR]

We propose an approach to a unified study of existence based on using new purely settheoretic notions of anti-cyclicity and cyclic anti-quasimonotonicity together with a given topological structure, without linear or (generalized) convexity structures. We first establish an extension of the classical Weierstrass extreme-value theorem to the bifunction case and its equivalent versions (with quite different formulations). Next, we apply these results to obtain sufficient conditions for the solution existence of various optimization-related problems. The proof technique of the results is simple and elementary, but seems to also be applicable for many other problems. [ABSTRACT FROM AUTHOR]

Summary: This work presents a novel framework based on adaptive learning techniques to solve the continuous‐time open‐loop Stackelberg games. The method yields real‐time approximations of the game value and convergence of the policies to the open‐loop Stackelberg‐equilibrium solution, while also guaranteeing asymptotic stability of the equilibrium point of the closed‐loop system. It is implemented as a separate actor/critic parametric network approximator structure for every player and involves simultaneous continuous‐time adaptation. To introduce and implement the hierarchical structure to the coupled optimization problem, we adjoin to the leader the controller dynamics of the follower. A persistence of excitation condition guarantees convergence of both critics to the actual game values that eventually solve the hierarchical optimization problem. A simulation example shows the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the impact of social externalities (SEs) on the stability of an international environmental agreement (IEA). We consider a framework in which players are divided into two homogeneous groups, namely, developed and developing countries. We assume that members of an IEA get some additional benefits, to which we refer as SEs. One main result is that any coalition that is internally stable will expand to include all countries, which is related to the minimum participation clause considered in some papers. However, our minimum, which is endogenously defined, is not the largest stable coalition size, but the grand coalition. [ABSTRACT FROM AUTHOR]

Data-driven segmentation is the powerhouse behind the success of online advertising. Various underlying challenges for successful segmentation have been studied by the academic community, with one notable exception—consumers' incentives have been typically ignored. This lacuna is troubling, as consumers have much control over the data being collected. Missing or manipulated data could lead to inferior segmentation. The current work proposes a model of prior-free segmentation, inspired by models of facility location and, to the best of our knowledge, provides the first segmentation mechanism that addresses incentive compatibility, efficient market segmentation, and privacy in the absence of a common prior. [ABSTRACT FROM AUTHOR]

We consider a target selection problem for multitarget tracking in a multifunction radar network from a game-theoretic perspective. The problem is formulated as a noncooperative game. The radars are considered to be players in this game with utilities modeled using a proper tracking accuracy criterion and their strategies are the observed targets whose number is known. Initially, for the problem of coordination, the Nash equilibria are characterized and, in order to find equilibria points, a distributed algorithm based on the best response dynamics is proposed. Afterward, the analysis is extended to the case of partial target observability and radar connectivity and heterogeneous interests among radars. The solution concept of correlated equilibria is employed and a distributed algorithm based on the regret matching is proposed. The proposed algorithms are shown to perform well compared to the centralized approach of significantly higher complexity. [ABSTRACT FROM AUTHOR]

This paper reports experiments designed to measure strategic sophistication, the extent to which players' behavior reflects attempts to predict others' decisions, taking their incentives into account. Subjects played normal-form games with various patterns of iterated dominance and unique pure-strategy equilibria without dominance, using a computer interface that allowed them to look up hidden payoffs as often as desired, one at a time, while automatically recording their look-ups. Monitoring information search allows tests of game theory's implications for cognition as well as decisions, and subjects' deviations from search patterns suggested by equilibrium analysis help to predict their deviations from equilibrium decisions.

A semi-parametric, information-based estimator is used to estimate strategies in prices and advertising for Coca-Cola and Pepsi-Cola. Separate strategies for each firm are estimated with and without restrictions from game theory. These information/entropy estimators are consistent, are efficient, and do not require distributional assumptions. These estimates are used to test theories about the strategies of firms and to see how changes in incomes or factor prices affect these strategies.

Generalized maximum entropy may be used to estimate mixed strategies subject to restrictions from game theory. This method avoids distributional assumptions and is consistent and efficient. We use this method to estimate the mixed strategies of duopolistic airlines.