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This paper investigates a fast and efficient dynamic channel access method for distributed channel access scenarios with strong jamming and limited channel resources to achieve effective anti-jamming communication performance. The proposed problem is constructed as a correlated equilibrium (CE)-based game model with jamming signals designed as coordination signals. To effectively raise the convergence performance under different jamming patterns, the event counters (ECs) are designed, where the coordination signal is improved according to the characteristics of the jamming signal. Next, a distributed cooperative anti-jamming approach is constructed based on coordinated learning, which effectively accelerates the generation of CE points. Based on the above approach, this paper designs a distributed channel access anti-jamming algorithm based on coordination signal optimization, and the simulation results show that the proposed approach can effectively achieve cooperative anti-jamming and channel access. Compared with the existing work, the proposed approach can achieve better communication performance and fairness in the face of sweep jamming. In the face of random jamming, it can achieve faster and better communication performance without losing fairness. [ABSTRACT FROM AUTHOR]

The existence of simple uncoupled no-regret learning dynamics that converge to correlated equilibria in normal-form games is a celebrated result in the theory ofmulti-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normalform game, the empirical frequency of play converges to a normal-form correlated equilibrium. Extensiveform (that is, tree-form) games generalize normal-form games by modeling both sequential and simultaneous moves, as well as imperfect information. Because of the sequential nature and presence of private information in the game, correlation in extensive-form games possesses significantly different properties than in normalform games, many of which are still open research directions. Extensive-form correlated equilibrium (EFCE) has been proposed as the natural extensive-form counterpart to the classical notion of correlated equilibrium in normal-form games. Compared to the latter, the constraints that define the set of EFCEs are significantly more complex, as the correlation device (a.k.a. mediator) must take into account the evolution of beliefs of each player as they make observations throughout the game. Due to that significant added complexity, the existence of uncoupled learning dynamics leading to an EFCE has remained a challenging open research question for a long time. In this article, we settle that question by giving the first uncoupled no-regret dynamics that converge to the set of EFCEs in n-player general-sum extensive-form games with perfect recall.We show that each iterate can be computed in time polynomial in the size of the game tree, and that, when all players play repeatedly according to our learning dynamics, the empirical frequency of play after T game repetitions is proven to be a O(1/√ T )-approximate EFCE with high probability, and an EFCE almost surely in the limit. [ABSTRACT FROM AUTHOR]

I consider a generalizarion of Vanderschraaf's correlated conventions to Quasi-Conventions, using the concept of coarse correlated equilibria. I discuss the possibility of improved payoffs and the question of learnability by simple uncoupled learning dynamics. Laboratory experiments are surveyed. The generalization introduces strains of commitment, which can be see from different points of view. I conclude that the strains of commitment preclude using the generalization as a stand-alone definition of convention, but that in certain settings Quasi-Conventions can be important modules within larger true conventions.

In many practical applications, such as poker, chess, drug interdiction, cybersecurity, and national defense, players often have adversarial stances, i.e., the selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Therefore, adversarial games are important in real-world applications. However, only special adversarial games, such as Bayesian games, are reviewed in the literature. In this respect, this study aims to provide a systematic survey of three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg (security) games, and zero-sum differential games, from an array of perspectives, including basic knowledge of game models, (approximate) equilibrium concepts, problem classifications, research frontiers, (approximate) optimal strategy-seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games. [ABSTRACT FROM AUTHOR]

In many strategic environments, information acquisition is a central component of the game that is played. Being uncertain about a payoff‐relevant state, a player in a game has a twofold incentive to acquire information: learning the state and learning what others know. We develop a model of information acquisition in games that accounts for players' incentive to learn what others know. In applications to rational inattention and global games, we prove the power of this incentive. When information acquisition is "independent," that is, players can acquire information only about the state, severe coordination problems emerge among rationally inattentive players. When information acquisition is "unrestricted," that is, players can acquire information about the state and each other's information in a flexible way, we show that rational inattention admits a sharp logit characterization and we provide a new rationale for selecting risk dominant equilibria in coordination games. [ABSTRACT FROM AUTHOR]

In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner outcomes than would result from the Nash equilibrium. The correlated equilibrium is evolutionarily stable because any mutant fares worse than a signal-following player when facing two players who follow their own correlated signals. The critical quality of the correlation device is to make this true both for potential mutants who would disobey their signal and instead choose the action which would beat the action signaled to the player, as well as for potential mutants who would deviate to the action that would be beaten by what the device signals to the player. These findings reveal how a strict correlated equilibrium can produce evolutionarily stable strategies for rock-paper-scissors with three players. [ABSTRACT FROM AUTHOR]

In this paper, we consider constrained discounted stochastic games with a countably generated state space and norm continuous transition probability having a density function. We prove existence of approximate stationary equilibria and stationary weak correlated equilibria. Our results imply the existence of stationary Nash equilibrium in ARAT stochastic games. [ABSTRACT FROM AUTHOR]

We consider repeated games where the players behave according to cumulative prospect theory (CPT). We show that, when the players have calibrated strategies and behave according to CPT, the natural analog of the notion of correlated equilibrium in the CPT case, as defined by Keskin, is not enough to capture all subsequential limits of the empirical distribution of action play. We define the notion of a mediated CPT correlated equilibrium via an extension of the stage game to a so-called mediated game. We then show, along the lines of the result of Foster and Vohra about convergence to the set of correlated equilibria when the players behave according to expected utility theory that, in the CPT case, under calibrated learning the empirical distribution of action play converges to the set of all mediated CPT correlated equilibria. We also show that, in general, the set of CPT correlated equilibria is not approachable in the Blackwell approachability sense. We observe that a mediated game is a specific type of a game with communication, as introduced by Myerson, and as a consequence, we get that the revelation principle does not hold under CPT. [ABSTRACT FROM AUTHOR]

• Design a Correlated equilibrium Routing Mechanism (CeRM) for traffic congestion mitigation. • Develop a distributed algorithm to solve the CeRM efficiently involving a large scale of travelers. • Prove the solution algorithm's robustness against random communication failures. • Design an acceleration scheme-aided solution algorithm and prove the resilience of the convergence. • Conduct experiments to validate the performance of the CeRM and its solution algorithms. With the rapid development of wireless communication, mobile computing, and GPS technologies, drivers' route decisions nowadays rely more on navigation services, such as Google or Waze. However, these navigation services don't always come with improved traffic conditions. Individual drivers often make independent and selfish route decisions that are not systematically favorable and thus often result in severe congestions. This study aims to alleviate such problems by exploiting the information gaps between individuals and the central planner (CP). Specifically, we develop a correlated equilibrium routing mechanism (CeRM) for the CP, which drives a group of vehicles' route choices to an equilibrium with a systematically optimal traffic condition while still satisfying individuals' selfish nature. Participating drivers would only be better off by following the suggested routing guidance than navigating on their best responses to real-time traffic information. The CeRM is modeled as a nonconvex and nonlinear program involving a large-scale of users. A distributed Augmented Lagrangian algorithm (D-AL) is developed to efficiently solve the CeRM to provide online real-time navigation service, taking advantage of the on-board computation resources of individual vehicles. Considering the D-AL relies on the wireless communications between vehicles and the CP, we proved the convergence robustness of the D-AL against random communication failures and derived the convergence rate upper bound as a function of the communication failure probability. It is noticed that the convergence rate of the D-AL degrades dramatically as the communication failure probability increases, which hampers the applicability of implementing the CeRM in practice. To improve the solution algorithm's resilience in the computation performance, we further designed and proved an acceleration scheme aided D-AL (aD-AL) to expedite the convergence rate under the high likelihood of communication failures. Numerical experiments conducted on the Sioux Falls city network confirmed the D-AL's convergence properties, robustness against random communication failures, and the resilience of the aD-AL to solve the CeRM. The experiments also show that the CeRM results in better system performance (have less system cost) compared with the existing Independent Routing (IR) mechanism and user-oriented Equilibrium Routing (uoER) mechanism. [ABSTRACT FROM AUTHOR]

Correlated equilibrium (Aumann, 1974, 1987) is an important generalization of the Nash equilibrium concept for multiplayer non-cooperative games. In a correlated equilibrium, players rationally condition their strategies on realizations of a common external randomization device and, as a consequence, can achieve payoffs that Pareto dominate any of the game's Nash equilibria. In this paper we explore whether such correlated equilibria can be learned over time using an evolutionary learning model where agents do not start with any knowledge of the distribution of random draws made by the external randomization device. Furthermore, we validate our learning algorithm findings by comparing the end behavior of simulations of our algorithm with both the correlated equilibrium of the game and the behavior of human subjects that play that same game. Our results suggest that the evolutionary learning model is capable of learning the correlated equilibria of these games in a manner that approximates well the learning behavior of human subjects and that our findings are robust to changes in the specification and parameterization of the model.

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We study new non-Bayesian solutions of games in strategic form, based on four notions of dominance: weak or strict domination by either a pure or a mixed strategy. For each of these types of dominance, d , we define a family of sets of strategy profiles, called d-correlated equilibria. We study the structure and properties of these families. A player is d-dominance rational when she does not play a strategy that is d -dominated relative to what she knows about the play of the other players. A set of profiles is a d -correlated equilibrium if and only if it is the set of profiles played in a model where d -dominance rationality is commonly known. When d denotes strict domination by a mixed strategy, a set of profiles is a d -correlated equilibrium if and only if it is the set of profiles played in a model where Bayesian rationality is commonly known. [ABSTRACT FROM AUTHOR]

In the context of simple finite-state discrete time systems, we introduce a generalization of a mean field game solution, called a correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of a solution is justified in two ways: we prove that correlated solutions arise as limits of exchangeable correlated equilibria in restricted (Markov open-loop) strategies for the underlying N-player games, and we show how to construct approximate N-player correlated equilibria starting from a correlated solution to the mean field game. [ABSTRACT FROM AUTHOR]

In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner outcomes than would result from the Nash equilibrium. The correlated equilibrium is evolutionarily stable because any mutant fares worse than a signal-following player when facing two players who follow their own correlated signals. The critical quality of the correlation device is to make this true both for potential mutants who would disobey their signal and instead choose the action which would beat the action signaled to the player, as well as for potential mutants who would deviate to the action that would be beaten by what the device signals to the player. These findings reveal how a strict correlated equilibrium can produce evolutionarily stable strategies for rock-paper-scissors with three players.

In this paper, I present a game-theoretic solution to the rule-following paradox in terms of what I will call basic constitutive practices. The structure of such a practice P constitutes what it is to take part in P by defining the correctness conditions of our most basic concepts as those actions that lie on the correlated equilibrium of P itself. Accordingly, an agent S meant addition by his use of the term ‘+’ because S is taking part in a basic constitutive practice of adding where quus-like answers are ruled out by not lying on the equilibrium. The resulting picture of language will preserve the objectivity and correctness conditions of meaning, all the while providing room for the community as a whole to make a mistake. I also argue that by accepting the account presented, we have a strong reason to reject the idea that language is rule-governed. [ABSTRACT FROM AUTHOR]

The increasing demand for energy storage systems (ESSs) alongside the continuous enhancements to storage technology have been of great positive impact on the electric grid. Their unceasing development has been driven by the need to accommodate increased penetration of renewable energy resources and defer capital investments, among other benefits. Moreover, ESSs have played a key role in the grid's ability to cope with its ever-shifting load profiles, resulting in large economic gain for ESS owners. For this reason, this prospective study was designed to investigate privately-owned energy storage hubs (ESHs) and their interactions with potential customers as well as with the electric grid. This research examined two contrasting interaction approaches for customer-owned stationary energy storage hubs: a cooperative and a non-cooperative game-theoretic approach. The goal of the cooperative technique is to conduce to a correlated equilibrium increasing the social welfare of all players involved using a regret matching algorithm. On the other hand, in the non-cooperative approach, modeled as an ascending price-clinching auction, each player acts greedily, maximizing only their individual welfare. Implementing both case studies resulted in important insights into ESH players' interactions and provided contrasting methods of modeling their behaviors. Finally, depending on the application at hand, the choice of one approach may be more realistic than the other. [ABSTRACT FROM AUTHOR]

In the context of normal-form games with complete information, we introduce a notion of correlated equilibrium that allows partial delegation to a mediator and ambiguity in the correlation device. Without ambiguity, the sets of equilibrium action distributions are equivalent to those for coarse correlated equilibrium (Moulin and Vial, 1978). With correlation devices that incorporate ambiguity, any action distribution that Pareto dominates a coarse correlated equilibrium or a correlated equilibrium (Aumann, 1974), can be approximated with an arbitrary degree of precision using the proposed equilibrium notion. These approximations are attained in one-shot, static strategic interactions, and do not require repeated play. We also analyze such equilibria when the set of feasible posteriors is exogenously constrained, which yields, as a special case, a definition and characterization of an "ambiguous correlated equilibrium" that does not require delegation to the mediator. [ABSTRACT FROM AUTHOR]

We define and characterize the notion of strong robustness to incomplete information, whereby a Nash equilibrium in a game u is strongly robust if, given that each player knows that his payoffs are those in u with high probability, all Bayesian–Nash equilibria in the corresponding incomplete-information game are close—in terms of action distribution—to that equilibrium of u . We prove, under some continuity requirements on payoffs, that a Nash equilibrium is strongly robust if and only if it is the unique correlated equilibrium. We then review and extend the conditions that guarantee the existence of a unique correlated equilibrium in games with a continuum of actions. The existence of a strongly robust Nash equilibrium is thereby established for several domains of games, including those that arise in economic environments as diverse as Tullock contests, all-pay auctions, Cournot and Bertrand competitions, network games, patent races, voting problems and location games. [ABSTRACT FROM AUTHOR]

The importance of transaction fees in maintaining blockchain security and sustainability has been confirmed by extensive research, although they are not mandatory in most current blockchain systems. To enhance blockchain in the long term, it is crucial to design effective transaction pricing mechanisms. Different from the existing schemes based on auctions with more consideration about the profit of miners, we resort to game theory and propose a correlated equilibrium based transaction pricing mechanism through solving a pricing game among users with transactions, which can achieve both the individual and global optimum. To avoid the computational complexity exponentially increasing with the number of transactions, we further improve the game-theoretic solution with an approximate algorithm, which can derive almost the same results as the original one but costs significantly reduced time. We also propose a truthful assessment model for pricing mechanism to collect the feedback of users regarding the price suggestion. Extensive experimental results demonstrate the effectiveness and efficiency of our proposed mechanism.

We extend Aumann's (1974) model of correlated equilibrium by requiring each player to bear an exogenously given cost if s/he disobeys the recommendation of the mediator. Calling the modified solution the costly correlated equilibrium (costly-CE), we show that in any finite normal-form game that has an unpure Nash equilibrium, the set of costly-CE strictly expands even with an arbitrarily small increase in the disobedience cost provided that the game is non-trivial and there is room for expansion. We also study the effects of the disobedience cost on the total welfare of players and the value of mediation. • We introduce a disobedience cost to the correlated equilibrium notion. • The set of costly correlated equilibria may expand with arbitrarily small cost rises. • An expansion arises if and only if the following three conditions are met: (i) the normal-form game is non-trivial; (ii) there is room for expansion; (iii) the normal-form game has an unpure Nash equilibrium. [ABSTRACT FROM AUTHOR]

Game theory is a very profound study on distributed decision-making behavior and has been extensively developed by many scholars. However, many existing works rely on certain strict assumptions such as knowing the opponent's private behaviors, which might not be practical. In this work, we focused on two Nobel winning concepts, the Nash equilibrium, and the correlated equilibrium. We proposed a policy-based deep reinforcement learning model which instead of just learning the regions for corresponding strategies and actions, it learns why and how the rational opponent plays. With our proposed policy-based deep reinforcement learning model, we successfully reached the correlated equilibrium which maximizes the utility for each player. Depending on the scenario, the equilibrium can reach outside of the Nash equilibrium convex hull to achieve higher utility for the players, while the traditional non-regret algorithms cannot. In addition, we also proposed a mathematical model to inverse the calculation of the correlated equilibrium probability to estimate the rational opponent player's payoff. Through simulations, with limited interaction among the players, we showed that our proposed method can achieve the optimal correlated equilibrium where each player gains an equal or higher utility than the Nash equilibrium.

We report experimental evidence showing a positive effect of redistribution on economic efficiency via the self-enforcement of property rights, and identify which status groups benefit more and which less. We model an economy in which wealth is produced if players voluntarily comply with the—efficient but inequitable—prevailing social order. We vary exogenously whether redistribution is feasible, and how it is organized. We find that redistribution benefits all status groups as property disputes recede. It is most effective when transfers are not discretionary but instead imposed by some exogenous administration. In the absence of coercive means to enforce property rights, it is the higher status groups, not the lower status groups, who benefit from redistribution being compulsory rather than voluntary. [ABSTRACT FROM AUTHOR]

The notion of communication equilibrium extends Aumann's (J Math Econ 1:67–96, 1974, https://doi.org/10.1016/0304-4068(74)90037-8) correlated equilibrium concept for complete information games to the case of incomplete information. This paper shows that this solution concept has the following property: for the class of incomplete information games with compact metric type and action spaces, and with payoff functions jointly measurable and continuous in actions, limits of Bayes-Nash equilibria of finite approximations to an infinite game are communication equilibria (and, in general, not Bayes-Nash equilibria) of the limit game. Stinchcombe's (J Econ Theory 146:638–655, 2011b, https://doi.org/10.1016/j.jet.2010.12.006) extension of Aumann's (J Math Econ 1:67–96, 1974, https://doi.org/10.1016/0304-4068(74)90037-8) solution concept to the case of incomplete information fails to satisfy this condition. [ABSTRACT FROM AUTHOR]

Institutions generate cooperative benefits that explain why they exist and persist. Therefore, their etiological function is to promote cooperation. The function of a particular institution, such as money or traffic regulations, is to solve one or more cooperation problems. We go on to argue that the teleological function of institutions is to secure values by means of norms. Values can also be used to redesign an institution and to promote social change. We argue, however, that an adequate theory of institutions should not be 'moralized' in that they should not be defined in terms of the values they are supposed to promote. [ABSTRACT FROM AUTHOR]

In this letter, we investigate the distributed power control problem in downlink cognitive satellite-terrestrial networks (CSTNs) while considering the quality of service (QoS) requirements of the primary satellite links. Specifically, a game-theoretic approach is employed to analyze the distributed but mutually affected power control decision-making problem. With the perspective of resource efficiency enhancement and interference mitigation, a novel utility function based on the trade-off between transmission rate and mutual interference is properly designed for all players in the power control game. Then, the existence of correlated equilibrium (CE) of the proposed game is discussed, and the criteria of optimality for the CE solution is introduced. Moreover, we design a regret-matching based distributed adaptive learning algorithm to obtain the CE solution and demonstrate it through representative numerical simulations. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs) are becoming increasingly popular, but the frequent charging and large charging latency remain major obstacles to the EV industry. This article focuses on the charging scheduling of on-the-move EVs in a transportation network to minimize EVs’ charging latency, including driving time to charging stations (CSs), wait time and charging time. We formulate this charging scheduling problem as a graphical game to characterize the strong couplings of charging latency among neighboring EV players. Specially, we investigate correlated equilibrium (CE) to describe the joint strategies of EV players, which is expected to further reduce the charging latency of EVs compared with Nash equilibrium (NE). It is shown that CE always exists in a finite game, and can be found by linear programming tools. In addition, we propose a method of wait time prediction, which can improve the prediction accuracy by combining the data of deterministic EV arrivals and the stochastic property of potential EV arrivals. Simulation studies are used to examine the performance of the proposed game-based approach, the efficiency of CE, the preciseness of our proposed wait time prediction method, the impacts of CS deployment on EVs’ charging latency, etc. We can draw a conclusion that our method has apparent advantages in situations where the locations of EV players are in dense manners. [ABSTRACT FROM AUTHOR]

Players' choices in quantum game schemes are often correlated by a quantum state. This enables players to obtain payoffs that may not be achievable when classical pure or mixed strategies are used. On the other hand, players' choices can be correlated due to a classical probability distribution, and if no player benefits by a unilateral deviation from the vector of recommended strategies, the probability distribution is a correlated equilibrium. The aim of this paper is to investigate relation between correlated equilibria and Nash equilibria in the MW-type schemes for quantum games. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the multi-user anti-jamming spectrum access problem. Using the idea of “converting harm into benefit,” the malicious jamming signals projected by the enemy are utilized by the users as the coordination signals to guide spectrum coordination. An “internal coordination-external confrontation” multi-user anti-jamming access game model is constructed, and the existence of Nash equilibrium (NE) as well as correlated equilibrium (CE) is demonstrated. A coordination-learning based anti-jamming spectrum access algorithm (CLASA) is designed to achieve the CE of the game. Simulation results show the convergence, and effectiveness of the proposed CLASA algorithm, and indicate that our approach can help users confront the malicious jammer, and coordinate internal spectrum access simultaneously without information exchange. Last but not least, the fairness of the proposed approach under different jamming attack patterns is analyzed, which illustrates that this approach provides fair anti-jamming spectrum access opportunities under complicated jamming pattern. [ABSTRACT FROM AUTHOR]

Studies of strategic sophistication in experimental normal form games commonly assume that subjects' beliefs are consistent with independent choice. This paper examines whether beliefs are consistent with correlated choice. Players play a sequence of 2 × 2 normal form games with distinct opponents and no feedback. Another set of players, called predictors, report a likelihood ranking over possible outcomes. A substantial proportion of the reported rankings are consistent with the predictors believing that the choice of actions in the 2 × 2 game are correlated. Predictions seem to be correlated around focal outcomes and the extent of correlation over action profiles varies systematically between games (i.e., prisoner's dilemma, stag hunt, coordination, and strictly competitive). [ABSTRACT FROM AUTHOR]