Conventional Game Theory Research Articles

Matrix games involving interval-valued hesitant fuzzy linguistic sets and its application to electric vehicles

Game theory has been successfully applied in a variety of domains to deal with competitive environments between individuals or groups. The matrix games involving fuzzy, interval fuzzy, and intuitionistic fuzzy numbers exclusively examine the numeric components of an issue. However, several researchers have also examined various extensions of conventional game theory, considering the ambiguous situations for payoffs and goals. In many real-life scenarios, qualitative information is often critical in expressing the payoffs of a matrix game. Thus, the present work contributes to the field of matrix games where the payoffs have been quantified via qualitative variables, termed interval-valued hesitant fuzzy linguistic sets. The mathematical formulation and solution concept for matrix games involving interval-valued hesitant fuzzy linguistic numbers is designed by utilizing an aggregation operator supported by linguistic scale function and solving them by employing score function. Finally, the proposed approach is validated by applying it to electric vehicle sales.

Optimization-based spectrum sensing in crn for effective utilization of available channel

Cognitive radio networks (CRN) are subjected to the challenge of demand in available resources, limited fair resource allocation between users in the heterogeneous CRN. The availability of minimal resources affects the channel allocation between Primary Users (PUs) and Secondary Users (SUs). In heterogeneous CRNs, efficient resources are available to SUs with fair resource allocation in a multi-hop environment. This paper proposed an efficient resource allocation in multi-hop CRN through Monte-Carlo Normal Form (MCNF). The proposed MCNF is involved in the optimization of the available resources through the estimation of the objective function. With Monte-Carlo estimation, MCNF computes the optimal resource availability within the CRN. Based on the Normal Form game theory resource availability of the network is computed and allocated between the users. The performance of the proposed MCNF is computed in terms of throughput, PDR, and running time. The proposed MCNF is comparatively examined with conventional game theory and the Monte-Carlo technique. The simulation analysis of the proposed MCNF expressed that running time is reduced with increased Packet delivery rate (PDR) and throughput.

On David Gauthier’s Theories of Coordination and Cooperation

In 1975, Gauthier discussed Schelling’spure coordination gamesand Hodgson’sHi-Lo game. While developing an original analysis of how rational players coordinate on ‘focal points,’ Gauthier argued, contrary to Schelling and Hodgson, that successful coordination in these games does not depend on deviations from conventional principles of individually rational choice. I argue that Gauthier’s analysis of constrained maximization inMorals by Agreement, which famously deviates from conventional game theory, has significant similarities with Schelling’s and Hodgson’s analyses of coordination. Constrained maximization can be thought of as a pragmatic and contractarian variant of the team-reasoning approach pioneered by Hodgson.

Load Shifting in the Smart Grid: To Participate or Not?

Demand-side management (DSM) has emerged as an important smart grid feature that allows utility companies to maintain desirable grid loads. However, the success of DSM is contingent on active customer participation. Indeed, most existing DSM studies are based on game-theoretic models that assume customers will act rationally and will voluntarily participate in DSM. In contrast, in this paper, the impact of customers' subjective behavior on each other's DSM decisions is explicitly accounted for. In particular, a noncooperative game is formulated between grid customers in which each customer can decide on whether to participate in DSM or not. In this game, customers seek to minimize a cost function that reflects their total payment for electricity. Unlike classical game-theoretic DSM studies which assume that customers are rational in their decision-making, a novel approach is proposed, based on the framework of prospect theory (PT), to explicitly incorporate the impact of customer behavior on DSM decisions. To solve the proposed game under both conventional game theory and PT, a new algorithm based on fictitious player is proposed using which the game will reach an epsilon-mixed Nash equilibrium. Simulation results assess the impact of customer behavior on demand-side management. In particular, the overall participation level and grid load can depend significantly on the rationality level of the players and their risk aversion tendency.

The Evolution of Strategic Sophistication

This paper investigates the evolutionary foundation for our ability to attribute preferences to others, an ability that is central to conventional game theory. We argue here that learning others' preferences allows individuals to efficiently modify their behavior in strategic environments with a persistent element of novelty. Agents with the ability to learn have a sharp, unambiguous advantage over those who are less sophisticated because the former agents extrapolate to novel circumstances information about opponents' preferences that was learned previously. This advantage holds even with a suitably small cost to reflect the additional cognitive complexity involved. (JEL C73, D11, D83)

Adaptive Selection of Cryptographic Protocols in Wireless Sensor Networks using Evolutionary Game Theory

Game theory applies to scenarios wherein multiple players with contrary motives contend with each other. Various solutions based on Game theory have been recently proposed which dealt with security aspects of wireless sensor networks (WSNs). However, the nodes have limited capability of rationality and evolutionary learning which makes it unfavorable to apply conventional game theory in WSNs. Evolutionary Game Theory (EGT) relies on bounded rationality assumption which is in harmony with the wireless sensor networks characteristics. Based on EGT, authors propose an adaptive security model for WSNs for the selection of cryptographic protocols during runtime. The authors formulate this selection in WSNs with the help of an evolutionary game to obtain the evolutionarily stable strategy (ESS) for the system. In this model, the sensor nodes dynamically adapt their defensive strategies to attain the most efficient defense, corresponding to the attackers’ varied strategies. Further, the simulations convey that the proposed system converges rapidly to the Evolutionary Stable Strategy. Not only the system converges, but also forms a stable system which was verified by deliberately destabilizing the system. Results show that the nodes quickly return to ESS even after perturbation.

Minilateralism matters more? Exploring opportunities to end climate negotiations gridlock

Multilateral negotiations to reach a universal, binding international agreement on measures that curb greenhouse gas (GHG) emissions have repeatedly failed since a scientific consensus on global warming formed in the late 1970s. The 1997 Kyoto Protocol was famously never ratified by the United States, the biggest emitter, and the 2009 Copenhagen conference only produced a narrow deal between the USA, China, India, Brazil and South Africa. Numerous attempts to involve international financial institutions or the G7/G8 have also been unsuccessful. Given the present crisis of multilateralism it can be argued that the time is ripe to engage fully in minilateral climate diplomacy, conferring ownership of the process to the main stakeholders. An informally orchestrated, minilateral diplomacy based on rationalist insights from conventional game and negotiation theory would then sway polluters to press ahead with measures that mitigate and adapt to the anticipated repercussions of climate change. Only after a political deal has been struck between major stakeholders may opportunities arise for ex post authorization and agenda control mechanisms involving the wider international community.

Games Played under Fuzzy Constraints

Psychological experiment studies reveal that human interaction behaviors are often not the same as what game theory predicts. One of important reasons is that they did not put relevant constraints into consideration when the players choose their best strategies. However, in real life, games are often played in certain contexts where players are constrained by their capabilities, law, culture, custom, and so on. For example, if someone wants to drive a car, he/she has to have a driving license. Therefore, when a human player of a game chooses a strategy, he/she should consider not only the material payoff or monetary reward from taking his/her best strategy and others' best responses but also how feasible to take the strategy in that context where the game is played. To solve such a game, this paper establishes a model of fuzzily constrained games and introduces a solution concept of constrained equilibrium for the games of this kind. Our model is consistent with psychological experiment results of ultimatum games. We also discuss what will happen if Prisoner's Dilemma and Stag Hunt are played under fuzzy constraints. In general, after putting constraints into account, our model can reflect well the human behaviors of fairness, altruism, self-interest, and so on, and thus can predict the outcomes of some games more accurate than conventional game theory.

The Evolution of Cooperation: How Patience Matters

The evolution of cooperation has been the focus of much attention from evolutionary game theorists. Of course, conventional game theorists often cite the Folk Theorem to suggest that cooperation is very likely as long as people are patient. However, experimental and real world evidence of the Folk Theorem has been sparse. We investigate whether cooperation can evolve endogenously in a population where people have different patience levels. We motivate our model by asking the following question: why don’t biologists cooperate with each other by contributing to biological databases? We apply the Folk theorem from conventional game theory and assume that patient people cooperate while impatient people do not. Further, we allow people to be heterogenous in the patience trait. We then show, using evolutionary game theory, how patience may matter in the evolution of cooperation. Computer simulations check for the robustness of our results. We suggest therefore that experimental evidence for the Folk theorem has been scarce because these experiments ignore patience endogeneity.

Action Being Character: A Promising Perspective on the Solution Concept of Game Theory

The inconsistency of predictions from solution concepts of conventional game theory with experimental observations is an enduring question. These solution concepts are based on the canonical rationality assumption that people are exclusively self-regarding utility maximizers. In this article, we think this assumption is problematic and, instead, assume that rational economic agents act as if they were maximizing their implicit utilities, which turns out to be a natural extension of the canonical rationality assumption. Implicit utility is defined by a player's character to reflect his personal weighting between cooperative, individualistic, and competitive social value orientations. The player who actually faces an implicit game chooses his strategy based on the common belief about the character distribution for a general player and the self-estimation of his own character, and he is not concerned about which strategies other players will choose and will never feel regret about his decision. It is shown by solving five paradigmatic games, the Dictator game, the Ultimatum game, the Prisoner's Dilemma game, the Public Goods game, and the Battle of the Sexes game, that the framework of implicit game and its corresponding solution concept, implicit equilibrium, based on this alternative assumption have potential for better explaining people's actual behaviors in social decision making situations.

Adaptive Routing Strategies in IEEE 802.16 Multi-Hop Wireless Backhaul Networks Based On Evolutionary Game Theory

The high frequency segment (10-66 GHz) of the IEEE 802.16 standard seems promising for the implementation of wireless backhaul networks carrying large volumes of Internet traffic. In contrast to wireline backbone networks, where channel errors seldom occur, routing decisions in IEEE 802.16 networks are conditioned by wireless channel impairments rather than by congestion, exclusively. This renders a cross-layer routing approach between the routing and the physical layers more appropriate during fading periods. In this paper, an adaptive cross-layer routing scheme is presented based on the selection of the most reliable path in terms of packet error ratio (unipath routing). The paper argues that routing Internet traffic through wireless backhaul networks is modeled more realistically employing evolutionary rather than conventional game theory. The stability of the proposed routing algorithm is proven and the dependence of the speed of convergence on various physical layer parameters is investigated. Is is also shown that convergence may be further accelerated by increasing the amount of information from the physical layer, specifically the physical separation between the alternative paths provided to the routing layer.

A Satisficing Approach to Aircraft Conflict Resolution

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Future generations of air traffic management systems may give appropriately equipped aircraft the freedom to change flight paths in real time. This would require a conflict avoidance and resolution scheme that is both decentralized and cooperative. We describe a multiagent solution to aircraft conflict resolution based on satisficing game theory. A key feature of the theory is that satisficing decision makers form their preferences by taking into consideration the preferences of others, unlike conventional game theory that models agents that maximize self-interest metrics. This makes possible situational altruism, a sophisticated form of unselfish behavior in which the preferences of another agent are accommodated provided that the other agent will actually take advantage of the sacrifice. This approach also makes possible the creation of groups in which every decision maker receives due consideration. We present simulation results from a variety of scenarios in which the aircraft are limited to constant-speed heading-change maneuvers to avoid conflicts. We show that the satisficing approach results in behavior that is attractive both in terms of safety and performance. The results underscore the applicability of satisficing game theory to multiagent problems in which self-interested participants are inclined to cooperation. </para>

Matrix games with interval data

The conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. In the real world, sometimes the payoffs are not known and have to be estimated, and sometimes the payoffs are only approximately known. This paper develops a solution method for the two-person zero-sum game where the payoffs are imprecise and are represented by interval data. Since the payoffs are imprecise, the value of the game should be imprecise as well. A pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the value of the game. Based on the duality theorem and by applying a variable substitution technique, the pair of two-level mathematical programs is transformed to a pair of ordinary one-level linear programs. Solving the pair of linear programs produces the interval of the value of the game. It is shown that the two players in the game have the same upper bound and lower bound for the value of the imprecise game. An example illustrates the whole idea and sheds some light on imprecise game.

Statistical Prediction of the Outcome of a Noncooperative Game

Conventionally, game theory predicts that the joint mixed strategy of players in a noncooperative game will satisfy some concept. Relative probabilities of the joint strategies satisfying the concept are unspecified, and all strategies not satisfying it are assigned probability zero. As an alternative, we recast the prediction problem of game theory as statistically estimating the joint strategy, from data that consists of the game specification. This replaces the focus of game theory, on specifying a set of equilibrium mixed strategies, with a new focus, on specifying a probability density over all mixed strategies. We explore a Bayesian version of such a Predictive Game Theory (PGT). We show that for some games the peaks of the posterior over joint strategies approximate quantal response equilibria. We also show how PGT provides a best single prediction for any noncooperative game, i.e., a universal refinement. We also show how regulators can use PGT to make optimal decisions in situations where conventional game theory cannot provide advice.

Solution of fuzzy matrix games: An application of the extension principle

Conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. This article develops a solution method for the two-person zero-sum game where the payoffs are only approximately known and can be represented by fuzzy numbers. Because the payoffs are fuzzy, the value of the game is fuzzy as well. Based on the extension principle, a pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the value of the game at possibility level α. By applying a dual formulation and a variable substitution technique, the pair of two-level mathematical programs is transformed to a pair of ordinary one-level linear programs so they can be manipulated. From different values of α, the membership function of the fuzzy value of the game is constructed. It is shown that the two players have the same fuzzy value of the game. An example illustrates the whole idea of a fuzzy matrix game. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 891–903, 2007.

Restricted Non-Cooperative Games

Traditional non-cooperative game theory has been an extraordinarily powerful tool in modeling biological and economic behavior, as well as the effect of legal rules. And, although it contains plausible concepts of equilibrium behavior, it does not a theory of dynamics as to how equilibria are to be reached. This paper on Restricted Non-Cooperative Games inserts dynamic content into traditional game theory and thus permits modeling of more realistic settings by imposing topologies that restrict the strategies available to player. It uses Mathematica to show how the payoff array used in conventional game theory can operate to generate a game network from the players' strategy topologies. Mathematica is likewise used to visualize this process and analyze the resulting game networks for properties such as maximal cycle lengths, stationary probabilities of associated Markov transition matrices, and scores for each of the players. The framework further analyzes settings in which each player has the ability to engineer its own strategy topology and suggests other potential extensions of Restricted Non-Cooperative Games.

On the Evolutionary Fitness of Bounded Rationality: Heterogeneous Populations in Antagonistic Interactions

Conventional game theory assumes hyper-rational players, while evolutionary game theory abandons the assumption. This paper studies what happens when agents of both profiles co-exist and get engaged in a series of antagonistic interactions (the Hawk-Dove game). It is shown that if rational agents are perfectly informed as to the type of their opponent, they find it optimal to always be aggressive (that is, always select “Hawk”) when paired with an irrational player. It is then shown that, generally, a similar result is also valid when rational agents fail to recognise the type of their opponent with certainty. Finally, a discussion on why it may be fruitful to consider populations heterogeneous as to the rationality of agents is provided.

FORMALIZATION OF MULTI-LEVEL GAMES

The article presents multilevel game theory, as a generalization of conventional single-level game theory as it has developed since von Neumann and Morgenstern (1944). We define a multilevel game structure, multilevel games, payoffs and distribution rules, upward feasible strategies and the solution concept multilevel Nash equilibrium (MNE) in such games. A MNE must be, for each player, a best reply against itself with respect to alternative strategies that may have other players deviate as well, in contrast to the NE for conventional games where simultaneous deviations by more than one player are not considered. Although every pure or mixed MNE must give the same outcome as a NE of the extensive form representation, a NE is not necessarily a MNE. It is shown that a MNE need not exist in pure or mixed strategies and, if it does, it may not be unique. In the former case, the multilevel structure is considered unmaintainable.

Skill in Games

Differences in players' skill are important determinants of relative player success in most real games such as poker, chess, basketball, business, and politics. Yet conventional game theory has concentrated primarily on games with no skill differences among players. This paper uses a simplified version of stud poker to better understand the concept of differential player skill in games. Players with very different strategies for playing this game are modeled algorithmically and pitted against one another in simulation tournaments.

Psychological games and sequential rationality

In psychological games the payoff to each player depends not only on what every player does but also on what he thinks every player believes, and on what he thinks they believe others believe, and so on. In equilibrium, beliefs are assumed to correspond to reality. Yet psychological games and psychological equilibria allow one to model belief-dependent emotions such as anger and surprise that are problematic for conventional game theory. We are particularly interested in issues of sequential rationality for psychological games. We show that although backward induction cannot be applied, and “perfect” psychological equilibria may not exist, subgame perfect and sequential equilibria always do exist.