Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Prices formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies. Evolutionary game theory differs from classical game theory in focusing more on the dynamics of strategy change. This is influenced by the frequency of the competing strategies in the population. Evolutionary game theory has helped to explain the basis of altruistic behaviours in Darwinian evolution. It has in turn become of interest to economists, sociologists, anthropologists, and philosophers. Classical non-cooperative game theory was conceived by John von Neumann to determine optimal strategies in competitions between adversaries. A contest involves players, all of whom ...

Many areas of game design and programming benefit from very simple premises found in the 50-year old discipline of game theory. When games go awry, it is often due to not applying one or more of these ideas. Online competitive games in particular are prone to tipping precariously out of balance. By comparing staple online games such as WORLD OF WARCRAFT, TEAM FORTRESS 2, and STARCRAFT to classic game theory examples such as Rock-Paper-Scissors and Prisoners Dilemma, this lecture offers practical tips on how game theory methodologies can be used to craft well-balanced games-and potentially avert disaster ...

This speculative section asks: to what extent can evolutionary game theory be useful for understanding macroevolution? A G-function is not unlike the German notion of a bauplan or body plan [88,89]. Organisms at higher taxonomic levels (e.g. phylum) might share a distinctive set of design rules. By its very definition, a G-function represents all individuals that share the same set of evolutionarily feasible strategies. If two individuals from the same G-function possess the same strategy in the same environment then they have the same expected fitness. In this sense, all within a G-function are evolutionarily identical [31] even if the existing populations (or species) possess very different strategies and ecologies. In time, all within a G-function have evolutionary access to their shared strategy set through recurrent mutations and/or selection. So what constitutes a different G-function?. If evolutionary constraints are indeed hierarchical, as suggested by many aspects of phylogenetics and ...

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CB600 Game Theory CHAPTER ONE. GAME THEORY 1. Introduction Game Theory is the mathematical modelling of situations of conflict and competition. These occur in many areas of life: we can think of.

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Standard Evolutionary Game Theory framework is a useful tool to study large interacting systems and to understand the strategic behavior of individuals in such complex systems. Adding an individual state to model local feature of each player in this context, allows one to study a wider range of problems in various application areas as networking, biology, etc. In this paper, we introduce such an extension of evolutionary game framework and particularly, we focus on the dynamical aspects of this system. Precisely, we study the coupled dynamics of the policies and the individual states inside a population of interacting individuals. We first define a general model by coupling replicator dynamics and continuous-time Markov Decision Processes and we then consider a particular case of a two policies and two states evolutionary game. We first obtain a system of combined dynamics and we show that the rest-points of this system are equilibria profiles of our evolutionary game with individual state dynamics.

If two players play prisoners dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoners dilemma. In addition to the general form above, the iterative version also requires that 2R , T + S, to prevent alternating cooperation and defection giving a greater reward than mutual cooperation. The iterated prisoners dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoners dilemma has also been referred to as the "Peace-War game".[9] If the game is played exactly N times and both players know this, then ...

Eight male and eight female subjects played a matrix form of the Prisoners Dilemma game; an additional eight male and eight female subjects played a non-matrix form of the game. Each subject played for both high monetary reward (maximum joint payoff of $1.00 per trial for 15 trials) and low monetary reward (maximum joint payoff of $.10 per trial for 15 trails). Half of the subjects played first for low reward and then for high. The order was reversed for the other half of the subjects. It was predicted that there would be greater cooperation when the subjects were given (1) large rewards as compared to small, and (2) non-matrix presentation as compared to matrix. The results failed to confirm these hypotheses. In addition, there were no sex differences in style of play nor were there significant interactions among the three variables. However, the overall level of cooperative play was considerably higher than is usually encountered in these games, averaging 55%, and the usual over trials decline

Downloadable ! Author(s): V. Bhaskar & Ichiro Obara. 2000 Abstract: We analyze the infinitely repeated prisoners dilemma with imperfect private monitoring and discounting. The main contribution of this paper is to construct ``belief-based strategies, where a players continuation strategy is a function only of his beliefs. This simplifies the analysis considerably, and allows us to explicitly construct sequential equilibria for such games, thus enabling us to invoke the one-step deviation principle of dynamic programming. By doing so, we prove that one can approximate the efficient payoff in any prisoners dilemma game provided that the monitoring is sufficiently accurate. Furthermore, for a class of prisoners dilemma games, one can approximate every individually rational feasible payoff. These results require that monitoring be sufficiently accurate, but only require a uniform lower bound on the discount rate.

Jan, youll find a good explanation of the role of reputation in game theory and really nice applications to bargaining processes in the business world in the book: "Games, Strategies, and Managers: How managers can use game theory to [View full text and thread] ...

Whenever computer scientists are dealing with problems consisting of multiple self-interested agents, we may face to strategic behavior which might deteriorate the quality of the solution. Game theory provides us many tools to analyse agents strategic behaviour, and concepts to incentivise them to behave according to the common interest. Those tools and concepts have been utilized to design, for example, efficient markets, voting rules and exchange mechanisms that incentivise agents to collaborate in order to achieve socially desirable outcomes. Furthermore, game theory has recently attracted more attention from computer scientists who have been interested in the computational tractability of those concepts when the number of agents is large. Now, more and more of these concepts can be applied to real-world applications including e-commerce, matching, cost-sharing, and ride-sharing, just to name a few. However, deploying innovative applications has been challenged by many issues raising from ...

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I am studying game theory as master degree. I examine linkage between asymetric information and game theory. I assume that we have two firms or countries or people. If one of siders have imperfect information at the other hand the [View full text and thread] ...

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I provide a (very) brief introduction to game theory. I have developed these notes to provide quick access to some of the basics of game theory; mainly as an a

The theory of games was devised by von Neumann & Morgenstern [1], and according to Aumann [2], game theory is an interactive decision theory, where an agents best strategy depends on her expectations on the actions chosen by other agents, and vice versa. As a result, the outcomes in question might have been intended by none of the agents [3]. To rank and order strategies, and to optimize individual payoffs, different systems to systematically identify equilibria have been defined. Most famously, the Nash equilibrium is a set of strategies such that no single agent can improve by switching to another strategy [4]. This concept includes mixed equilibria, which describe probability distributions over strategies. Such equilibrium concepts in game theory cover various kinds of patterns of play, i.e. simultaneous, non-simultaneous and asymmetric strategies [5]. This rich and complex framework allows for a wide application of game theory beyond economics, famously in ecology and evolution [6]. In ...

Replicator dynamics, the continuous-time analogue of Multiplicative Weights Updates, is the main dynamic in evolutionary game theory. In simple evolutionary zero-sum games, such as...

People make choices. Often, the outcome depends on choices other people make. What mental steps do people go through when making such choices? Game theory, the most influential model of choice in economics and the social sciences, offers an answer, one based on games of strategy like chess and checkers: the chooser considers the choices that others will make and makes a choice that will lead to a better outcome for the chooser, given all those choices by other people. It is universally established in the social sciences that classical game theory (even when heavily modified) is bad at predicting behavior. But instead of abandoning classical game theory, various social scientists have mounted an ambitious and energetic rescue operation under the name of "behavioral game theory." Its main tool is to propose systematic deviations from the predictions of game theory, such as deviations that arise from character type. Other deviations purportedly come from cognitive overload or limitations. The ...

Although game-theoretical models to study social and economic problems have existed for a long time, they have been sparsely used for the design of engineering systems. This is due to the significant theoretical hurdles posed by game formulations for real engineering environments /problems. In this study we show our first attempt at adapting the frame-work of game-theoretical models for engineering problems, in particular the aero-mechanical optimization of a notional turbine blade. We pose the design problem as a series of games, starting with the determination of the Pareto front, the non-cooperative (disagreement) point and the optimal solution as the tangent intersection of the Pareto front and contours of the overall system objective. We present gradient-based algorithms that determine the Pareto front, the non-cooperative solution and the tangent solution. The solution to this series of games provides the basis of a new equilibrium concept namely, System Optimal Cooperative Solution ...

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Game Theory: introduction and applications to computer networks Lecture 3: two-person non zero-sum games Giovanni Neglia INRIA - EPI Maestro 6 January 2010 Slides are based on a previous course with D. Figueiredo (UFRJ) and H. Zhang (Suffolk University) Outline Two-person zero-sum games Slideshow 21588 by Audrey

A payoff matrix, or payoff table, is a simple chart used in basic game theory situations to analyze and evaluate a situation in which two parties have a decision to make. The matrix is typically a...

When two individuals face off in conflict, the classic problem in evolutionary biology known as the prisoners dilemma says that the individuals are not likely to cooperate even if it is in their best interests to do so. But a new study suggests that with incentives to cooperate, natural selection can minimize conflict, changing the game from one of pure conflict to one of partial cooperation.. The findings, published online in the Proceedings of the Royal Society B, suggest that the prisoners dilemma game, which has reigned as the dominant theoretical paradigm used to explain the costs and benefits of the evolution of cooperation, is not as evolutionarily stable a strategy as once assumed.. In the prisoners dilemma game, both players have the incentive not to cooperate independently. Collectively, they would be better off if they did cooperate. Evolutionary biologists have long sought to explain how cooperation can be maintained in such conflict by considering conditional behaviors in ...

An essay which applies game theory to women. The Disguised Defection and Marginal Defection strategies are detailed, plus a description of how the end-game can play out.

Background From the simplest living organisms to human societies, cooperation among individuals emerges as a paradox difficult to explain and describe mathematically, although very often observed in reality. Evolutionary game theory offers an excellent toolbar to investigate this issue. Spatial structure has been one of the first mechanisms promoting cooperation; however, alone it only opens a narrow window of viability. Methodology/Principal Findings Here we equip individuals with incipient cognitive abilities, and investigate the evolution of cooperation in a spatial world where retaliation, forgiveness, treason and mutualism may coexist, as individuals engage in Prisoners Dilemma games. In the model, individuals are able to distinguish their partners and act towards them based on previous interactions. We show how the simplest level of cognition, alone, can lead to the emergence of cooperation. Conclusions/Significance Despite the incipient nature of the individuals cognitive abilities,

We compare female inmates and students in a simultaneous and a sequential Prisoners Dilemma. In the simultaneous Prisoners Dilemma, the cooperation rate among inmates exceeds the rate of cooperating students. Relative to the simultaneous dilemma, cooperation among first-movers in the sequential Prisoners Dilemma increases for students, but not for inmates. Students and inmates behave identically as second movers. Hence, we find a similar and significant fraction of inmates and students to hold social preferences…. ...

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This collection of selected contributions gives an account of recent developments in dynamic game theory and its applications, covering both theoretical advances and new applications of dynamic games

CiteSeerX - Scientific documents that cite the following paper: I.: A pure Nash equilibrium guaranteeing game theoretical replica allocation method for reducing web access time

A public lecture at the London School of Economics about the origins of game theory and computer science to their modern roles in billion-dollar auctions.

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Game Theory is based largely on the idea of John von Neumann. von Neumann wrote a book explaining his ideas in a publication entitled Theory of Ga...

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Here are 5 incredible breakthrough in Game Theory. Chess, Draughts, Othello, the Rubiks cube... these have been analyzed intensively and now we are seeing some major steps forward.

Downloadable! This paper studies the set of equilibrium payoffs in repeated games with long- and short-run players and little discounting. Because the short-run players are unconcerned about the future, each equilibrium outcome is constrained to lie on their static reaction (best-response) curves. The natural extension of the folk theorem to games of this sort would simply include this constraint in the definitions of the feasible payoffs and minmax values. In fact, this extension does obtain under the assumption that each players choice of a mixed strategy for the stage game is publicly observable but, in contrast to standard repeated games, the set of equilibrium payoffs is different if players can observe only their opponents realized actions.

(This abstract was borrowed from another version of this item.)

Cancer evolution and progression are shaped by Darwinian selection and cell-to-cell interactions. Evolutionary game theory incorporates both of these principles, and has been recently as a framework to describe tumor cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular birth and death rates in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape evolutionary timescales, ...

nothing against the those who ignore the opportunity and gaining when encoun- tering one another, thus ensuring that they fare better on average than those who play Out. Evolutionary stability thus directs our attention to the more plausible Nash equilibrium.. One could also justify equilibrium (In, In) by appealing to the cornerstone of the equilibrium refinements literature of the 1980s, that players should avoid weakly dominated strategies. Strategy In is the only undominated strategy in this game. Selten (1975) introduced the concept of a perfect equilibrium to capture the sense in which dominance considerations make (In, In) more appealing than (Out, Out) in Figure 2. The intuition behind perfect equilibria is that there is always some chance that any strategy might be played, perhaps by mistake or through some environmental tremble, and so one should protect oneself against the unexpected by avoiding dominated strategies. The concept of a proper equilibrium (Myerson, 1978) strengthens this ...

Baigger, Gunter. 1985. Die Nichtkonstruktivitat des Brouwerschen Fixpunktsatzes. Arch. Math. Logik Grundlag., 25(3-4):183--188.. BBC NEWS (Asia-Pacific): Vanuatu cargo cult marks 50 years. http://news.bbc.co.uk/2/hi/asia-pacific/6363843.stm (accessed March 31, 2007).. Binmore, K. 1987. Modelling rational players. Part I. Economics and Philosophy, 3:179-214.. Binmore, K. 1988. Modelling rational players. Part II. Economics and Philosophy, 4:9-55.. Binmore, Ken. 1998. Game Theory and the Social Contract, Vol. 2: Just Playing. The MIT Press.. Binmore, Ken. 1990. Essays on the foundations of game theory. Oxford: Basil Blackwell.. Binmore, Ken. 1991. Fun and Games: A Text on Game Theory. D.C. Heath.. Brattka, Vasco. 2001. Recursion and Computability over Topological Structures. Electronic Notes in Theoretical Computer Science 40:5.. Bridges, Douglas S., and Fred Richman. 1991. A recursive counterexample to Debreus theorem on the existence of a utility function. Mathematical Social Sciences 21, no. 2 ...

Update: Several readers have emailed me to point out, correctly, that the game in this video differs from a prisoners dilemma because one strategy is weakly, rather than strictly, dominant. Problem: List all the Nash equilibria. How does the analysis change if I, as a player, am slightly altruistic toward the other player (or slightly vengeful)? What if I think the other player might be slightly altruistic toward me? The situation is wonderful for class discussion ...

Known Issues == * Any bugs or requests should go to mantis: https://bugtracker.arcengames.com/view_all_bug_page.php * Multiplayer is disabled but coming very soon. We first focused on tightening up the single-player loop ([https://forums.arcengames.com/ai-war-ii/from-the-dev-notes-on-where-im-at-regarding-multiplayer-right-now-(729)/ more info here]), so thanks for your patience! == Whats this phase all about? == Now that weve got the first expansion under our belt, and the game is feeling large and solid at the equivalent of "first AI War plus four expansions," were ready to tackle the next big thing: multiplayer! We also are going to be adding interplanetary weapons to the base game as a free update (thats the last of the kickstarter stretch goals). This phase should wrap up all our kickstarter promises (including a laundry list of other smaller items), and we expect to have multiplayer fully functional by August. Multiplayer should be in a beta form where folks can test on it and ...

Malaria infection is a major problem in many countries. The use of the Insecticide-Treated BedNets (ITNs) has been shown to significantly reduce the number of malaria infections; however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individuals self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease.. ...

The substantial vaccine-induced morbidity and mortality associated with smallpox vaccination make pre-emptive mass vaccination controversial. If vaccination is voluntary, then there is a conflict between self- and group interests. This conflict can be framed as a tragedy of the commons, in which herd immunity plays the role of the commons, and free-riding (i.e. not vaccinating pre-emptively) is analogous to exploiting the commons. A previous game-theoretical study by Bauch et al. [4] examined this conflict of interest, and focused on the trade-off between prophylactic vaccination and post-outbreak mass vaccination (which has been shown to outperform contact-traced vaccination in a bioterrorism setting [10]). In particular, they showed that if the decision regarding pre-emptive vaccination is left to the individual, then the vaccine coverage achieved will be suboptimal from the group perspective. Bauch et al. [4] assumed that, once a post-outbreak vaccination campaign begins, individuals will be ...

We consider a repeated two-person zero-sum game in which the payoffs in the stage game are given by a 2 % 2 matrix. This is chosen (once) by chance, at the beginning of the game, to be either G1 or G², with probabilities p and 1 - p respectively. The maximizer is informed of the actual payoff matrix chosen but the minimizer is not. Denote by vn(p) the value of the n -times repeated game (with the payoff function defined as the average payoff per stage), and by v%(p) the value of the infinitely repeated game. It is proved that vn(p)=v%(p) + %(p)%(p)/%n + %%1/%n% , where %(p) is on appropriately scaled normal distributiondensity function evaluated at its p-quantile, and the coefficient K(p) is either 0 or the absolute value of a linear function in p.. ...

Recently, Ive been thinking a lot about small projects to get students started with evolutionary game theory. One idea that came to mind is to look at games that have been analyzed in the inviscid regime then spatialize them and reanalyze them. This is usually not difficult to do and provides some motivation to solving…

If a developer makes a game and nobody plays it, does it exist? Sure, but if a developer makes a game for commercial reasons and he or she doesnt spend enough time or effort marketing it, that game will probably just melt into mist and leave behind a poorer studio. That goes double for a game thats meant to be sold during the busy holiday season. Happily, we live in such a connected world that effectively marketing a game at any time of the year need.... read more ...

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This text offers a systematic, rigorous, and unified presentation of evolutionary game theory, covering the core developments of the theory from its inception i...

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