Matrix Games, Mixed Strategies, and Statistical Mechanics
Johannes Berg,Andreas Engel +1 more
Reads0
Chats0
TLDR
In this article, the statistical properties of optimal mixed strategies of large matrix games with random payoff matrices were investigated and analytical expressions for the value of the game and the distribution of strategy strengths were derived.Abstract:
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties of optimal mixed strategies of large matrix games with random payoff matrices and derive analytical expressions for the value of the game and the distribution of strategy strengths. In particular the fraction of pure strategies not contributing to the optimal mixed strategy of a player is calculated. Both independently distributed as well as correlated elements of the payoff matrix are considered and the results are compared with numerical simulations.read more
Citations
More filters
Journal ArticleDOI
Evolutionary games on graphs
György Szabó,Gábor Fáth +1 more
TL;DR: The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Posted Content
An introduction to collective intelligence
David H. Wolpert,Kagan Tumer +1 more
TL;DR: This paper surveys the emerging science of how to design a “COllective INtelligence” (COIN) and introduces an entirely new, profound design problem: Assuming the RL algorithms are able to achieve high rewards, what reward functions for the individual agents will result in high world utility?
Journal ArticleDOI
Evolutionary game dynamics in a growing structured population
TL;DR: In this article, a model for evolutionary game dynamics in a growing, network-structured population is discussed, where new players can either make connections to random preexisting players or preferentially attach to those that have been successful in the past.
Journal ArticleDOI
Fixation times in evolutionary games under weak selection
Philipp M. Altrock,Arne Traulsen +1 more
TL;DR: It is shown analytically that these mean exit times depend on the payoff matrix of the game in an amazingly simple way under weak selection, i.e. strong stochasticity.
Journal ArticleDOI
Statistical mechanics of competitive resource allocation using agent-based models
Anirban Chakraborti,Damien Challet,Arnab Chatterjee,Arnab Chatterjee,Matteo Marsili,Yi-Cheng Zhang,Yi-Cheng Zhang,Bikas K. Chakrabarti,Bikas K. Chakrabarti +8 more
TL;DR: A broad spectrum of multi-agent models of competition and the methods used to understand them analytically are reviewed in this paper, where the power of concepts and tools from statistical mechanics to understand and explain fully collective phenomena such as phase transitions and long memory, and the mapping between agent heterogeneity and physical disorder are discussed.
References
More filters
Book
The Evolution of Cooperation
TL;DR: In this paper, a model based on the concept of an evolutionarily stable strategy in the context of the Prisoner's Dilemma game was developed for cooperation in organisms, and the results of a computer tournament showed how cooperation based on reciprocity can get started in an asocial world, can thrive while interacting with a wide range of other strategies, and can resist invasion once fully established.
Journal ArticleDOI
The Evolution of Cooperation
R. B. Greene,Robert Axelrod +1 more
TL;DR: A model is developed based on the concept of an evolutionarily stable strategy in the context of the Prisoner's Dilemma game to show how cooperation based on reciprocity can get started in an asocial world, can thrive while interacting with a wide range of other strategies, and can resist invasion once fully established.
Book
Products of random matrices in statistical physics
TL;DR: In this paper, the authors present a method for the computation of the Lyapunov exponent of PRM in the context of one-dimensional ising models and localization in two and three dimensions.
Book
The theory of games
Abstract: Part 1 Matrix games: introduction matrix games saddle points mixed strategies the Minimax theorem inductive proof of the Minimax theorem saddle points in mixed strategies optimal strategies and their properties domination of strategies solution of 2 x 2 matrix games graphical solution of 2 x n and m x 2 matrix games solution of 3 x 3 matrix games matrix games and linear programming. Part 2 Continuous games: zero-sum two-person infinitive games mixed strategies continuous games properties of optimal strategies convex games separable games an example of a game of timing. Part 3 N-person non-co-operative games: introduction existence of equilibrium point - Nash's theorem equilibrium points of 2 x 2 bimatrix games. Part 4 N-person co-operative games: introduction properties of characteristic functions imputations strategic equivalence and (0.1) normalization two-person co-operative games domination of imputations - three person co-operative games the core of a co-operative game stable sets of co-operative games pre-imputations and strong E-cores the kernel of a co-operative game the nucleolus of a co-operative game shapley value. References. Index.