Approximating n-player behavioural strategy nash equilibria using coevolution

Coevolutionary algorithms are plagued with a set of problems related to intransitivity that make it questionable what the end product of a coevolutionary run can achieve. With the introduction of solution concepts into coevolution, part of the issue was alleviated, however efficiently representing and achieving game theoretic solution concepts is still not a trivial task. In this paper we propose a coevolutionary algorithm that approximates behavioural strategy Nash equilibria in n-player zero sum games, by exploiting the minimax solution concept. In order to support our case we provide a set of experiments in both games of known and unknown equilibria. In the case of known equilibria, we can confirm our algorithm converges to the known solution, while in the case of unknown equilibria we can see a steady progress towards Nash. Copyright 2011 ACM

THE EQUIVALENCE OF EVOLUTIONARY GAMES AND DISTRIBUTED MONTE CARLO LEARNING

This paper presents a tight relationship between evolutionary game theory and distributed intelligence models. After reviewing some existing theories of replicator dynamics and distributed Monte Carlo learning, we make formulations and proofs of the equivalence between these two models. The relationship will be revealed not only from a theoretical viewpoint, but also by experimental simulations of the models by taking a simple symmetric zero-sum game as an example. As a consequence, it will be verified that seemingly chaotic macro dynamics generated by distributed micro-decisions can be explained with theoretical models.Research Methods/ Statistical Methods,

Fast Approximate Max-n Monte Carlo Tree Search for Ms Pac-Man

We present an application of Monte Carlo tree search (MCTS) for the game of Ms Pac-Man. Contrary to most applications of MCTS to date, Ms Pac-Man requires almost real-time decision making and does not have a natural end state. We approached the problem by performing Monte Carlo tree searches on a five player maxn tree representation of the game with limited tree search depth. We performed a number of experiments using both the MCTS game agents (for pacman and ghosts) and agents used in previous work (for ghosts). Performance-wise, our approach gets excellent scores, outperforming previous non-MCTS opponent approaches to the game by up to two orders of magnitude. © 2011 IEEE

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. 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.Comment: Review, final version, 133 pages, 65 figure

Informed Proposal Monte Carlo

Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a consequence of the the No-Free-Lunch Theorem, the only way we can ensure a significantly better performance of search and sampling algorithms is to build in as much information about the problem as possible. In the special case of Markov Chain Monte Carlo sampling (MCMC) we review how this is done through the choice of proposal distribution, and we show how this way of adding more information about the problem can be made particularly efficient when based on an approximate physics model of the problem. A highly nonlinear inverse scattering problem with a high-dimensional model space serves as an illustration of the gain of efficiency through this approach