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

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

Does bounded rationality lead to individual heterogeneity? The impact of the experimentation process and of memory constraints

In this paper we explore the effect of bounded rationality on the convergence of individual behavior toward equilibrium. In the context of a Cournot game with a unique and symmetric Nash equilibrium, firms are modeled as adaptive economic agents through a genetic algorithm. Computational experiments show that (1) there is remarkable heterogeneity across identical but boundedly rational agents; (2) such individual heterogeneity is not simply a consequence of the random elements contained in the genetic algorithm; (3) the more rational agents are in terms of memory abilities and pre-play evaluation of strategies, the less heterogeneous they are in their actions. At the limit case of full rationality, the outcome converges to the standard result of uniform individual behavior.bounded rationality; genetic algorithms; individual heterogeneitybounded rationality; genetic algorithms; individual heterogeneity

Agent-Based Models and Human Subject Experiments

This paper considers the relationship between agent-based modeling and economic decision-making experiments with human subjects. Both approaches exploit controlled ``laboratory'' conditions as a means of isolating the sources of aggregate phenomena. Research findings from laboratory studies of human subject behavior have inspired studies using artificial agents in ``computational laboratories'' and vice versa. In certain cases, both methods have been used to examine the same phenomenon. The focus of this paper is on the empirical validity of agent-based modeling approaches in terms of explaining data from human subject experiments. We also point out synergies between the two methodologies that have been exploited as well as promising new possibilities.agent-based models, human subject experiments, zero- intelligence agents, learning, evolutionary algorithms

Simulation models of technological innovation: A Review

The use of simulation modelling techniques in studies of technological innovation dates back to Nelson and Winter''s 1982 book "An Evolutionary Theory of Economic Change" and is an area which has been steadily expanding ever since. Four main issues are identified in reviewing the key contributions that have been made to this burgeoning literature. Firstly, a key driver in the construction of computer simulations has been the desire to develop more complicated theoretical models capable of dealing with the complex phenomena characteristic of technological innovation. Secondly, no single model captures all of the dimensions and stylised facts of innovative learning. Indeed this paper argues that one can usefully distinguish between the various contributions according to the particular dimensions of the learning process which they explore. To this end the paper develops a taxonomy which usefully distinguishes between these dimensions and also clarifies the quite different perspectives underpinning the contributions made by mainstream economists and non-mainstream, neo-Schumpeterian economists. This brings us to a third point highlighted in the paper. The character of simulation models which are developed are heavily influenced by the generic research questions of these different schools of thought. Finally, attention is drawn to an important distinction between the process of learning and adaptation within a static environment, and dynamic environments in which the introduction of new artefacts and patterns of behaviour change the selective pressure faced by agents. We show that modellers choosing to explore one or other of these settings reveal their quite different conceptual understandings of "technological innovation".economics of technology ;

Does bounded rationality lead to individual heterogeneity? The impact of the experimentation process and of memory constraints

In this paper we explore the effect of bounded rationality on the convergence of individual behavior toward equilibrium. In the context of a Cournot game with a unique and symmetric Nash equilibrium, firms are modeled as adaptive economic agents through a genetic algorithm. Computational experiments show that (1) there is remarkable heterogeneity across identical but boundedly rational agents; (2) such individual heterogeneity is not simply a consequence of the random elements contained in the genetic algorithm; (3) the more rational agents are in terms of memory abilities and pre-play evaluation of strategies, the less heterogeneous they are in their actions. At the limit case of full rationality, the outcome converges to the standard result of uniform individual behavior

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Detecting change and dealing with uncertainty in imperfect evolutionary environments

Imperfection of information is a part of our daily life; however, it is usually ignored in learning based on evolutionary approaches. In this paper we develop an Imperfect Evolutionary System that provides an uncertain and chaotic imperfect environment that presents new challenges to its habitants. We then propose an intelligent methodology which is capable of learning in such environments. Detecting changes and adapting to the new environment is crucial to exploring the search space and exploiting any new opportunities that may arise. To deal with these uncertain and challenging environments, we propose a novel change detection strategy based on a Particle Swarm Optimization system which is hybridized with an Artificial Neural Network. This approach maintains a balance between exploitation and exploration during the search process. A comparison of approaches using different Particle Swarm Optimization algorithms show that the ability of our learning approach to detect changes and adapt as per the new demands of the environment is high