Naive fictitious play in an evolutionary environment

A fictitious play algorithm with a unit memory length within an evolutionary environment is considered. The aggregate average behavior model is proposed and analyzed. The existence, uniqueness and global asymptotic stability of equilibrium is proved for games with a cycling property. Also, a noisy version of the algorithm is considered, which gives rise to a system with a unique, globally asymptotically stable equilibrium for any game

Evolutionary Tournament-Based Comparison of Learning and Non-Learning Algorithms for Iterated Games

Evolutionary tournaments have been used effectively as a tool for comparing game-playing algorithms. For instance, in the late 1970's, Axelrod organized tournaments to compare algorithms for playing the iterated prisoner's dilemma (PD) game. These tournaments capture the dynamics in a population of agents that periodically adopt relatively successful algorithms in the environment. While these tournaments have provided us with a better understanding of the relative merits of algorithms for iterated PD, our understanding is less clear about algorithms for playing iterated versions of arbitrary single-stage games in an environment of heterogeneous agents. While the Nash equilibrium solution concept has been used to recommend using Nash equilibrium strategies for rational players playing general-sum games, learning algorithms like fictitious play may be preferred for playing against sub-rational players. In this paper, we study the relative performance of learning and non-learning algorithms in an evolutionary tournament where agents periodically adopt relatively successful algorithms in the population. The tournament is played over a testbed composed of all possible structurally distinct 2×2 conflicted games with ordinal payoffs: a baseline, neutral testbed for comparing algorithms. Before analyzing results from the evolutionary tournament, we discuss the testbed, our choice of representative learning and non-learning algorithms and relative rankings of these algorithms in a round-robin competition. The results from the tournament highlight the advantage of learning algorithms over players using static equilibrium strategies for repeated plays of arbitrary single-stage games. The results are likely to be of more benefit compared to work on static analysis of equilibrium strategies for choosing decision procedures for open, adapting agent society consisting of a variety of competitors.Repeated Games, Evolution, Simulation

Rage Against the Machines: How Subjects Learn to Play Against Computers

We use an experiment to explore how subjects learn to play against computers which are programmed to follow one of a number of standard learning algorithms. The learning theories are (unbeknown to subjects) a best response process, fictitious play, imitation, reinforcement learning, and a trial & error process. We test whether subjects try to influence those algorithms to their advantage in a forward-looking way (strategic teaching). We find that strategic teaching occurs frequently and that all learning algorithms are subject to exploitation with the notable exception of imitation. The experiment was conducted, both, on the internet and in the usual laboratory setting. We find some systematic differences, which however can be traced to the different incentives structures rather than the experimental environment

CSMA Local Area Networking under Dynamic Altruism

In this paper, we consider medium access control of local area networks (LANs) under limited-information conditions as befits a distributed system. Rather than assuming "by rule" conformance to a protocol designed to regulate packet-flow rates (e.g., CSMA windowing), we begin with a non-cooperative game framework and build a dynamic altruism term into the net utility. The effects of altruism are analyzed at Nash equilibrium for both the ALOHA and CSMA frameworks in the quasistationary (fictitious play) regime. We consider either power or throughput based costs of networking, and the cases of identical or heterogeneous (independent) users/players. In a numerical study we consider diverse players, and we see that the effects of altruism for similar players can be beneficial in the presence of significant congestion, but excessive altruism may lead to underuse of the channel when demand is low