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Stochastic game
About: Stochastic game is a research topic. Over the lifetime, 9493 publications have been published within this topic receiving 202664 citations.
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TL;DR: It is shown that for sufficiently patient players, there is a unique perfect equilibrium payoff which Pareto dominates all other payoffs and generalizes to any finite number of players and any game in a class of asynchonrously repeated games which includes both stochastic and deterministic repetition.
Abstract: The standard model of repeated games assumes perfect synchronization in the timing of decisions between the players. In many natural settings, however, choices are made asynchronously so that only one player can move at any given time. This paper studies a family of repeated settings in which choices are asynchronous. Initially, we examine, as a canonical model, a simple two person alternating move game of pure coordination. There, it is shown that for sufficiently patient players, there is a unique perfect equilibrium payoff which Pareto dominates all other payoffs. The result generalizes to any finite number of players and any game in a class of asynchonrously repeated games which includes both stochastic and deterministic repetition. The results complement a recent Folk Theorem by Dutta (1995) for stochastic games which can be applied to asynchronously repeated games if a full dimensionality condition holds. A critical feature of the model is the inertia in decisions. We show how the inertia in asynchronous decisions determines the set of equilibrium payoffs.
106 citations
TL;DR: In this paper, the authors consider a game of strategic experimentation with two-armed bandits where the risky arm distributes lump-sum payoffs according to a Poisson process, and construct asymmetric equilibria in which players have symmetric continuation values at sufficiently optimistic beliefs.
Abstract: We study a game of strategic experimentation with two-armed bandits where the risky arm distributes lump-sum payoffs according to a Poisson process. Its intensity is either high or low, and unknown to the players. We consider Markov perfect equilibria with beliefs as the state variable. As the belief process is piecewise deterministic, payoff functions solve differential-difference equations. There is no equilibrium where all players use cut-off strategies, and all equilibria exhibit an 'encouragement effect' relative to the single-agent optimum. We construct asymmetric equilibria in which players have symmetric continuation values at sufficiently optimistic beliefs yet take turns playing the risky arm before all experimentation stops. Owing to the encouragement effect, these equilibria Pareto dominate the unique symmetric one for sufficiently frequent turns. Rewarding the last experimenter with a higher continuation value increases the range of beliefs where players experiment, but may reduce average payoffs at more optimistic beliefs. Some equilibria exhibit an 'anticipation effect': as beliefs become more pessimistic, the continuation value of a single experimenter increases over some range because a lower belief means a shorter wait until another player takes over.
106 citations
TL;DR: Marriage networks are the most frequent and stable network structures in the experiments and find that payoff efficiency is around 90 percent of the ex ante, payoff dominant strategies and the distribution of network structures is significantly different from that which would result from random play.
106 citations
TL;DR: This contribution breaks with the tradition to restrict stochastic evolutionary game dynamics to populations of constant size and introduces a theoretical framework to investigate relevant and natural changes arising in populations that vary in size according to fitness—a feature common to many real biological systems.
Abstract: Frequency-dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency-dependent selection, the average fitness of the population may increase or decrease based on interactions between individuals within the population. This should be reflected in fluctuations of the population size even in constant environments. Here, we propose a stochastic model that naturally combines these two evolutionary ingredients by assuming frequency-dependent competition between different types in an individual-based model. In contrast to previous game theoretic models, the carrying capacity of the population, and thus the population size, is determined by pairwise competition of individuals mediated by evolutionary games and demographic stochasticity. In the limit of infinite population size, the averaged stochastic dynamics is captured by deterministic competitive Lotka–Volterra equations. In small populations, demographic stochasticity may instead lead to the extinction of the entire population. Because the population size is driven by fitness in evolutionary games, a population of cooperators is less prone to go extinct than a population of defectors, whereas in the usual systems of fixed size the population would thrive regardless of its average payoff.
106 citations
TL;DR: In this article, the authors consider a k-player sequential bargaining model in which both the cake size and the identity of the proposer are determined by a stochastic process.
Abstract: We consider a k-player sequential bargaining model in which both the cake size and the identity of the proposer are determined by a stochastic process. For the case where the cake is a simplex (of random size) and the players share a common discount factor, we establish the existence of a unique stationary subgame perfect payoff which is efficient and characterize the conditions under which agreement is delayed. We also investigate how the equilibrium payoffs depend on the order in which the players move and on the correlation between the identity of the proposer and the cake size.
106 citations