Stochastic game

About: Stochastic game is a research topic. Over the lifetime, 9493 publications have been published within this topic receiving 202664 citations.

The Value of Information in Monotone Decision Problems

Abstract: February 2001 This paper studies decision problems under uncertainty where a decision-maker observes an imperfect signal about the true state of the world. We analyze the information preferences and information demand of such decision-makers, based on properties of their payoff functions. We restrict attention to "monotone decision problems," whereby the posterior beliefs induced by the signal can be ordered so that higher actions are chosen in response to higher signal realizations. Monotone decision problems are frequently encountered in economic modeling. We provide necessary and sufficient conditions for all decision makers with different classes of payoff functions to prefer one information structure to another. We also provide conditions under which two decision-makers in a given class can be ranked in terms of their marginal value for information and hence information demand. Applications and examples are given. Working Papers Index

How individuals learn to take turns: emergence of alternating cooperation in a congestion game and the prisoner's dilemma

Abstract: In many social dilemmas, individuals tend to generate a situation with low payoffs instead of a system optimum ("tragedy of the commons"). Is the routing of traffic a similar problem? In order to address this question, we present experimental results on humans playing a route choice game in a computer laboratory, which allow one to study decision behavior in repeated games beyond the Prisoner's Dilemma. We will focus on whether individuals manage to find a cooperative and fair solution compatible with the system-optimal road usage. We find that individuals tend towards a user equilibrium with equal travel times in the beginning. However, after many iterations, they often establish a coherent oscillatory behavior, as taking turns performs better than applying pure or mixed strategies. The resulting behavior is fair and compatible with system-optimal road usage. In spite of the complex dynamics leading to coordinated oscillations, we have identified mathematical relationships quantifying the observed transition process. Our main experimental discoveries for 2- and 4-person games can be explained with a novel reinforcement learning model for an arbitrary number of persons, which is based on past experience and trial-and-error behavior. Gains in the average payoff seem to be an important driving force for the innovation of time-dependent response patterns, i.e. the evolution of more complex strategies. Our findings are relevant for decision support systems and routing in traffic or data networks.

An Exponential Lower Bound for the Parity Game Strategy Improvement Algorithm as We Know it

Abstract: This paper presents a new lower bound for the discrete strategy improvement algorithm for solving parity games due to Voege and Jurdzinski. First, we informally show which structures are difficult to solve for the algorithm. Second, we outline a family of games on which the algorithm requires exponentially many strategy iterations, answering in the negative the long-standing question whether this algorithm runs in polynomial time. Additionally we note that the same family of games can be used to prove a similar result w.r.t. the strategy improvement variant by Schewe as well as the strategy iteration for solving discounted payoff games due to Puri.

Brownian ratchets and Parrondo's games.

Abstract: Parrondo’s games present an apparently paradoxical situation where individually losing games can be combined to win. In this article we analyze the case of two coin tossing games. Game B is played with two biased coins and has state-dependent rules based on the player’s current capital. Game B can exhibit detailed balance or even negative drift (i.e., loss), depending on the chosen parameters. Game A is played with a single biased coin that produces a loss or negative drift in capital. However, a winning expectation is achieved by randomly mixing A and B. One possible interpretation pictures game A as a source of “noise” that is rectified by game B to produce overall positive drift—as in a Brownian ratchet. Game B has a state-dependent rule that favors a losing coin, but when this state dependence is broken up by the noise introduced by game A, a winning coin is favored. In this article we find the parameter space in which the paradoxical effect occurs and carry out a winning rate analysis. The significance of Parrondo’s games is that they are physically motivated and were originally derived by considering a Brownian ratchet—the combination of the games can be therefore considered as a discrete-time Brownian ratchet. We postulate the use of games of this type as a toy model for a number of physical and biological processes and raise a number of open questions for future research.