Stochastic game

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

Global Games: Theory and Applications

Abstract: Global games are games of incomplete information whose type space is determined by the players each observing a noisy signal of the underlying state. With strategic complementarities, global games often have a unique, dominance solvable equilibrium, allowing analysis of a number of economic models of coordination failure. For symmetric binary action global games, equilibrium strategies in the limit (as noise becomes negligible) are simple to characterize in terms of 'diffuse' beliefs over the actions of others. We describe a number of economic applications that fall in this category. We also explore the distinctive roles of public and private information in this setting, review results for general global games, discuss the relationship between global games and a literature on higher order beliefs in game theory and describe the relationship to local interaction games and dynamic games with payoff shocks.

A General Class of Adaptive Strategies

Abstract: We exhibit and characterize an entire class of simple adaptive strategies, in the repeated play of a game, having the Hannan-consistency property: In the long-run, the player is guaranteed an average payoff as large as the best-reply payoff to the empirical distribution of play of the other players; i.e., there is no "regret." Smooth fictitious play (Fudenberg and Levine [1995]) and regret-matching (Hart and Mas-Colell [1998]) are particular cases. The motivation and application of this work come from the study of procedures whose empirical distribution of play is, in the long-run, (almost) a correlated equilibrium. The basic tool for the analysis is a generalization of Blackwell's [1956a] approachability strategy for games with vector payoffs.

Stochastic Games for Power Grid Protection Against Coordinated Cyber-Physical Attacks

Abstract: Due to the global reliance on the power grid, coordinated cyber-physical attacks on its critical infrastructure can lead to disastrous human and economic losses. In this paper, a stochastic game-theoretic approach is proposed to analyze the optimal strategies that a power grid defender can adopt to protect the grid against coordinated attacks. First, an optimal load shedding technique is devised to quantify the physical impacts of coordinated attacks. Taking these quantified impacts as input parameters, the interactions between a malicious attacker and the defender are modeled using a resource allocation stochastic game. The game is shown to admit a Nash equilibrium and a novel learning algorithm is introduced to enable the two players to reach their equilibrium strategies while maximizing their respective minimum rewards in a sequence of stages. The convergence of the proposed algorithm to a Nash equilibrium point is proved and its properties are studied. Simulation results of the stochastic game model on the WSCC 9-bus system and the IEEE 118-bus system are contrasted with those of static games, and show that different defense resources owned lead to different defense strategies.

The Game of Two Identical Cars

Abstract: This paper describes a third-order pursuit—evasion game in which both players have the same speed and minimum turn radius. The game of kind is first solved for thebarrier or envelope of capturable states. When capture is possible, the game of degree is then solved for the optimal controls of the two players as functions of the relative position. The solution is found to include a universal surface for the pursuer and a dispersal surface for the evader.