Robustness Properties in Fictitious-play-type
نویسندگان
چکیده
Fictitious play (FP) is a canonical game-theoretic learning algorithm which has been 4 deployed extensively in decentralized control scenarios. However standard treatments of FP, and of 5 many other game-theoretic models, assume rather idealistic conditions which rarely hold in realistic 6 control scenarios. This paper considers a broad class of best response learning algorithms, that we 7 refer to as FP-type algorithms. In such an algorithm, given some (possibly limited) information 8 about the history of actions, each individual forecasts the future play and chooses a (myopic) best 9 action given their forecast. We provide a unified analysis of the behavior of FP-type algorithms under 10 an important class of perturbations, thus demonstrating robustness to deviations from the idealistic 11 operating conditions that have been previously assumed. This robustness result is then used to de12 rive convergence results for two control-relevant relaxations of standard game-theoretic applications: 13 distributed (network-based) implementation without full observability and asynchronous deployment 14 (including in continuous time). In each case the results follow as a direct consequence of the main 15 robustness result. 16
منابع مشابه
A Fictitious Play Approach to Large-Scale Optimization
In this paper we investigate the properties of the sampled version of the fictitious play algorithm, familiar from game theory, for games with identical payoffs, and propose a heuristic based on fictitious play as a solution procedure for discrete optimization problems of the form max{u(y) : y = (y1, . . . , yn) ∈ Y1 × · · · × Yn}, i.e., in which the feasible region is a Cartesian product of fi...
متن کاملOn Best-Response Dynamics in Potential Games
This work studies the convergence properties of continuous-time fictitious play in potential games. It is shown that in almost every potential game and for almost every initial condition, fictitious play converges to a pure-strategy Nash equilibrium. We focus our study on the class of regular potential games; i.e., the set of potential games in which all Nash equilibria are regular. As byproduc...
متن کاملOn the Nonconvergence of Fictitious Play in Coordination Games
It is shown by example that learning rules of the fictitious play type fail to converge in certain kinds of coordination games. Variants of fictitious play in which past actions are eventually forgotten and that incorporate small stochastic perturbations are better behaved for this class of games: over the long run, players coordinate with probability one. Journal of Economic Literature Classif...
متن کاملFictitious play in coordination games
We study the Fictitious Play process with bounded and unbounded recall in pure coordination games for which failing to coordinate yields a payoff of zero for both players. It is shown that every Fictitious Play player with bounded recall may fail to coordinate against his own type. On the other hand, players with unbounded recall are shown to coordinate (almost surely) against their own type as...
متن کاملOn Similarities between Inference in Game Theory and Machine Learning
In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifi...
متن کامل