Robustness Properties in Fictitious-Play-Type Algorithms

Swenson, Brian and Kar, Soummya and Xavier, João and Leslie, David S. (2017) Robustness Properties in Fictitious-Play-Type Algorithms. SIAM Journal on Control and Optimization, 55. pp. 3295-3318. ISSN 0363-0129

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Abstract

Fictitious play (FP) is a canonical game-theoretic learning algorithm which has been deployed extensively in decentralized control scenarios. However standard treatments of FP, and of many other game-theoretic models, assume rather idealistic conditions which rarely hold in realistic control scenarios. This paper considers a broad class of best response learning algorithms, that we refer to as FP-type algorithms. In such an algorithm, given some (possibly limited) information about the history of actions, each individual forecasts the future play and chooses a (myopic) best action given their forecast. We provide a unifed analysis of the behavior of FP-type algorithms under an important class of perturbations, thus demonstrating robustness to deviations from the idealistic operating conditions that have been previously assumed. This robustness result is then used to derive convergence results for two control-relevant relaxations of standard game-theoretic applications: distributed (network-based) implementation without full observability and asynchronous deployment (including in continuous time). In each case the results follow as a direct consequence of the main robustness result.

Item Type:
Journal Article
Journal or Publication Title:
SIAM Journal on Control and Optimization
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
82032
Deposited By:
Deposited On:
07 Oct 2016 10:58
Refereed?:
Yes
Published?:
Published
Last Modified:
28 Nov 2020 04:05