Computing security strategies in finite horizon repeated Bayesian games

Type
Conference Paper

Authors
Lichun Li
Langbort, Cedric
Shamma, Jeff S.

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program

Online Publication Date
2017-07-10

Print Publication Date
2017-05

Date
2017-07-10

Abstract
This paper studies security strategies in two-player zero-sum repeated Bayesian games with finite horizon. In such games, each player has a private type which is independently chosen according to a publicly known a priori probability. Players' types are fixed all through the game. The game is played for finite stages. At every stage, players simultaneously choose their actions which are observed by the public. The one-stage payoff of player 1 (or penalty to player 2) depends on both players types and actions, and is not directly observed by any player. While player 1 aims to maximize the total payoff over the game, player 2 wants to minimize it. This paper provides each player two ways to compute the security strategy, i.e. the optimal strategy in the worst case. First, a security strategy that directly depends on both players' history actions is derived by refining the sequence form. Noticing that history action space grows exponentially with respect to the time horizon, this paper further presents a security strategy that depends on player's fixed sized sufficient statistics. The sufficient statistics is shown to consist of the belief on one's own type, the regret on the other player's type, and the stage, and is independent of the other player's strategy.

Citation
Lichun Li, Langbort C, Shamma J (2017) Computing security strategies in finite horizon repeated Bayesian games. 2017 American Control Conference (ACC). Available: http://dx.doi.org/10.23919/ACC.2017.7963514.

Acknowledgements
The authors acknowledge the financial support of ARO project #W911NF-09-1-0553 and the AFOSR/MURI project #FA9550-10-1-0573.

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
2017 American Control Conference (ACC)

Conference/Event Name
2017 American Control Conference, ACC 2017

DOI
10.23919/ACC.2017.7963514

Additional Links
http://ieeexplore.ieee.org/document/7963514/

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