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dc.contributor.authorLi, Lichun
dc.contributor.authorLangbort, Cedric
dc.contributor.authorShamma, Jeff S.
dc.date.accessioned2018-12-20T12:06:49Z
dc.date.available2018-12-20T12:06:49Z
dc.date.issued2018-12-07
dc.identifier.citationLi L, Langbort C, Shamma JS (2018) An LP approach for Solving Two-Player Zero-Sum Repeated Bayesian Games. IEEE Transactions on Automatic Control: 1–1. Available: http://dx.doi.org/10.1109/TAC.2018.2885644.
dc.identifier.issn0018-9286
dc.identifier.issn1558-2523
dc.identifier.issn2334-3303
dc.identifier.doi10.1109/TAC.2018.2885644
dc.identifier.urihttp://hdl.handle.net/10754/630327
dc.description.abstractThis paper studies two-player zero-sum repeated Bayesian games in which every player has a private type that is unknown to the other player, and the initial probability of the type of every player is publicly known. The types of players are independently chosen according to the initial probabilities, and are kept the same all through the game. At every stage, players simultaneously choose actions, and announce their actions publicly. For finite horizon cases, an explicit linear program is provided to compute players' security strategies. Moreover, based on the existing results in [1], this paper shows that a player's sufficient statistics, which is independent of the strategy of the other player, consists of the belief over the player's own type, the regret over the other player's type, and the stage. Explicit linear programs, whose size is linear in the size of the game tree, are provided to compute the initial regrets, and the security strategies that only depends on the sufficient statistics. For discounted cases, following the same idea in the finite horizon, this paper shows that a player's sufficient statistics consists of the belief of the player's own type and the anti-discounted regret with respect to the other player's type. Besides, an approximated security strategy depending on the sufficient statistics is provided, and an explicit linear program to compute the approximated security strategy is given. This paper also obtains a bound on the performance difference between the approximated security strategy and the security strategy, and shows that the bound converges to 0 exponentially fast.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.relation.urlhttps://ieeexplore.ieee.org/document/8567999
dc.rights(c) 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
dc.titleAn LP approach for Solving Two-Player Zero-Sum Repeated Bayesian Games
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.identifier.journalIEEE Transactions on Automatic Control
dc.eprint.versionPost-print
dc.contributor.institutionIndustrial and Manufacturing Engineering, FAMU-FSU college of engineering, Tallahassee, Florida United States of America 32310
dc.contributor.institutionAerospace Engineering, Univ of Illinois, Urbana-Champaign, Urbana, IL United States of America 61801
dc.identifier.arxivid1703.01957
kaust.personShamma, Jeff S.
refterms.dateFOA2018-12-23T07:55:54Z
dc.date.published-online2018-12-07
dc.date.published-print2018


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