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Structure in the Value Function of Two-Player Zero-Sum Games of Incomplete Information

Auke J. Wiggers, Frans A. Oliehoek, and Diederik M. Roijers. Structure in the Value Function of Two-Player Zero-Sum Games of Incomplete Information. In ECAI 2016 - 22nd European Conference on Artificial Intelligence, pp. 1628–1629, August 2016.
[Please also see the extended version on arXiv.

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Abstract

In this paper, we introduce a new formulation for the value function of a zero-sum Partially Observable Stochastic Game (zs-POSG) in terms of a `plan-time sufficient statistic', a distribution over joint sets of information. We prove that this value function exhibits concavity and convexity with respect to appropriately chosen subspaces of the statistic space. We anticipate that this result is a key pre-cursor for developing solution methods that exploit such structure. Finally, we show that the formulation allow us to reduce a finite zs-POSG to a `centralized' model with shared observations, thereby transferring results for the latter (narrower) class of games to games with individual observations

BibTeX Entry

@inproceedings{Wiggers16ECAI,
    title =         {Structure in the Value Function of Two-Player Zero-Sum Games of Incomplete Information}, 
    author =        {Auke J. Wiggers and Frans A. Oliehoek and Diederik M. Roijers},
    booktitle =     ECAI16, 
    year =          2016,
    month =         aug,
    pages =         {1628--1629},
    wwwnote =       {[Please also see the <a href="https://arxiv.org/abs/1606.06888">extended version on arXiv</a>.},
    abstract = {
    In  this  paper,  we  introduce  a  new  formulation  for  the value function
    of a zero-sum Partially Observable Stochastic Game (zs-POSG) in terms of a
    `plan-time sufficient statistic', a distribution over joint sets of
    information. We prove that this value function exhibits concavity and
    convexity with respect to appropriately chosen subspaces of the statistic
    space. We anticipate that this result is a key pre-cursor for developing
    solution methods that exploit such structure. Finally, we show that the
    formulation allow us to reduce a finite zs-POSG to a `centralized' model
    with shared observations, thereby transferring results for the latter
    (narrower) class of games to games with individual observations
    }
}

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