@inproceedings{Wiggers15MSDM,
title = {Structure in the value function of zero-sum games of incomplete information},
author = {Wiggers, Auke J. and Oliehoek, Frans A. and Roijers, Diederik M.},
booktitle = MSDM15,
year = 2015,
month = may,
note = {(To appear.)},
abstract = {
In this paper, we introduce plan-time sufficient statistics,
representing probability distributions over joint sets of private
information, for zero-sum games of incomplete information. We define
a family of zero-sum Bayesian Games (zs-BGs), of which the members
share all elements but the plan-time statistic. Using the fact that
the statistic can be decomposed into a marginal and a conditional
term, we prove that the value function of the family of zs-BGs
exhibits concavity in marginal-space of the maximizing agent and
convexity in marginal-space of the minimizing agent. We extend this
result to sequential settings with a dynamic state, i.e., zero-sum
Partially Observable Stochastic Games (zs-POSGs), in which the
statistic is a probability distribution over joint action- observation
histories. First, we show that the final stage of a zs-POSG
corresponds to a family of zs-BGs. Then, we show by induction that the
convexity and concavity properties can be extended to every time-step
of the zs-POSG.
}
}