2016/06/22 by Auke Wiggers, Wiggers, Auke J., Frans A. Oliehoek +3
Business, Management and Accounting · Decision Sciences · #Artificial Intelligence (cs.AI) #Computer Science and Game Theory (cs.GT) #Decision-Making and Behavioral Economics #FOS: Computer and information sciences #Risk and Portfolio Optimization #Supply Chain and Inventory Management
paper · pdf · doi:10.48550/arxiv.1606.06888
openalex publication_date 2016/06/22 · openalex created_date 2016/07/22 · openalex updated_date 2026/08/01
Zero-sum stochastic games provide a rich model for competitive decision making. However, under general forms of state uncertainty as considered in the Partially Observable Stochastic Game (POSG), such decision making problems are still not very well understood. This paper makes a contribution to the theory of zero-sum POSGs by characterizing structure in their value function. In particular, we introduce a new formulation of the value function for zs-POSGs as a function of the "plan-time sufficient statistics" (roughly speaking the information distribution in the POSG), which has the potential to enable generalization over such information distributions. We further delineate this generalization capability by proving a structural result on the shape of value function: it exhibits concavity and convexity with respect to appropriately chosen marginals of the statistic space. This result is a key pre-cursor for developing solution methods that may be able to exploit such structure. Finally, we show how these results allow us to reduce a zs-POSG to a "centralized" model with shared observations, thereby transferring results for the latter, narrower class, to games with individual (private) observations.