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Partially observable stochastic games provide a rich mathematical paradigmfor modeling multi-agent dynamic decision making under uncertainty and partialinformation. However, they generally do not admit closed-form solutions and arenotoriously difficult to solve. Also, in reality, each agent often does nothave complete knowledge of the other agent. This paper studies aleader-follower partially observable stochastic game where the leader haslittle knowledge of the adversarial follower's reward structure, level ofrationality, and process for gathering and transmitting data relevant fordecision making. We introduce the worst-case analysis to the partiallyobservable stochastic game to cope with this lack of knowledge and determinethe best worst-case value function of the leader. The resulting problem fromthe leader's perspective has a simple sufficient statistic; however, differentfrom a classical partially observable Markov decision process, the valuefunction of the resulting problem may not be convex. We design a viable andcomputationally attractive solution procedure for computing a lower bound ofthe leader's value function as well as its associated control policy in thefinite planning horizon. We illustrate the use of the proposed approach in aliquid egg production security problem.

Worst-Case Analysis for a Leader-follower Partially Observable Stochastic Game