  Partially observable stochastic games provide a rich mathematical paradigm
for modeling multi-agent dynamic decision making under uncertainty and partial
information. However, they generally do not admit closed-form solutions and are
notoriously difficult to solve. Also, in reality, each agent often does not
have complete knowledge of the other agent. This paper studies a
leader-follower partially observable stochastic game where the leader has
little knowledge of the adversarial follower's reward structure, level of
rationality, and process for gathering and transmitting data relevant for
decision making. We introduce the worst-case analysis to the partially
observable stochastic game to cope with this lack of knowledge and determine
the best worst-case value function of the leader. The resulting problem from
the leader's perspective has a simple sufficient statistic; however, different
from a classical partially observable Markov decision process, the value
function of the resulting problem may not be convex. We design a viable and
computationally attractive solution procedure for computing a lower bound of
the leader's value function as well as its associated control policy in the
finite planning horizon. We illustrate the use of the proposed approach in a
liquid egg production security problem.
