  This paper considers a two-player game where each player chooses a resource
from a finite collection of options. Each resource brings a random reward. Both
players have statistical information regarding the rewards of each resource.
Additionally, there exists an information asymmetry where each player has
knowledge of the reward realizations of different subsets of the resources. If
both players choose the same resource, the reward is divided equally between
them, whereas if they choose different resources, each player gains the full
reward of the resource. We first implement the iterative best response
algorithm to find an $\epsilon$-approximate Nash equilibrium for this game.
This method of finding a Nash equilibrium may not be desirable when players do
not trust each other and place no assumptions on the incentives of the
opponent. To handle this case, we solve the problem of maximizing the
worst-case expected utility of the first player. The solution leads to
counter-intuitive insights in certain special cases. To solve the general
version of the problem, we develop an efficient algorithmic solution that
combines online convex optimization and the drift-plus penalty technique.
