  This paper considers a multi-player resource-sharing game with a fair reward
allocation model. Multiple players choose from a collection of resources. Each
resource brings a random reward equally divided among the players who choose
it. We consider two settings. The first setting is a one-slot game where the
mean rewards of the resources are known to all the players, and the objective
of player 1 is to maximize their worst-case expected utility. Certain special
cases of this setting have explicit solutions. These cases provide interesting
yet non-intuitive insights into the problem. The second setting is an online
setting, where the game is played over a finite time horizon, where the mean
rewards are unknown to the first player. Instead, the first player receives, as
feedback, the rewards of the resources they chose after the action. We develop
a novel Upper Confidence Bound (UCB) algorithm that minimizes the worst-case
regret of the first player using the feedback received.
