  Coordination is a desirable feature in multi-agent systems, allowing the
execution of tasks that would be impossible by individual agents. We study
coordination by a team of strategic agents choosing to undertake one of the
multiple tasks. We adopt a stochastic framework where the agents decide between
two distinct tasks whose difficulty is randomly distributed and partially
observed. We show that a Nash equilibrium with a simple and intuitive linear
structure exists for diffuse prior distributions on the task difficulties.
Additionally, we show that the best response of any agent to an affine strategy
profile can be nonlinear when the prior distribution is not diffuse. Finally,
we state an algorithm that allows us to efficiently compute a data-driven Nash
equilibrium within the class of affine policies.
