Consider a firm deciding which job to assign to a worker. The worker's ability can be high

or low (H or L) with equal probability, and the jobs can require high or low ability (H or L).

Suppose initially that both the worker and the firm get a payoff of 2 when the worker is

matched to the corresponding job and 0 when mismatched. If the worker can send a costless

message m {H, L} to the firm, what is the best equilibrium outcome? What are the

payoffs to each type of worker and what are the payoffs to the firm in this equilibrium?