Ramsey's Conjecture in Dynamic Contests

ABSTRACT We investigate the extent to which Ramsey's conjecture holds in an infinite‐horizon model with two agents in strategic interaction. Our model can also be interpreted as a dynamic contest game with resource constraints and an endogenous winning prize. We show that the most patient agent holds all productive resources in the long run (consistent with Ramsey's conjecture) if he is sufficiently productive. However, under different parameter values, a steady state may arise in which both agents have positive amounts of resources or, surprisingly, in which the least patient agent holds all resources. Our results also shed light on the comparative effects of ability versus patience on the long‐run equilibrium behavior in dynamic contests.