This paper studies the problem of allocating a good between two players in each period of an infinite-horizon game. The players' valuations in each period are private information, and the valuations change over time. We analyze two special cases for the dynamics of valuations: correlated where players' valuations are exogenous but serially correlated; and learning by doing, where a player's past consumption improves his current distribution of valuations, but his valuations are otherwise uncorrelated. We analyze conditions under which there exists an efficient, Bayesian incentive-compatible (BIC), individually rational (IR), budget-balanced (BB) mechanism, when the mechanism designer has commitment power. We consider
