On budget balance of the dynamic pivot mechanism

We modify the dynamic pivot mechanism of Bergemann and Välimäki (Econometrica, 2010) in such a way that lump-sum fees are collected from the players. We show that the modified mechanism satisfies ex-ante budget balance as well as ex-post efficiency, periodic ex-post incentive compatibility, and periodic ex-post individual rationality, as long as the Markov chain representing the evolution of players' private information is irreducible and aperiodic and players are sufficiently patient. We also show that the diverse preference assumption of Bergemann and Välimäki may preclude budget balance.