(Joint with Alex Ellis), Games and Economic Behavior, Volume 147, 2024. Link
We consider first-price auctions with independent and private valuations that have asymmetric valuation distributions and supports. We first show the existence of equilibrium in these auctions through a perturbation approach, thereby establishing that the limit of Bayesian Nash equilibria (BNE) of such perturbed auctions is indeed the Bayesian Nash equilibrium (BNE) of the limit auction with asymmetric supports. We then characterize this BNE and show that the ε-equilibrium (ε-BNE) of the auction with asymmetric supports is a BNE of “close” auctions with common supports. We then demonstrate some numerical examples.
(Joint with JC Carbajal) Link
We investigate the equilibrium equivalence between pay-as-bid auctions and first-price auctions when bidders may be budget-constrained. This equivalence requires additional conditions which translate to the global concavity of the bidder's expected payoff function. We show that, when these conditions are present, the symmetric equilibrium strategies in the pay-as-bid auction are a modification of the equilibrium strategies in Che and Gale’s (1998) first-price auction under budget constraints. Our analysis captures a new economic trade-off for a budget-constrained bidder that only appears in multi-unit auctions and has no analogue in single-unit auctions. We also show that our conditions collapse in a sufficiently large market. In at least one instance, the equilibrium equivalence fails with three or more bidders. Therefore, despite its theoretical appeal, the equilibrium link between pay-as-bid auctions and first-price auctions is fragile.
(Joint with Anuj Bhowmik) Link
Equivalence between rejective core and set of dividend equilibria allocations is studied in finite economy and double infinity economy frameworks in presence of indivisibilities of commodities while also allowing the presence of satiated agents. It is further shown that in the finite economy and the double infinity economy, the core of every renegotiation core, the rejective core of every replica economy and the set of dividend equilibria are identical. Hence, core equivalence is demonstrated in both frameworks.