The Variable Value Environment: Auctions and Actions

This paper introduces and formally models the variable value environment and proposes an auction mechanism appropriate for it. In the variable value environment, bidders’ private values may change over time as a result of both private actions and exogenous shocks. Examples of private actions and exogenous shocks are complementary investments and exogenous changes in bidder's business, respectively. We consider a three-period model of the variable value environment where agents receive signals about their values in the first and the third periods and in the second period they take actions. This setting captures essential features of auctions of objects available for use at a future date (e. g. , a sale of a military base scheduled to close in a few years). We study mechanisms that lead to efficient allocations, i. e. those in which the final value of the object to the winning bidder net of the total cost of private actions undertaken by all agents is maximized. We characterize the first best allocation, and propose a mechanism that yields the first best allocation in equilibrium. This mechanism has an inefficient pooling equilibrium along with an efficient separating equilibrium. To rule out the pooling equilibrium, we introduce a class of e -efficient mechanisms that force players to coordinate on the separating equilibrium. We prove that one can always choose an e -efficient mechanism that yields an efficient allocation with probability arbitrarily close to one.