An ascending auction with multi-dimensional signals

This paper examines a single-unit ascending auction where agents observe two-dimensional Gaussian signals. The model combines the pure private-values model with the pure common-values model. The challenge is to characterize how the multi-dimensional signals observed by an agent are aggregated onto that agent's one-dimensional bid. The challenge is solved by projecting an agent's private signals onto a one-dimensional equilibrium statistic; the equilibrium bidding strategies are constructed as if each agent observed only his own equilibrium statistic. An agent's equilibrium statistic aggregates this agent's private signals while taking into account the additional information deduced from the other agents' bids. In contrast to one-dimensional environments, an ascending auction may have multiple symmetric equilibria that yield different social surpluses.