B. Tsirelson

Correlated signals against monotone equilibria

Recent works

Michael Landsberger, Boris Tsirelson,
"Correlated signals against monotone equilibria."
SSRN 222308.
Available online (free of charge) from Social Science Research Network:

A research preprint, 27 pages, bibl. 21 refs.

We consider symmetric auctions that may be multi-unit, with multi-dimensional bids and correlated multi-dimensional signals. Payment and allocation mechanisms are quite arbitrary. There are n potential bidders and the process of submitting a bid involves cost, which may be random and may vary across bidders. The number of effective bidders is part of an equilibrium. In fact, our model addresses more general games of which auction games are a special case. However, given the importance of auctions in economic theory and their prevalence in reality, they can be considered as a perfect archetype of our model.

We prove that if n is sufficiently large and signals behave in a burst mode (which appears to be rather typical under interdependence), there is no equilibrium supported by monotone strategies. Since results obtained in the auction literature rely on monotonicity of strategies, even very basic results, such as existence and uniqueness of a symmetric equilibrium, become open questions, even for single unit first price auctions.

We establish some properties of equilibria. They seem very innocuous and yet, they have power in the sense that they are incompatible with monotone strategies.

  1. Introduction.
  2. A General Auction Model.
  3. The General Model.
  4. Some Properties of Equilibria.
  5. Dependence and Burst.
  6. Nonexistence of Monotone Equilibria.
  7. Mitigated Properties of Equilibria.
  8. Calibrating Bursts.
  9. Nonexistence of Monotone Equilibria, Revisited.
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