# Collusive communication schemes in a first-price auction

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## Abstract

We study optimal bidder collusion in an independent private value first-price auction with two bidders and two possible valuations. There is a benevolent center that knows the bidders’ valuations and sends private signals to the bidders in order to maximize their expected payoffs. After receiving their signals, bidders compete in a standard first-price auction, that is, without side payments or bid restrictions. We find that to improve on the bidders’ payoffs, the signals must depend upon the valuations. If the bidders’ signals are restricted to be non-correlated (depend only on the opponent’s valuation), then the bidders’ payoffs are strictly higher than the larger possible set of signals. If the signals are restricted to be perfectly correlated (public), only two possible signals are needed to achieve the highest bidder payoffs. However, these payoffs can be improved upon if the two signals are allowed to be imperfectly correlated.

## Keywords

Bidder-optimal signal structure Bid coordination mechanism Collusion (Bayes) correlated equilibrium First-price auction Public and private signals## JEL Classification

D44 D82## References

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