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AbstractWe study optimal bidder collusion at …rst-price auctions when the collusive mechanism only relies on signals about bidders' valuations. We build on Fang and Morris (2006) when two bidders have low or high private valuation of a single object and additionally each receives a private noisy signal from an incentiveless center about the opponent's valuation. We derive the unique symmetric equilibrium of the …rst price auction for any symmetric, possibly correlated, distribution of signals, when these can only take two values. Next, we …nd the distribution of 2-valued signals, which maximizes the joint payo¤s of bidders. We prove that allowing signals to take more than two values will not increase bidders'payo¤s if the signals are restricted to be public. We also investigate the case when the signals are chosen conditionally independently and identically out of n 2 possible values. We demonstrate that bidders are strictly better o¤ as signals can take on more and more possible values. Finally, we look at another special case of the correlated signals, namely, when these are independent of the bidders' valuations. We show that in any symmetric 2-valued strategy correlated equilibrium, the bidders bid as if there were no signals at all and, hence, are not able to collude.
I consider the problem of assigning agents to objects where each agent must pay the price of the object he gets and prices must sum to a given number. The objective is to select an assignment-price pair that is envyfree with respect to the true preferences. I prove that the proposed mechanism will implement both in Nash and strong Nash the set of envy-free allocations. The distinguishing feature of the mechanism is that it treats the announced preferences as the true ones and selects an envy-free allocation with respect to the announced preferences.Journal of Economic Literature classification numbers: C78, C71, D78
The existence of ex-ante strong incumbents may constitute a barrier to entry in auctions for goods such as licenses. Favoring the allocation to entrants is a way to induce entry and thus create competition. Designs such as the Anglo-Dutch auction have been proposed with this goal in mind. We first show that the Anglo-Dutch auction does indeed foster entry and increases the revenues of the seller. However, we argue that a more effective way could be to stage the allocation of the good so that each stage reveals information about the participants. We show that a sequence of English auctions, with high reserve prices in early rounds, fulfils this property and is more efficient than any one-stage entry auction. Moreover, it also outperforms the Anglo-Dutch auction in terms of seller's revenues.
Assuming constant marginal cost, it is shown that a switch from specific to ad valorem taxation that results in the same collusive price has no effect on the critical discount factor required to sustain collusion. This result is shown to hold for Cournot oligopoly when collusion is sustained with Nash-reversion strategies or optimal-punishment strategies. In a Cournot duopoly model with linear demand and quadratic costs, it is shown that the critical discount factor is lower with an ad valorem tax than with a specific tax that results in the same collusive price. However, in contrast to Colombo and Labrecciosa (J Public Econ 97:196-205, 2013) it is shown that the revenue is always higher with an ad valorem tax than with a specific tax.
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