Core-stable rings in second price auctions with common values.

In a commonvalueauction in which the information partitions of the bidders are connected, all rings are core-stable. More precisely, the ex ante expected utilities of rings, at the (noncooperative) sophisticated equilibrium proposed by Einy et al. [Einy, E., Haimanko, O., Orzach, R., Sela, A., 2002. Dominance solvability of second-pricesauctions with differential information. Journal of Mathematical Economics 37, 247–258], describe a cooperative games in characteristic function form, in spite of the underlying strategic externalities. A ring is core-stable if the core of this characteristic function is not empty. Furthermore, every ring can implement its sophisticated equilibrium strategy by means of an incentive compatible mechanism. An example shows that, if the bidders’ information partitions are not connected, rings may no longer be core-stable.Characteristic function; Partition form game; Core; Collusion; Bayesian game; Auctions;

Core-stable rings in auctions with independent private values.

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders' final utility possibly depends on the winner's identity. We show that such direct externalities offer a possible explanation for cartels'structures (not) observed in practice.Core; partition function game; Collusion; Auctions; Bayesian game;

Core-stable Rings in Auctions with Independent Private Values

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders’ final utility possibly depends on the winner’s identity. We show that such direct externalities offer a possible explanation for cartels’ structures (not) observed in practice.auctions, Bayesian game, collusion, core, partition function game

Core-stable Rings in Second Price Auctions with Common Values

In a common value auction in which the information partitions of the bidders are connected, all rings are core-stable. More precisely, the ex ante expected utilities of rings, at the (noncooperative) sophisticated equilibrium proposed by Einy, Haimanko, Orzach and Sela (Journal of Mathematical Economics, 2002), describe a cooperative game, in characteristic function form, in spite of the underlying strategic externalities. A ring is core-stable if the core of this characteristic function is not empty. Furthermore, every ring can implement its sophisticated equilibrium strategy by means of an incentive compatible mechanism.Auctions, Bayesian Game, Collusion, Core, Partition Form Game, Characteristic Function

Core stable bidding rings in independent private value auctions with externalities

We consider a second price auction between bidders with independently and identically distributed valuations, where a losing bidder suffers a negative direct externality. Considering ex-ante commitments to form bidding rings we study the question of core stability of the grand coalition, namely: is there a subset of bidders that prefers forming a small bidding ring rather than participating in the grand cartel? We show that in the presence of direct externalities between bidders the grand coalition is not necessarily core stable, as opposed to the zero externality case, where the stability of the grand coalition is a known result. Finally, we study collusion in auctions as a mechanism design problem, insisting on the difficulty to compare ex-ante and interim commitments. In particular, we show that there are situations in which bidders prefer colluding before privately learning their types.Auctions; collusion; externalities; Bayesian games; core; partition function game; mechanism design.

Core stable bidding rings in independent private value auctions with externalities

We consider a second price auction between bidders with independently and identically distributed valuations, where a losing bidder suffers a negative direct externality. Considering ex-ante commitments to form bidding rings we study the question of core stability of the grand coalition, namely: is there a subset of bidders that prefers forming a small bidding ring rather than participating in the grand cartel? We show that in the presence of direct externalities between bidders the grand coalition is not necessarily core stable, as opposed to the zero externality case, where the stability of the grand coalition is a known result. Finally, we study collusion in auctions as a mechanism design problem, insisting on the difficulty to compare ex-ante and interim commitments. In particular, we show that there are situations in which bidders prefer colluding before privately learning their types.Auctions;collusion;externalities;Bayesian games;core; partition function game;mechanism design