Core-stable rings in second price auctions with common values

Abstract

SummaryIn 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 corestable 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. Keywords AbstractIn 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.

Monotonic Knowledge Models, Cycles, Linear Versions and Auctions with Differential, Finite Information

“…This paper makes explicit the links between the connectedness condition found in the literature on common‐value, second‐price auctions with differential information (Einy et al . (), also studied by Forges & Orzach ()) and the concept of monotonic partitions (Rodrigues‐Neto, ) that is associated with Harsanyi Consistency Problem (common prior existence). When bidders’ partitions are not monotonic, it is no longer always the case that the bidder with superior information will do better than others.…”

“…One is the literature on common‐value, second‐price auctions with differential (and finite) information introduced by Einy et al . (), also studied by Forges & Orzach (). They introduce the concept of partitions that are ‘connected’ with respect to some real‐valued function on the state space, and always assume that there is such a function.…”

“…2 This paper establishes formal links between two streams of the literature that work with information structures used in games of incomplete information. One is the literature on common-value, second-price auctions with differential (and finite) information introduced by Einy et al (2002), also studied by Forges & Orzach (2011). They introduce the concept of partitions that are 'connected' with respect to some real-valued function on the state space, and always assume that there is such a function.…”

Common-value all-pay auctions with asymmetric information and bid caps

“…This partition representation is equivalent to the more common Harsanyi-type formulation of Bayesian games. 5 In our model of asymmetric information we assume that information sets of each player are connected with respect to the value of winning the contest (see Einy et al 2001Einy et al , 2002Forges and Orzach 2011). This means that if a player's information partition does not enable him to distinguish between two possible values of winning, then he also cannot distinguish between these and all intermediate values.…”

“…also condsidered individual bid caps in a broad class of all-pay contests, though under the complete information assumption. 4 Several researchers used the same framework as ours to analyze common-value second-price auctions and common-value first price auctions (seeEiny et al 2001Einy et al , 2002Forges and Orzach 2011;Orzach 2012, andAbraham et al 2014).…”