An extensive form interpretation of the private core

Abstract

The private core of an economy with differential information, (Yannelis (1991)), is the set of all state-wise feasible and private information measurable allocations which cannot be dominated, in terms of ex ante expected utility functions, by state-wise feasible and private information measurable net trades of any coalition. It is coalitionally Bayesian incentive compatible and also takes into account the information superiority of an individual. We provide a noncooperative extensive form interpretation of the private core for three person games. We construct game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. In the spirit of the Nash programme, the private core is thus shown to be supported by the perfect Bayesian equilibrium of a noncooperative game. The discussion contributes not only to the development of ideas but also to the understanding of the dynamics of how coalitionally incentive compatible contracts can be realized.We would like to thank the referees of this journal for their invaluable comments. In particular one of the referees made extensive suggestions which improved the final version of the paper.

An interim core for normal form games and exchange economies with incomplete information

“…In such a circumstance, let us say in the sequel that S blocks x at w 0 . 10 see also Glycopantis et al [2001], footnote p. 297, and Allen and Yannelis [2001] 11 In which it is mentioned that the existence of this issue is an open problem, p. 528.…”

Advances in Mathematical Economics

“…Ui (cj, Xi (a;)) = x^ and every player has the same prior distribution p{{uj}) = ^, for UJ eft. It was shown in Glycopantis et al (2001) that, without free disposal, a private core allocation is given by…”

“…This allows for transfers between the members of a coalition, and is therefore a strengthening of the concept of Coalitionally Bayesian Incentive Compatibility (CBIC), (see Glycopantis et al (2001)). …”

“…Here we draw upon the discussion in Glycopantis et al (2001Glycopantis et al ( , 2003. In the case we consider now there is no court and therefore the agents in order to decide must listen to the choices of the other agents before them.…”

On extensive form implementation of contracts in differential information economies

“…In Glycopantis, Muir, and Yannelis (2001) we provided a noncooperative interpretation of the private core for a three persons economy without free disposal. We constructed game trees which indicate the sequence of decisions and the information of the agents, and explained the rules for calculating ex ante, expected payoffs, through the reallocation of initial endowments.…”