Information in Tullock contests

In Tullock contests in which the common value of the prize is uncertain and the elasticity of the marginal cost of effort is increasing (decreasing), the effect of changes of players’ information on the equilibrium efforts and payoffs is unambiguous: if information is symmetric, then expected effort decreases (increases) as players become better informed; in two-player contests, the expected effort of a player with information advantage is less (greater) than that of his opponent. Sharper results arise when the cost of effort is linear: Under symmetric information, expected effort and payoff are invariant to changes in the players’ information. In two-player contests, both players exert the same expected effort regardless of their information, although expected effort is smaller when one player has information advantage than when both players have the same information. Interestingly, the expected payoff of a player with information advantage is larger than that of his opponent, even though he wins the prize less frequently.Acknowledgments of financial support: Israel Science Foundation, Grant 648/2 (Einy); Ministerio Economía (Spain), Grants ECO2014-55953-P and MDM2014-0431, and Comunidad de Madrid, Grant S2015/HUM-3444 (Moreno)

A characterization of vNM-stable sets for linear production games

Rosenmüller J, Shitovitz B. A characterization of vNM-stable sets for linear production games. INTERNATIONAL JOURNAL OF GAME THEORY. 2000;29(1):39-61.We discuss linear production games or market games with a continuum of players which are represented as minima of finitely many nonatomic measures. Within this context we consider vNM-Stable Sets according to von Neumann and Morgenstern. We classify or characterize all solutions of this type which are convex polyhedra, i.e., which are the convex hull of finitely many imputations. Specifically, in each convex polyhedral vNM-Stable Set (and not only in the symmetric ones), the different types of traders must organize themselves into cartels. The vNM-Stable Set is then the convex hull of the utility distributions of the cartels. Using the results from the continuum, we obtain a similar characterization also for finite glove market games

(Sophisticated) Stable Sets in Exchange Economies

Within the framework of (pure) exchange economies, we demonstrate that the von Neumann and Morgenstern stable set in the allocation space may differ from that in the corresponding utility space. Following Harsanyi (1974, Management Sci.20, 1472–1495), we then define the notion of the sophisticated stable set and establish an equivalence theorem: like the core, the sophisticated stable set in the allocation space coincides with that in the utility space. We also show that the sophisticated stable set has the desirable property of individual rationality. Journal of Economic Literature Classification Numbers: D51, C70, C71

Restricted Coalition Formation

Very often in social life individuals take decisions within groups (households, friendships, trade unions, local jurisdictions, networks, etc.). The formation of coalition may imply some theoretical difficulties, such as costs arising from forming a coalition or sharing information among agents. Coalition formation has the explicit purpose to represent the process of formation of coalitions of agents and hence modelling a number of relevant economic and social phenomena. Moreover, following this theoretical and applied literature on coalitions, the seminal chapter by Jackson and Wolinsky (1996) opened the way to a new stream of contributions using networks (graphs) to model the formation of links among individuals. In this chapter we will assume that only a subset S of the set of all possible coalitions in an economy is the set of admissible coalitions. We define the S -core concept, as in Hervès-Moreno. We will extend to a model with both uncertainty and asymmetric informations the results showed in Okuda and Shitovitz