On the Core of Dynamic Cooperative Games

Dynamic Games and Applications. Forthcoming

25 Pages Posted: 11 Mar 2012 Last revised: 13 Jul 2013

See all articles by Ehud Lehrer

Ehud Lehrer

Tel Aviv University - School of Mathematical Sciences

Marco Scarsini

Luiss University Dipartimento di Economia e Finanza

Date Written: March 13, 2012

Abstract

We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and thereby to give rise to a new environment. A coalition that considers a deviation needs to take the consequences into account because from the deviation point on, the game is no longer played with the original set of players. The deviating coalition becomes the new grand coalition which, in turn, induces a new dynamic game. The stage games of the new dynamical game depend on all previous allocation including those that have materialized from the deviating time on.

We define three types of core solutions: fair core, stable core and credible core. We characterize the first two in case where the instantaneous game depends on the last allocation (rather than on the whole history of allocations) and the third in the general case. The analysis and the results resemble to a great extent the theory of non-cooperative dynamic games.

Keywords: fair core, stable core, credible core, convexification of a game

JEL Classification: C71

Suggested Citation

Lehrer, Ehud and Scarsini, Marco, On the Core of Dynamic Cooperative Games (March 13, 2012). Dynamic Games and Applications. Forthcoming, Available at SSRN: https://ssrn.com/abstract=2019910 or http://dx.doi.org/10.2139/ssrn.2019910

Ehud Lehrer

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Marco Scarsini (Contact Author)

Luiss University Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

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