Multicoalitional solutions

Abstract

International audienceThe paper proposes a new concept of solution for TU games, calledmulticoalitional solution, which makes sense in the context of production games,that is, where $v(S)$ is the production or income per unit of time. By contrastto classical solutions where elements of the solution are payoff vectors,multicoalitional solutions give in addition an allocation time to eachcoalition, which permits to realize the payoff vector. We give two instances ofsuch solutions, called the d-multicoalitional core and the c-multicoalitionalcore, and both arise as the strong Nash equilibria of two strategic games, where in thefirst utility per active unit of time is maximized, while in the second it isthe utility per total unit of time. We show that the d-core (or aspiration core)of Benett, and the c-core of Guesnerie and Oddou are strongly related to thed-multicoalitional and c-multicoalitional cores, respectively, and that thelatter ones can be seen as an implementation of the former ones in anoncooperative framework