For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept.Convexity can be defined in a number of ways, each having its own specific attractions.Basically, these definitions fall into two categories, namely those based on a...

Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up...

We apply the procedure to both existing and new classes of cooperative situations: sequencing situations without initial ordering, maintenance problems, minimum cost spanning tree situations, travelling salesman problems, shared taxi problems and travelling repairman problems.

In this paper, we characterise the compromise value of a game as the barycentre of the edges of its core cover.For this, we introduce the value, which extends the adjusted proportional rule for bankruptcy situations and coincides with the compromise value on a large class of games.

This paper analyses the role of transfer payments and strategic con- tracting within two-person strategic form games with monetary pay- offs. First, it introduces the notion of transfer equilibrium as a strat- egy combination for which individual stability can be supported by allowing the...

In this paper we consider a proper Shapley value (the V L value) for cooperative network games.This value turns out to have a nice interpretation.We compute the V L value for various kinds of networks and relate this value to optimal strategies in an associated matrix game.

In a deposit game coalitions are formed by players combining their capital. The proceeds of their investments then have to be divided among those players. The current model extends earlier work on capital deposits by allowing reinvestment of returns. Two specific subclasses of deposit games are...

We consider the problem of ranking sets of objects, the members of which are mutually compatible.Assuming that each object is either good or bad, we axiomatically characterize three cardinality-based rules which arise naturally in this dichotomous setting.They are what we call the symmetric...

This paper provides an overview of the various shapes the best- reply multifunctions can take in 2×2×2 trimatrix games. It is shown that, unlike in 2×2 bimatrix games, the best replies to the opponents’ pure strategies do not completely determine the structure of the Nash equilibrium set.

Abstract: Proper equilbrium plays an importent role in the literature on non-cooperative games. The underlying thought experiment is, however, unsatisfying, as it gives no justification for its fundamental idea that severe mistakes are made with a significantly smaller probability than innocuous...