The Optimal Principle of Stable Solutions in Lexicographic Cooperative Games

Additive stable solutions on perfect cones of cooperative games

Optimal Coalition Structures in Cooperative Graph Games

Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inherent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is computationally to optimize and solve such games. One prominent such language is the simple yet expressive Weighted Graph Games (WGGs) representation [14], which maintai...

Weakly monotonic solutions for cooperative games

The principle of weak monotonicity for cooperative games states that if a game changes so that the worth of the grand coalition and some player’s marginal contribution to all coalitions increase or stay the same, then this player’s payoff should not decrease. We investigate the class of values that satisfy effi ciency, symmetry, and weak monotonicity. It turns out that this class coincides with...

Solutions to Cooperative Games without Side Payments

An extension of Von Neumann Morgenstern solution theory to cooperative games without side payments has been outlined in [1]. In this paper we revise some of the definitions given in [1] and prove that in the new theory every threeperson constant sum game is solvable (see [1, Theorem 1]). Other results that were formulated in [1] had already been proved in [2]. [1 ; 2] are also necessary for a f...

Consistent solutions for cooperative games with externalities

In order to calculate the worth of a coalition of players, the coalition needs to predict the actions of outsiders. We propose that, for a given solution concept, such predictions should be made by applying the solution concept to the “reduced society” consisting of the non-members. We illustrate by computing the r-core for the case of Bertrand competition with differentiated commodities.  200...