The Nucleolus of Large Majority Games

Noncooperative foundations of the nucleolus in majority games

This paper studies coalition formation, payoff division and expected payoffs in a ”divide the dollar by majority rule” game with random proposers. A power index is called self-confirming if it can be obtained as an equilibrium of the game using the index itself as probability vector. Unlike the Shapley value and other commonly used power indices, the nucleolus has this property. The proof uses ...

The Nucleolus of Directed Acyclic Graph Games

In this paper we consider a natural generalization of standard tree games where the underlying structure is a directed acyclic graph. We analyze the properties of the game and illustrate its relation with other graph based cost games. We show that although the game is not convex its core is always non-empty. Furthermore we provide a painting algorithm for large families of directed acyclic grap...

Finding the nucleoli of large cooperative games

The nucleolus is one of the most important solution concepts in cooperative game theory as a result of its attractive properties it always exists, is unique, and is always in the core (if the core is non-empty). However, computing the nucleolus is very challenging because it involves the lexicographical minimization of an exponentially large number of excess values. We present a method for comp...

The Modified Nucleolus as Canonical Representation of Weighted Majority Games

On the Nucleolus of Neighbour Games

The class of neighbour games is the intersection of the class of assignment games (cf. Shapley and Shubik (1972)) and the class of component additive games (cf. Curiel et al. (1994)). For assignment games and component additive games there exist polynomially bounded algorithms of order p for calculating the nucleolus, where p is the number of players. In this paper we present a polynomially bou...