Voting Paradoxes and the Human Intuition

Brams (2003) presents three paradoxes for power indices: some rather counter-intuitive behaviour that is exhibited by both the Shapley-Shubik and the Banzhaf indices. We show that the proportional index is free from such paradoxical behaviour. This result suggests that our intuition may be based on the proportional index and as such its use in evaluating power measures is limited.Economics (Jel: A)

Strategic power indices: Quarrelling in coalitions

While they use the language of game theory known measures of a priory voting power are hardly more than statistical expectations assuming the random behaviour of the players. Focusing on normalised indices we show that rational players would behave differently from the indices predictions and propose a model that captures such strategic behaviour.Economics (Jel: A)

Stationary quasi-perfect equilibrium partitions constitute the recursive core

We present sucient conditions for the implementation of the (pessimistic) recursive core (Kóczy, 2007) in discrete partition function form games using a modified version of the sequential coalition formation game by Bloch (1996) extending the results of Kóczy (2008) and - in a slightly different setup - Huang and Sjöström (2006) to games with empty residual cores (respectively, to games that are not r-balanced).Economics (Jel: A)

The Core can be accessed in a Bounded Number of Steps

We prove the existence of an upper bound for the number of blockings required to get from one imputation to another provided that accessibility holds. The bound depends only on the number of players in the TU game considered. For the class of games with non-empty cores this means that the core can be reached via a bounded sequence of blockings. Primitive recursive algorithms are provided to locate accessibility paths.

Strategic Aspects of the 1995 and 2004 EU Enlargements

We discuss the two latest enlargements of the EU. While the 1995 entrants are by now fully integrated, the 2004 entrants will ``enjoy'''' a secondary status for a number of years. We attribute this difference to the fact that unlike the former EFTA members joining in 1995, the 2004 entrants formed a group with heterogenous interests, one that lacked the same strong internal economic ties. Not being able to act as a unified block they had a considerably weaker bargaining position. We support our arguments by qualitative results from a simple model, a dynamic partition function game based on Yi (1997) and Morelli and Penelle (1997).Strategy;

The Core Can Be Accessed in a Bounded Number of Steps

This paper strengthens the result of Sengupta and Sengupta (1996). We show that for the class of games with nonempty cores the core can be reached in a bounded number of proposals and counterproposals. Our result is more general than this: the boundedness holds for any two imputations with an indirect dominance relation between them.dynamic cooperative game, indirect dominance, core.

The Core of a Normal Form Game

Due to the externalities, in normal form games a deviation changes the payoff of all players inducing a retaliation by the remaining or residual players. The stability of an outcome depends on the expectations potential deviators have about this reaction, but so far no satisfactory theory has been provided. The present paper continues the work of Chander and Tulkens (1997) where deviators consider residual equilibria, but we allow coalitions to form, moreover introduce consistency between the residual solution and the solution of the original game. Optimistic and pessimistic considerations produce a pair of cores. These cores are compared to some existing cooperative concepts such as the gamma- and r-cores and the equilibrium binding agreements. In our final section we discuss the predominance of the grand coalition and suggest a generalisation of the normal form where such a precedence can be removed.externalities, residual game, cohesiveness, partition function

The Core of a Partition Function Game

We consider partition function games and introduce new defini-tions of the core that include the effects of externalities. We assume that all players behave rationally and that all stable outcomes arising are consistent with the appropriate generalised concept of the core. The result is a recursive definition of the core where residual subgames are considered as games with fewer players and with a partition function that captures the externalities of the deviating coalition. Some properties of the new concepts are discussed.core, partition function, externalities

Prospects after the voting reform of the Lisbon Treaty

The European Union used to make decisions by unanimity or near unanimity. After a series of extensions, with 27 member states the present decision making mechanisms have become very slow and assigned power to the members in an arbitrary way. The new decision rules accepted as part of the Lisbon Treaty did not only make decision making far easier, but streamlined the process by removing the most controversial element: the voting weights. The new system relies entirely on population data. We look at the immediate impact of the reform as well as the long term effects of the different demographic trends in the 27 member states. We find that the Lisbon rules benefit the largest member states, while medium sized countries, especially Central Eastern European countries suffer the biggest losses.European Union, Council of Ministers, qualied majority voting, Banzhaf index, Shapley-Shubik index, a priori voting power, demographics.

Stationary consistent equilibrium coalition structures constitute the recursive core

We study coalitional games where the proceeds from cooperation depend on the entire coalition structure. The coalition structure core (Kóczy, GEB, 2007) is a generalisation of the coalition structure core for such games. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core. In order to extend past results to games that are not totally balanced (understood in this special setting) we introduce subgame-consistency that requires perfectness in relevant subgames only, while subgames that are never reached are ignored.partition function, externalities, implementation, recursive core, stationary perfect equilibrium, time consistent equi- librium