The Harsanyi paradox and the “right to talk” in bargaining among coalitions

Juan Vidal-Puga

doi:10.1016/j.mathsocsci.2012.05.002

Abstract

We describe a coalitional value from a non-cooperative point of view, assuming coalitions are formed for the purpose of bargaining. The idea is that all the players have the same chances to make proposals. This means that players maintain their own “right to talk” when joining a coalition. The resulting value coincides with the weighted Shapley value in the game between coalitions, with weights given by the size of the coalitions. Moreover, the Harsanyi paradox (forming a coalition may be disadvantageous) disappears for convex games.

Highlights

Many economic situations can be modelled as a set of agents or players with independent interests who may benefit from cooperation
There is an extensive literature on axiomatic characterization of coalitional values: Aumann and Dreze (1974); Owen (1977); Hart and Kurz (1983); Levy and Mc Lean (1989); AlonsoMeijide and Fiestras-Janeiro (2002); Amer et al (2002); Mlodak (2003); Carreras and Puente (2006); Kamijo (2009, 2013); Gomez-Rua and Vidal-Puga (2010); Calvo and Gutierrez (2010), among others
We focus on TU games with coalition structure

Summary

Introduction

Many economic situations can be modelled as a set of agents or players with independent interests who may benefit from cooperation. Assume two players decide to join forces and act as one single player Harsanyi claims that this situation is equivalent to a symmetric (n − 1)-person unanimity game and each player’s expectation should be a pie of size 1/ (n − 1). For example in the n-person unanimity game where two players act as one unit, the proposal should come from one of the members of the joined coalition with a probability 1/ (n − 1), whereas when no coalition is formed the proposal should come from one of them with probability 2/n. With probability 1 − ρ, the proposer leaves the game and the mechanism is repeated with the rest of the players In our model, this procedure is played in two stages.

Preliminaries

The coalitional value

The non-cooperative mechanism

Concluding remark