The Effects of Excluding Coalitions

Tobias Hiller

doi:10.3390/g9010001

Abstract

One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions). One example of such exclusions is the coalition statements of parliamentary parties. Other situations in which incompatible players affect the outcome are teams in firms and markets, for example. To model these exclusions in cooperative game theory, the excluded coalitions value ( φ E value) was introduced. This value is based on the Shapley value and takes into account that players exclude coalitions with other players. In this article, we deduce some properties of this new value. After some general results, we analyze the apex game that could be interpreted as a team situation and the glove game that models markets where sellers and buyers deal. For team situations, we show that all employees have a common interest for cooperation. On asymmetric markets, excluding coalitions affect the market players of the scarce side to a higher extent.

Highlights

One problem in cooperative game theory is to model situations when two players refuse to cooperate
The φ E value for cooperative games was introduced and axiomatized [1]. This value is based on the Shapley value [2] and takes into account that players exclude coalitions with other players
Using the φ E value, the excluded coalition between the left and the right players is considered in a way that precludes a coalition of all three players

Summary

Introduction

One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions) One example of such exclusions is the coalition statements of parliamentary parties. Using the φ E value, the excluded coalition between the left and the right players is considered in a way that precludes a coalition of all three players Another enhancement of the approach by [3] was introduced by [4]. Using exclusions of coalitions strategically was analyzed by [10,11] In these articles, a non-cooperative game models the strategic decision of players whereas the values of cooperative game theory determine the payoffs at the last stage.

Basic Notation

Results

Discussion

⇧ References