Bilateral associated game: Gain and loss in revaluation

Wenna Wang

doi:10.1371/journal.pone.0254218

Abstract

Hamiache introduces associated game to revalue each coalition’s worth, in which every coalition redefines his worth based on his own ability and the possible surpluses cooperating with other players. However, as every coin has two sides, revaluation may also bring some possible losses. In this paper, bilateral associated game will be presented by taking into account the possible surpluses and losses when revaluing the worth of a coalition. Based on different bilateral associated games, associated consistency is applied to characterize the equal allocation of non-separable costs value (EANS value) and the center-of-gravity of imputation-set value (CIS value). The Jordan normal form approach is the pivotal technique to accomplish the most important proof.

Highlights

For any game, players may elaborate the game’s expectations and be willing to revalue their payments in accordance with these new expectations
Hamiache [1] initially introduces to us the idea of associated game, which is a modified game, for each coalition revaluing its worth in terms of a rule related to the original game
Xu et al [3] considers the possible surpluses according to the sharing of the non-separable cost, and propose another type of associated game to axiomatize the EANS value within Hamiache’s axiom system

Summary

OPEN ACCESS

Data Availability Statement: All relevant data are within the paper. Hamiache introduces associated game to revalue each coalition’s worth, in which every coalition redefines his worth based on his own ability and the possible surpluses cooperating with other players. As every coin has two sides, revaluation may bring some possible losses. Bilateral associated game will be presented by taking into account the possible surpluses and losses when revaluing the worth of a coalition. Based on different bilateral associated games, associated consistency is applied to characterize the equal allocation of non-separable costs value (EANS value) and the center-of-gravity of imputation-set value (CIS value).

Introduction

Bilateral associated games

GN and

1Þl n

ÞðSÞ X

Conclusion