A Solution Concept and Its Axiomatic Results under Non-Transferable-Utility and Multi-Choice Situations

Yu-Hsien Liao,Yan-An Hwang

doi:10.3390/math8091559

Abstract

In real situations, agents might take different energy levels to participate. On the other hand, agents always face an increasing need to focus on non-transferable-utility situations efficiently in their operational processes. Thus, we introduce the replicated core under non-transferable-utility situations, and analyze non-emptiness of the replicated core by means of a balanced result. In order to express the rationality of the replicated core, we also define different reduced games to axiomatize the replicated core.

Highlights

Each agent of a standard game is either completely concerned or departed from all participation with some other members
We present that the replicated core of a multi-choice non-transferable utility (NTU) game coincides with a replicated subset of the traditional core of a replicated NTU game
We show that there exists an unique solution other than the replicated core satisfying standard for one-person game (SOPG), single rationality (SRY), MCONY, and converse M-consistency (CMCONY) on MG

Summary

Introduction

Each agent of a standard game is either completely concerned or departed from all participation with some other members. The date of finalization hinges on the endeavor of how all of the members participate in the program: the greater they employ themselves, the sooner the program will be finished This situation could be treated as a multi-choice game. The merit of a coalition where each member participates at a definite energy level is defined as the minus of the fine which requires to be remunerated for giving the date of finalization of the program when each member presents the relative endeavor. The agents face the problem of choosing a payoff that is feasible for the entire coalition This is a bargaining condition and its solution may be rationally required to satisfy various criteria, and different collections of axioms will characterize different solutions.

Preliminaries

Balancedness and Non-Emptiness

Axiomatic Result

Another Reduction

Discussion

Conclusions