Game-Theoretic Dynamic Procedure for a Power Index under Relative Symmetry

Jong-Chin Huang,Kelvin H.-C Chen,Yu-Hsien Liao

doi:10.3390/sym13101921

Abstract

In many operational processes, a suitable combination of participating elements has a huge impact throughout the entire process. In the real environment, however, many combinations show less than expected results in the initial stage. In consideration of the many subjective and objective factors such as equipment, time, capital, materials, and so forth, it seems that the aforementioned combinations cannot be used to re-configure. It is important that these initial unsatisfactory combinations can gradually approach some equilibrium states or results through some rolling adjustment processes. In order to improve the above problem, this study attempts to use a game-theoretic dynamic procedure to establish a mechanism that can be dynamically modified under relative symmetry at any time during operational processes. Under such a dynamic procedure, an undesirable combination of participating elements can gradually approach a useful combination.

Highlights

Dynamic Procedure for a PowerIn many modern academic studies, game theory is often applied to the equilibrium analysis of many operating systems
Motivated by the above results, we propose a dynamic procedure to reach the multi-choice level-individual index (MLII) for participating elements that start from a level complete combination and make consecutive amendments
We show that any combination will be dynamically adjusted continuously through the above procedure, and it will gradually approach the MLII, reaching its limit

Summary

Introduction

Dynamic Procedure for a PowerIn many modern academic studies, game theory is often applied to the equilibrium analysis of many operating systems. The axiomatic procedures in game theory often use various fields of mathematics to construct many concepts of fair and efficient distribution, and prove that these concepts of equilibrium and only conform to some principles of fairness and justice, so as to analyze their mathematical correctness, application rationality, and actual acceptability. Owen [3] defined the self-reduction and the axioms of covariance, efficiency, standardness for games and symmetry to analyze the axiomatic results of the Shapley value, respectively. By applying the disputing-conception of the EANSC, the elements first obtain their marginal contributions, and allot the rest of profit . Moulin [5] defined the complement-reduction and the axioms of consistency, efficiency and equal treatment for equal and zero-independence to demonstrate that the EANSC is a steady allocation for sharing-profit

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