Deciding game invariance

Cooperative Benefit and Cost Games under Fairness Concerns

Solution concepts in cooperative games are based on either cost games or benefit games. Although cost games and benefit games are strategically equivalent, that is not the case in general for solution concepts. Motivated by this important observation, a new property called invariance property with respect to benefit/cost allocation is introduced in this paper. Since such a property can be regar...

Using Satisficing Game Theory for Performance Evaluation of Banks’ Branches (Case Study in the Mellat Bank)

Due to its role in the identification of inefficient branches and deciding the consistency of their activities, evaluating the performance of a bankchr('39')s branches is one of the most important decisions in the field of development and regulation of branch network. In this paper, the satisfactory functions based on game theory strategies have been utilized in order to evaluate the individual...

Friendly Frogs, Stable Marriage, and the Magic of Invariance

We introduce a two-player game involving two tokens located at points of a fixed set. The players take turns to move a token to an unoccupied point in such a way that the distance between the two tokens is decreased. Optimal strategies for this game and its variants are intimately tied to Gale-Shapley stable marriage. We focus particularly on the case of random infinite sets, where we use invar...

A Game-Theoretic Approach to Deciding Higher-Order Matching

Strong Addition Invariance and axiomatization of the weighted Shapley value

This paper shows a new axiomatization of the Shapley value by using two axioms. First axiom is Dummy Player Property and second axiom is Strong Addition Invariance. Strong Addition Invariance states that the payoff vector of a game does not change even if we add some specific games to the game. By slightly changing the definition of Strong Addition Invariance, we can also axiomatize the weighte...