On some conditions for the existence of strong Nash equilibrium for multiplayer game

Date of Publication

2016

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Game Design | Mathematics | Theory and Algorithms

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Ederlina Nocon

Abstract/Summary

The Nash equilibrium (NE) is known to be a very important solution concept in game theory. However, it is strictly used in a non-cooperative games where no cooperation among the players is allowed. On the other hand, strong Nash equilibrium (SNE) is an appealing solution concept in cooperative games where the players can form coalitions. An SNE must be a Nash equilibrium and at the same time considered to be a Pareto optimal of the game. In this paper, we discuss three conditions for the existence of the strong Nash equilibrium: two necessary conditions and one sufficient condition. Forcing an SNE to be resilient to pure multilateral deviations is one of the necessary conditions. By applying the Karush-Kuhn-Tucker conditions, we provide another necessary but not sufficient condition. Lastly, an NE to be a Pareto efficient with respect to coalition correlated strategies is a sufficient but not necessary condition. Then we introduce the spatial branch-and-bound algorithm for SNE finding which finds a candidate solution and then verifies the candidate whether it is a strong Nash equilibrium or not. An application of the algorithm is also presented to validate the algorithm and to show how it works in the specific game. All of the three discussions are based on the article Algorithms for Strong Nash Equilibrium with More than Two Agents by Gatti, Rocco, and Sandholm [5].

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTU019989

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

1 computer disc ; 4 3/4 in.

Keywords

Game theory; Algorithms

Embargo Period

5-11-2021

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