Volume 55, Number 2, March-April 2021
|Page(s)||395 - 413|
|Published online||23 March 2021|
A new tensor approach of computing pure and mixed Unilateral Support Equilibria
Faculty of Economics and Business Administration, Lebanese University, Beirut, Lebanon
* Corresponding author: email@example.com
Accepted: 2 January 2021
In this paper, pure unilateral support equilibrium (USE) is located among pure Nash and pure Berge equilibrium using tensors. The differences between these equilibria are shown using tensor form of a game and are illustrated with numerical examples. Tensors will help specify the location of each equilibrium using a system of coordinates that brings a solid mathematical foundation of all equilibria and provides the possibility to solve high dimensional problems. A numerical example with a 15-player game is studied to demonstrate the efficiency. Besides, we extend the notion of pure USE to mixed USE when the sets of strategies of all players are finite. We prove a lemma dedicated to inaugurate a method of computing mixed USE profiles. We write corresponding formulas using tensors and their operations, and then we illustrate the new method and lemma method by a numerical example of a 7-player game.
Mathematics Subject Classification: 91A99
Key words: Game theory / Pure unilateral support equilibrium / mixed unilateral support equilibrium / Berge equilibrium / Nash equilibrium / tensors
© EDP Sciences, ROADEF, SMAI 2021
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