Zola, Maurizio Angelo (2024): A Novel Dominance Principle based Approach to the Solution of Two Persons General Sum Games with n by m moves.
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Abstract
In a previous paper [1] the application of the dominance principle was proposed to fi nd the noncooperative solution of the two by two general sum game with mixed strategies; in this way it was possible to choose the equilibrium point among the classical solutions avoiding the ambiguity due to their noninterchangeability, moreover the noncooperative equilibrium point was determined by a new geometric approach based on the dominance principle. Starting from that result it is here below proposed the extension of the method to two persons general sum games with n by m moves. The algebraic two multilinear forms of the expected payoffs of the two players are studied. From these expressions of the expected payoffs the derivatives are obtained and they are used to express the probabilities distribution on the moves after the two defi nitions as Nash and prudential strategies [1]. The application of the dominance principle allows to choose the equilibrium point between the two solutions avoiding the ambiguity due to their noninterchangeability and a conjecture about the uniqueness of the solution is proposed in order to solve the problem of the existence and uniqueness of the noncooperative solution of a two persons n by m game. The uniqueness of the noncooperative solution could be used as a starting point to find out the cooperative solution of the game too. Some games from the sound literature are discussed in order to show the effectiveness of the presented procedure.
Item Type:  MPRA Paper 

Original Title:  A Novel Dominance Principle based Approach to the Solution of Two Persons General Sum Games with n by m moves 
English Title:  A Novel Dominance Principle based Approach to the Solution of Two Persons General Sum Games with n by m moves 
Language:  English 
Keywords:  Dominance principle; General sum game; two persons n by m moves game 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  122312 
Depositing User:  Mr Maurizio Angelo Zola 
Date Deposited:  08 Oct 2024 13:33 
Last Modified:  11 Nov 2024 13:54 
References:  [1] Zola M.A. (2024) A Novel Integrated Algebraic/Geometric Approach to the Solution of Two by Two Games with Dominance Principle. Munich Personal RePEc Archive MPRApaper121935  10 Sep 2024. [2] Nash J.F. (1951) NonCooperative Games. Annals of Mathematics, Second Series 54(2), 286–295, Mathematics Department, Princeton University. [3] Nash J.F. (1950) The bargaining problem. Econometrica, 18(2), 155–162. [4] Nash J.F. (1950) Equilibrium points in nperson games. Proceedings of the National Academy of Sciences of the United States of America, 36(1), 48–49. [5] Nash J.F. (1953) Twoperson cooperative games. Econometrica, 21(1), 128–140. [6] Luce R.D., Raiffa H. (1957) Games and decisions: Introduction and critical survey. Dover books on Advanced Mathematics, Dover Publications. [7] Owen G. (1968) Game theory. New York: Academic Press (I ed.), New York: Academic Press (II ed. 1982), San Diego (III ed. 1995), United Kingdom: Emerald (IV ed. 2013). [8] Straffin P.D. (1993) Game Theory and Strategy. The Mathematical Association of America, New Mathematical Library. [9] Van Damme E. (1991) Stability and Perfection of Nash Equilibria. SpringerVerlag. Second, Revised and Enlarged Edition. [10] Dixit A.K., Skeath S. (2004) Games of Strategy. Norton & Company. Second Edition. [11] Tognetti M. (1970) Geometria. Pisa, Italy: Editrice Tecnico Scientifica. [12] Maschler M., Solan E., Zamir S. (2017) Game theory. UK: Cambridge University Press. [13] Esposito G., Dell’Aglio L. (2019) Le Lezioni sulla teoria delle superficie nell’opera di RicciCurbastro. Unione Matematica Italiana. [14] Bertini C., Gambarelli G., Stach I. (2019) Strategie – Introduzione alla Teoria dei Giochi e delle Decisioni. G. Giappichelli Editore. [15] Vygodskij M.J. (1975) Mathematical Handbook Higher Mathematics. MIR, Moscow. [16] Von Neumann J., Morgenstern O. (1944) Theory of Games and Economic Behavior. New Jersey Princeton University Press. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/122312 