Financial Engineering
E-ISSN: 2945-1140
Volume 3, 2025
Novel Dominance Principle Based Approach to the Solution of Two-person General Sum Games with n by m Moves
Author:
Abstract: In a previous paper, the application of the dominance principle was proposed to find the noncooperative
solution of the two-person, two-strategy general sum game with mixed strategies; in the
literature, two different approaches are found: a prudential and a Nash approach leading to two
different mixed strategies. Also, if the expected payoffs are equal in the two cases, the two strategies
are not interchangeable. By the application of the dominance principle to the four combinations of the
two classical solutions, it was possible to choose the equilibrium point avoiding the ambiguity due to
their non-interchangeability. Starting from that result, it is here below proposed the extension of the
method to two-person general sum games with n by m moves. The algebraic two multi-linear 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 find the dominating probability distribution on the
moves. A conjecture about the uniqueness of the solution is proposed in order to solve the problem of
the existence and uniqueness of the non-cooperative solution of a two-person n by m game. The unique
non-cooperative 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.
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Pages: 172-186
DOI: 10.37394/232032.2025.3.14