On the Solutions of Games in Normal Forms: Particular Models based on Nash Equilibrium Theory

Abstract

The main objective of this paper is to present in a deductive way, solutions for general games played under normal conditions following competitive paths, applying core principles of Nash equilibrium. Here the normal approach implies strategic choices available for each player, formulated and implemented without any information concerning specific choices to be made by others players. It is convenient to keep in mind that John von Neumann and Oskar Morgenstern outlined a set of conditions for Nash equilibrium for a game in normal form, proposed as the basic framework to analyze the conditions and requirements for a particular Nash equilibrium to be the solution of the game. Theorems that exhibit imbedding relations among the Nash equilibriums of the game are given to examine the role of pre-play communication and the imbedding order in equilibrium selection. A core argument to claim here is that a generic case of Nash equilibriums that are strategically unstable relative to maxi-min strategies is given to emphasize the role of moves of the third kind and pre-play communication in correlated and coordinated solutions and the need to account for cases where Nash equilibriums are not plausible or even desirable as solutions for a game in normal form.