The main objective of this paper is to present in a deductive way, solutions for general games playedunder normal conditions following competitive paths, applying core principles of Nash equilibrium. Herethe normal approach implies strategic choices available for each player, formulated and implementedwithout any information concerning specific choices to be made by others players. It is convenient tokeep in mind that John von Neumann and Oskar Morgenstern outlined a set of conditions for Nashequilibrium for a game in normal form, proposed as the basic framework to analyze the conditions andrequirements for a particular Nash equilibrium to be the solution of the game. Theorems that exhibitimbedding relations among the Nash equilibriums of the game are given to examine the role of pre-playcommunication and the imbedding order in equilibrium selection. A core argument to claim here is that ageneric case of Nash equilibriums that are strategically unstable relative to maxi-min strategies is givento emphasize the role of moves of the third kind and pre-play communication in correlated andcoordinated solutions and the need to account for cases where Nash equilibriums are not plausible oreven desirable as solutions for a game in normal form.
