Probabilistic Tit-for-Tat Strategy versus Nash Equilibrium for Infinitely Repeated Games

In Game theory, Nash equilibrium is a fundamental concept where any player in a game cannot unilaterally change his/her behavior(s) and obtain a higher payoff. When players obtain equal payoffs in a game or repeated games, it is better not to use Nash equilibrium solution every time. In this paper, we have proved that Nash equilibrium does not give an optimal solution for repeated games; the payoffs can be transformed into a robust shape (Pareto optimality) through PTFT (probabilistic tit-for-tat) strategy with case studies illustrated. We have applied the `invented and derived' results to Braess's paradox that could fetch an optimal network path by removing a shortest path through the benefits of using PTFT strategy.