The theory of Nash equilibrium by John Nash (1951) has been a central concept in game theories and further more for a wide range from economics even to the social and environmental sciences studies. Besides the game theory, David (2012) has recalled that, there are three unrealistic traits of standard economic model of human behavior – “unbounded rationality, unbounded willpower, and unbounded selfishness – all of which behavioral economics modifies.” However, consider the assumption of Nash equilibrium theory, there is a hypothesis about all players in the game they are rational and understand the rule of the game. Which means they do know about their opponents choices and what reaction they are going to choose with the goal of profit maximization (or their own objectively goal). In the following there will be a further discussion and line out the practicality of Nash equilibrium.
2. Model and Discussion
Nash equilibrium is the set of result with none of the players have incentive to change their strategies (either pure or mixed) with their profit maximization (or own objectively goal).(Martin,2009;Michael et al.,2013)By using the very famous non-zero-sum game example in game theory, prisoner’s dilemma, it is the easiest way for us to understand the basic means of Nash equilibrium. The police caught two thefts and now they are referencing. Once it gives out a payoff matrix of the thefts (Fig 1.) and result in how many months they are in jail, as the theft is telling the truth (Cooperate) or lying (Defect), first payoff will be player 1’s and the second following will represent as player 2’s. (James et al., 1993)
Fig 1. The Prisoner’s Dilemma
‘Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence ‘(James et al., 1993:p.572).
In brief words, the best payoff for them individually will be choosing to lie to the police as we seen. However, they don’t know which choices each other is going to choose, so they will try to maximize their own benefit. For player 1, no matter the choice of player 2 react, 7<12 and 0<4, which he will “cooperate” as his dominated strategy rather than “defect”. Which player 2 will give it’s a same result.
However, prisoner’s dilemma is the only game with strategy will last Nash equilibrium till a long term in reality.
Consider another more realistic example, the assurance game of Russia and US...