This article contains excerpts of chapter 5 in my upcoming book "The Illusion of Peace in Social Hierarchy."
Nash Equilibrium is a concept of game theory where the optimum outcome of a game is one where no player has an incentive to deviate from his/her chosen strategy after considering an opponent choice. Overall an individual can receive no incremental benefit from changing actions assuming other players remains constant in their strategies. A game may have multiple Nash equilibria or non at all.
If you want to test for a Nash Equilibrium simply reveal each person's strategy to all players, the Nash Equilibrium will exist if no player has changed their strategy despite knowing the actions of their opponents. For example let examine a game between Tom and Sam, in this simple game both players can choose:
(a) Receive a Dollar or
(B) Lose one Dollar
Logically both players choose strategy (a) and receive a pay of one dollar. If you reveal Sam's strategy to Tom and vice versa you will see that no player deviates from their original choice. Knowing the other player moves means little and does not change behaviour.
I will further explain Nash Equilibrium using the prisoner Dilemma scenario. Let us say Mr. Blue and Mr. Red have each been arrested for some minor crime. The police think they committed a more serious crime but they do not have enough evidence to convict them, they need a confession. They take them and put them in separate rooms so they can't talk, and the police play's a little game.
To try to force a confession the police give them two choice:
- Admit your partner committed the crime and you will go free, we will pardon you for the minor crime but your partner will have to spend 3 years in prison.
- If you stay silent and your partner let us know that you were the one who really did it then you are gonna have to go away with 3 years.
They know that the police do not really have any evidence and if they both stay silent, then they will both only go to prison 1 year each for their minor crime, if they both betray each other, then they will go to jail for 2 years each.
In this scenario, cooperation between the two (staying silent) will give a better outcome but since the suspects see that they will gain by betraying the other, they are likely going to betray each other.
According to the Nash Equilibrium, despite that each player is perceived to know the opponent strategies, they are unwilling to change their initial strategy since there is nothing to gain by changing their strategy, Hence, both players stick to their initial strategies rather than switching to a new strategy.
If Mr. Blue doesn't snitch he is prolly going to spend 3 years in prison because Mr. Red would likely snitch on him (everyone's selfish) and goes scot free. If perhaps Mr. Red does not snitch and he (Mr. Blue) snitches, he will be free and Mr. Red spends 3 years in prison, so Mr. Blue decides to snitch. Mr Blue sees nothing to gain by changing his strategy so he sticks to this initial strategy, likewise Mr. Red.
Tags:
Psychology