Game Theory – Nash Equilibrium

In my last post on Game Theory I started by introducing Game Theory and the Matching Pennies game. In this post I’m going to explore the Nash Equilibrium to try and further my knowledge about Game Theory. In a game of two or more players where there isn’t a definative winner and looser the two players might be able to find a middle ground. This ‘middle ground’ might be described as the Nash Equilibrium, it occurs when all the players in a game are getting the best payoff for the move they make (i.e. no player can benefit by deviating from his strategy).

An example of this can be found in a Game where a couple who fail to make a decision about what to do in the evening get split up and so they each have to decide which event to go to. It just so happens that each person in the couple has a favourite activity which they may have wanted to do in the eveing. The man favours going to watch sports and the woman favours going to the cinema. If the man chooses to go to watch sports then he is getting the most enjoyment out of the activity and likewise, if the woman goes to the cinema she will get her best payoff.  If they meet then the woman will enjoy the sports slightly and the man will enjoy the cinema slightly, however, if they fail to meet then they will both not enjoy the activity.

Following is the payoff table for this game.

Male
Sport
Male
Cinema
Female
Sport
+2
+1
0
0
Female
Cinema
0
0
+1
+2

Here you can see that there are two Nash Equilibrium for this Game if either player knows what the other person is going to do. If the Male knows the Female will go to the Cinema it is in his best interest to go to the Cinema as well. This simply shows what a Nash Equilibrium is and it requires that each participant knows what the other persons best payoff is and so what they are going to do.

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