If both prisoners betray each other, each serves five years in prison.

If A betrays B but B remains silent, prisoner A is set free and prisoner B serves 10 years in prison, or vice versa.

If you revealed Sam's strategy to Tom and vice versa, you see that no player deviates from the original choice.

Knowing the other player's move means little and doesn't change either player's behavior. The prisoner's dilemma is a common situation analyzed in game theory that can employ the Nash equilibrium.

Nash equilibrium is named after its inventor, John Nash, an American mathematician.

It is considered one of the most important concepts of game theory, which attempts to determine mathematically and logically the actions that participants of a game should take to secure the best outcomes for themselves.

More specifically, the Nash equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his chosen strategy after considering an opponent's choice.Finally, we analyze a game in which a firm has to decide whether to invest in a machine that will reduce its costs of production.We learn that the strategic effects of this decision–its effect on the choices of other competing firms–can be large, and if we ignore them we will make mistakes.There are three Nash equilibria in the dating subgame.We construct three corresponding subgame perfect equilibria of the whole game by rolling back each of the equilibrium payoffs from the subgame.

More specifically, the Nash equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his chosen strategy after considering an opponent's choice.Finally, we analyze a game in which a firm has to decide whether to invest in a machine that will reduce its costs of production.We learn that the strategic effects of this decision–its effect on the choices of other competing firms–can be large, and if we ignore them we will make mistakes.There are three Nash equilibria in the dating subgame.We construct three corresponding subgame perfect equilibria of the whole game by rolling back each of the equilibrium payoffs from the subgame.The first game involves players’ trusting that others will not make mistakes.