Introduction to Game Theory and Nash Equilibrium

Game Theory

A way of describing various possible outcomes in any situation involving two or more interacting individuals.

Nash Equilibrium

The result of all players playing their best strategy given what their competitors are doing.

Dominant Strategy

The best strategy regardless of what other players do.

Dominated Strategy

A strategy in which another strategy yields the player a higher payoff regardless of what other players do.

Pareto Optimum

The result that benefits both players the most.

Perfect Information

Players observe all of their rivals' previous moves.

Common Knowledge

All players know the structure of the game, know that their rivals know it and their rivals know that they know it.

Prisoner's Dilemma Game

A game involving two players where each has two possible strategies: Confess (C) or Do Not Confess (DNC).

Strictly Dominant Strategies

Strategies that are better than any other strategy for a player, regardless of what the other player does.

Strictly Dominated Strategies

Strategies that are worse than another strategy for a player, regardless of what the other player does.

Payoffs

The utility/profit for each of the strategy combinations.

Years in Jail

The negative numbers expressed as payoffs in the Prisoner's Dilemma Game.

Eliminate Strictly Dominated Strategies

The process of removing strategies that are not beneficial for the player.

Best Response

The strategy that yields the highest payoff for a player given the strategy of the other player.

Nash Equilibrium vs. Pareto Outcome

Nash Equilibrium is the result when both players act strategically given what the other is going to do, while Pareto Optimum is the result that benefits both players the most.

Another Game

A game involving two players, Row and Column, with two strategies each: Row can go Up or Down, and Column can go Left or Right.

Star Method

A technique to identify the best payoffs for players when locked into a strategy.

Society Payoff

The total payoff for society, which can be maximized in a Nash Equilibrium.