Prisoner’s Dilemma Definition Beyond any doubt, Prisoner’s Dilemma is the best-known situation in which self-interest and collective interest are at odds. Yet irrespective of the fellow prisoner’s choice, the choice to confess yielded a better outcome (or less worse outcome) than did the choice not to confess.

“Game theory is the study of how people behave in strategic situations. This means that firms in oligopoly markets are playing a ‘game’ against each other. • To understand how they might act, we need to understand how players play games.

In the prisoner’s dilemma, the dominant strategy for both players is to confess, which means that confess-confess is the dominant strategy equilibrium (underlined in red), even if this equilibrium is not a Pareto optimal equilibrium (underlined in green).

Nash’s theorem states that every game with a finite number of players and a finite number of pure strategies has at least one Nash equilibrium. As a result, a game with infinitely many strategies might have no equilibria. Even if we cannot draw a game’s matrix or game tree, we can still analyze it.

While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. However, many games do have pure strategy Nash equilibria (e.g. the Coordination game, the Prisoner’s dilemma, the Stag hunt). Further, games can have both pure strategy and mixed strategy equilibria.

A Nash Equilibrium is a set of strategies that players act out, with the property that no player benefits from changing their strategy. For example, in the game of trying to guess 2/3 of the average guesses, the unique Nash equilibrium is (counterintuitively) for all players to choose 0.

2 Answers. A pure strategy determines all your moves during the game (and should therefore specify your moves for all possible other players’ moves). A mixed strategy is a probability distribution over all possible pure strategies (some of which may get zero weight).

Example: There can be mixed strategy Nash equilibrium even if there are pure strategy Nash equilibria. At the mixed Nash equilibrium Both players should be indifferent between their two strategies: Player 1: E(U) = E(D) ⇒ 3q = 1 − q ⇒ 4q = 1 ⇒ q = 1/4, Player 2: E(L) = E(R) ⇒ p = 3 × (1 − p) ⇒ 4p = 3 ⇒ p = 3/4.

According to game theory, the dominant strategy is the optimal move for an individual regardless of how other players act. A Nash equilibrium describes the optimal state of the game where both players make optimal moves but now consider the moves of their opponent.

The optimal strategy for the column player is to set the probability of playing Column 1 equal to q = d − b a − b − c + d The column player’s probability of playing Column 2 is then determined as 1 − q. ν = ad − bc a − b − c + d .

A mixed strategy Nash equilibrium. involves at least one player playing a randomized strategy and no player being able to increase his or her expected payoff by playing an alternate strategy. Then Row’s payoffs must be equal for all strategies that Row plays with positive probability.

A firm can choose a mixed strategy because a pure and simple strategy is often predictable. A mixed strategy on the other hand has probability to each of the strategy employed and therefore will provide the firm with an infinite number of the strategies that can be used.