What is the difference between mixed strategy and pure strategy?

What is the difference between mixed strategy and pure strategy?

A pure strategy involves all players making their moves simultaneously, while a mixed strategy minimizes the losses of players.

What are the pure strategy Nash equilibria?

A pure-strategy Nash equilibrium is an action profile with the property that no single player i can obtain a higher payoff by choosing an action different from ai, given every other player j adheres to aj. For example, a game involves two players, each of whom could choose two available actions, which are X and Y.

What is the difference between dominant strategy equilibrium and Nash equilibrium?

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.

How do you find the pure and mixed strategy Nash equilibrium?

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.

What is pure strategy in operations research?

Pure Strategy: If a player knows exactly what the other player is going to do, a deterministic situation is obtained and objective function is to maximize the gain. Therefore, the pure strategy is a decision rule always to select a particular course of action.

Does a mixed strategy Nash equilibrium always exist?

A mixed strategy is a distribution over pure strategies, leading to the notion of mixed strategy profiles and to expected utility. player i. There does not always exist a pure Nash equilibrium. Theorem 1 (Nash, 1951) There exists a mixed Nash equilibrium.