Question

Distinguish among dominant, secure, Nash, mixed, and subgame perfect equilibrium strategies, and identify such strategies in various games.

Short answer

a) Dominance strategy: A strategy for one player.

b) Secure: It ensures the maximum potential return in the worst-case situation.

c) Nash equilibrium: A strategy profile where a particular strategy is the best answer for each player.

d) Mixed strategy: It refers to a strategy in which players make a random choice among two or more possible actions based on a set of probabilities.

e) Sub-game perfect equilibrium:A sub-game is a portion of a bigger way that begins with a deciding node and includes anything that branches off to the right.

Step-by-step solution

Strategy

Setting objectives and priorities, defining steps to achieve the aims and objectives, as well as mobilizing resources to carry out the activities are all part of the strategy. A strategy specifies how the methods will be used to attain the ends (goals) (resources). An overall direction is established for the firm and its many parts to reach the desired future scenario.

Explanation for dominance, Secure, Nash, Mixed,and subgame perfect equilibrium strategies

a) Dominant Strategy:It is a strategy for a player, i.e., the optimum reaction to the other player's entire strategy profile. If all of the participants in a game use the same dominating strategy, the game is said to have dominant strategy equilibrium.

b) Secure: It ensures the maximum potential return in the worst-case situation.

c) Nash Equilibrium:Nash equilibrium is a strategy profile that is the optimal response for each player's specified strategy. Nash equilibrium, on the other hand, is a set of strategies in which each actor does their best given the other player's strategy. The theory behind Nash equilibrium is as follows: "I'm trying my best to give what you're doing, and you're doing your best to give what I'm doing."

d) Mixed strategy:It is a strategy in which players choose at random between two or more alternative actions based on a set of possibilities. It is distinct from pure strategy, in which players make particular decisions or perform specified actions.

e) Sub-game perfect equilibrium:A sub-game is a branch of an extended form that begins with a decision node and includes everything to the right of it. A valid sub-game begins at a decision node in a dataset unrelated to another. In theory, it means that the player who acts first in a suitable sub-game is aware of the actions taken by others leading up to that moment