Answer to Question #287854 in Microeconomics for Bunnybear

Question

Gametheory

9.1What is the difference between a cooperative and a noncooperative game?

Give an example of each. (4)

9.2What is a dominant strategy? Why is an equilibrium stable in dominant

strategies? (4)

9.3Explain the meaning of a Nash equilibrium. How does it differ from an

equilibrium in dominant strategies? (4)

9.4Explain your understanding of the prisoners’ dilemma game and give an

example of a pay-off matrix in this game. (9)

Answer 1

9.1.A cooperative game is a game in which both players can communicate and cooperate, and a non-сoperative game is a game in which no cooperation is possible.

A cooperative game is a buyer and a seller, and a non-cooperative game is a monopoly.

9.2A dominant strategy is a strategy that is optimal regardless of the other player's strategy. The dominant strategy leads to the maximum win unconditionally, that is, it always leads to the best result regardless of what the opponent does. The existence of dominant strategies for all players leads to an equilibrium, which is called equilibrium in dominant strategies.

9.3The Nash equilibrium is named after John Forbes Nash — this is the name in game theory for a type of solutions to a game of two or more players in which no participant can increase the winnings by changing his decision unilaterally when other participants do not change their decisions. Such a set of strategies chosen by the participants and their winnings are called the Nash equilibrium. Unlike the equilibrium of dominant strategies and the Nash equilibrium, this type of equilibrium always exists.

9.4The prisoners' dilemma is a classic example of a game involving two suspects, say P and Q, arrested by the police and who have to decide whether to confess to them or not.

If one confesses and the other does not, then the prisoner who confesses gets a lighter prison sentence, say 1 year, and the prisoner who does not confess gets a very harsh sentence, say 8 years.

If neither of them confesses, they both get lighter sentences, say 2 years each; but if both confess, then both get a strict sentence, say 4 years each.