ECON 1000 Chapter Notes - Chapter 15: Perfect Competition, Oskar Morgenstern, Nash Equilibrium

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Economists think about oligopoly as a game between two or a few players, and to study oligopoly markets they use game theory. Game theory is a set of tools for studying strategic behaviour behaviour that takes into account the expected behaviour of others and the recognition of mutual interdependence. John von neumann in 1937 and extended by von neumann and oskar morgenstern in. Today, it is one of the major research fields in economics. To find the nash equilibrium, we compare all the possible outcomes associated with each choice and eliminate those that are dominated that are not as good as some other choice. To u(cid:374)dersta(cid:374)d price fi(cid:454)i(cid:374)g, we"re goi(cid:374)g to stud(cid:455) the special case of duopol(cid:455) an oligopoly with two firms. Duopoly is easier to study than oligopoly with three or more firms, and it captures the essence of all oligopoly situations. Somehow, the two firms (cid:373)ust share the (cid:373)arket.

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4. Game theory terminology

Select the term that best describes each definition listed in the following table.

Definition	Nash Equilibrium	Dominant Strategy	Collusion	Tit-for-tat Strategy	Payoff Matrix	Prisoners' Dilemma
A player's best choice, if it exists, regardless of his or her opponent's strategy
A set of strategies (one for each player) in which each player's strategy is the best option for that player, given the chosen strategy of the player's opponents
A case in which individually rational behavior leads to a jointly inefficient outcome
A visual representation of a game showing all possible strategies for each player and all potential outcomes and payoffs

periwinklebuffalo937

Problem 1

In each of the three games shown below, let p be the probability that player 1 plays cooperates (and 1- p the probability that player 1 defects), and let q be the probability that Player 2 plays cooperates (and 1- q the probability that player 2 defects).

PrisonerÃ¢â¬â¢s Dilemma

	Player 2
Player 1		cooperate	defect
	cooperate	70,70	10,80
	defect	80,10	40,40

Stag Hunt

	Player 2
Player 1		cooperate	defect
	cooperate	70,70	5,40
	defect	40,5	40,40

Chicken

	Player 2
Player 1		cooperate	defect
	cooperate	70,70	50,80
	defect	80,50	40,40

1. For each game, draw a graph with player 1Ã¢â¬â¢s best response function (choice of p as a function of q), and player 2Ã¢â¬â¢s best response function (choice of q as a function of p), with p on the horizontal axis and q on the vertical axis.

2. Using this graphs, find all the Nash equilibriums for the game, both pure and mixed strategy Nash equilibriums (if any). Label these equilibriums on the corresponding graph.

3. In those games that have multiple pure strategy Nash equilibriums, how do the expected payoffs from playing the mixed strategy Nash equilibrium compare with the payoffs from playing the pure strategy Nash equilibriums? Which type of strategy (mixed or pure) would players prefer to play in these games?

Problem 2

Two people are involved in a dispute. Player 1 does not know whether player 2 is strong or weak; she assigns probability ÃÂ± to player 2 being strong. Player 2 is fully informed. Each player can either fight or yield. Each player obtains a payoff of 0 is she yields (regardless of the other personÃ¢â¬â¢s action) and a payoff of 1 if she fights and her opponent yields. If both players fight, then their payoffs are (-1; 1) if player 2 is strong and (1;-1) if player 2 is weak. The Bayesian game is the following, depending on the type of player 2:

	Y	F		Y	F
Y	0, 0	0, 1	Y	0, 0	0, 1
F	1, 0	-1, 1	F	1, 0	1, -1
Player 2 is strong (ÃÂ±)			Player 2 is weak (1-ÃÂ±)			Player 2 is strong (ÃÂ±)

After writing all the strategies and payoffs in the same matrix, find the Bayesian Nash equilibriums, depending on the value of ÃÂ± (ÃÂ± Ã¢â°Â¤ 1/2 or ÃÂ± Ã¢â°Â¥1/2).

jadebuffalo465

1. Which of the following statements about oligopolies is not correct?

a.		Oligopolistic firms always charge the monopoly price.
b.		Oligopolistic firms are interdependent in a way that firms in perfect competition are not.
c.		An oligopolistic market has only a few sellers.
d.		The actions of any one seller can have a large impact on the profits of all other sellers.

2. Which is true of an oligopoly market that reaches a Nash equilibrium?

a.		The firms will not have behaved as profit maximizers.
b.		A firm will have chosen its best strategy, given the strategies chosen by other firms in the market.
c.		A firm will not take into account the strategies of competing firms.
d.		The market price will be different for each firm.

3. In game theory, what is a dominant strategy?

a.		the best strategy for a player to follow, regardless of the what strategies other players use
b.		a strategy that makes every player better off
c.		a strategy that must appear in every game
d.		the best strategy for a player to follow only if other players are cooperative

4. Which of the following situations produces the largest profits for oligopolists?

a.		The firms reach a Nash equilibrium.
b.		The firms combine to produce the monopoly output level.
c.		The firms set prices equal to marginal cost.
d.		The firms produce a quantity of output that lies between the competitive outcome and the monopoly outcome.

ECON 1000 Chapter Notes - Chapter 15: Perfect Competition, Oskar Morgenstern, Nash Equilibrium

ECON 1000 Full Course Notes

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