ECN 200C Midterm: ECN 200C Midterm Version 1 Spring 2016

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turquoisegnu128

9 Jan 2019

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Answer all questions (total 100 points) i . {1, 2: [20 points] consider the strategic-form game with cardinal payoffs below, call it g, where, for. 2 (a) [10 points] prove that player 1 does not have a weakly dominant strategy. (b) [10 points] suppose we increase payoff entry. 1a in such a way that the sign of a. Explain why g must also have one and only one completely mixed nash equilibrium. c does not. Find all the pure-strategy weak sequential equilibria of the following game with cardinal payoffs. a. We saw in class that if the firms are not too close then there exists a nash equilibrium in prices, while if the firms are too close then there is no nash equilibrium. Initially there are three firms in this industry. We will consider a number of different alternatives. (a) (a. 1) [9 points] suppose that all the firms have the same cost function given by c(q) = 3q.

Related Questions

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

The correct statements are [mark all that apply]:

A. The concept of best response strategy played in equilibrium by all players and no unilateral deviation are applicable for Bayesian games.

B. A game, where there are one firm 1 and two types of firms 2 (strong or weak) but firm 1 knows that firm 2 is strong with probability 0.7, can be described as a game of incomplete information.

C. A Bayesian Nash equilibrium is totally different from a Nash equilibrium in Bayesian games.

D. To be uncertain about others players' payoff functions is equivalent to saying that player 1 may be uncertain about the types of the other players.

QUESTION 1

Stackelberg duopoly game is also known as the ________ model. If we change the Stackelberg ______ competition game to a simultaneous-move game, we get the ______ game results.

	A.	leader-follower, quantity; Cournot
	B.	Competitive fringe; price; backward induction
	C.	leader-follower, quantity; Bertrand
	D.	entry, price; Cournot

QUESTION 2

Comparing Stackelberg and Cournot competition results, we can say that the _____ is better off while the ______ is worse off under Stackelberg than under Cournot results. This result show that there is _______________ advantage.

	A.	entrant, incumbent, investment
	B.	leader, follower, first-mover
	C.	follower, leader, a size
	D.	incumbent, entrant, first-mover

QUESTION 3

Mark all the FALSE statements

	A.	An equilibrium is a collection of strategies (and a strategy is a complete plan of action), whereas an outcome describes what will happen only in the contingencies that are expected to arise, not in every contingency that might arise.
	B.	In games of complete but imperfect information, backward induction is still the strongest process to solve the model to get unique equilibrium.
	C.	All subgame perfect Nash equilibria (SPNE) are Nash equilibria (NE), but not all Nash equilibria is SPNE
	D.	We cannot apply the notion of Nash equilibrium to dynamic games of complete information if we allowed a player s strategy to leave unspecified actions in some contingencies.
	E.	A game can be of perfect information whenever Nature or Luck does not play, each information set does not necessarily need to have a single node.

QUESTION 4

True or false. Mark the correct sequence:
I. Simultaneity of moves means that these games have imperfect information.
II. Dynamic games of complete and perfect information do not necessarily need that a player observes all the previous moves, just part of them are fine.
III. Backward induction and subgame perfect equilibrium concept lead to the same result in games of incomplete information.
IV. Any game in extensive form is a subgame itself.

	A.	TFFT
	B.	TTTF
	C.	FTFF
	D.	TTFT

QUESTION 5

The subgame perfect Nash equilibrium is the equilibrium associated with ____________ outcome. Subgame perfect equilibrium ________ non-credible threats.

	A.	Maxmin; involves
	B.	the backward induction; does not involve
	C.	Iterative deletion of weakly dominated strategies; rules out
	D.	the backward induction; includes

ECN 200C Midterm: ECN 200C Midterm Version 1 Spring 2016

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