1. Consider the following game, which has been loosely based on the trust modelsstudied in class. For the purposes of this game, focus on pure-strategies only.Each agent moves simultaneously. Agent 1 can take either action T, M or B, whereasAgent 2 can take actions L, C, or R.The payoffs are shown in the following normal form game.1TMBL5,57,10,02C1,74,40,0R0,00,01,1a. Outline and explain the Nash equilibria if the game is played once. (Again, focusonly on pure-strategy equilibria.)b. Now consider the case when the game is played twice. That is, in the first period atthe firm, Agents 1 and 2 simultaneously choose their actions. Their choices arerevealed before in the second period, again the agents simultaneously choose theiractions. Then the game ends. There is no discounting of payoffs between periods. Outline how, as part of a subgame equilibrium that the threat to play either B or R inthe final period rather than M or C can help sustain the cooperative outcome of (T,L)in the first period. Interpret this two-period game as a trust game. Explain why 'trust'(or cooperation) can be achieved in the first period of this game without having toresort to an infinite-horizon game.

Given pay-off matrix Player 2 L C R Player 1 T 5,5 1,7 0,0 M 7,1 4,4 0,0 B 0,0…

1. Consider the following game, which has been loosely based on the trust models studied in class. For the purposes of this game, focus on pure-strategies only. Each agent moves simultaneously. Agent 1 can take either action T, M or B, whereas Agent 2 can take actions L, C, or R. The payoffs are shown in the following normal form game. 2

1. Consider the following game, which has been loosely based on the trust models studied in class. For the purposes of this game, focus on pure-strategies only. Each agent moves simultaneously. Agent 1 can take either action T, M or B, whereas Agent 2 can take actions L, C, or R. The payoffs are shown in the following normal form game. 2

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. The following is an interpretation of the rivalry between the United States (USA) and the Soviet Ünion (USSR) during the cold war. Each side has the choice of two strategies: Aggressive and Restrained. The payoff table is given as follows: USSR Restrained Aggressiveness Restrained 4,3 1,4 USA Aggressiveness 3,1 2,2 a) Consider this game when the two countries move simultaneously. Find all pure strategy Nash equilibria. b) Next consider three alternative ways in which the game could be played with sequential moves: (i) The USA moves first and the USSR moves second. (i) the USSR moves first and the USA moves second. (i) The USSR moves first, and the USA moves second, but the USSR has a further move after the USA moves. For each case, draw the game tree and find the subgame-perfect Nash equilibrium. c) What are the key strategic issues (commitment, credibility and so on) for the two countries. (Note: Be concise. Your answer should not exceed 300 words].
33. When neither player has a dominant strategy, A) game theory will not provide information.B) no Nash-Equilibrium exists.C) at least one Nash-Equilibrium exists.D) the game cannot be analyzed.
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1. Consider the following N-player game. Each agent has a choice of strategy A or B. The state variable is x, the proportion of agents choosing strategy A. For every agent, the utility of choosing strategy A is U(A) = 10 +2x and the utility of choosing strategy B is U(B) = 10+3x. What is the Nash equilibrium to this game? Explain.
Can you explain the "altruism and reciprocity" game theory, and provide an example? Is this the same as the "trust game?"
The count is three balls and two strikes, and the bases are empty. The batter wants to maximize the probability of getting a hit or a walk, while the pitcher wants to minimize this probability. The pitcher has to decide whether to throw a fast ball or a curve ball, while the batter has to decide whether to prepare for a fast ball or a curve ball. The strategic form of this game is shown here. Find all Nash equilibria in mixed strategies.
Consider a simultaneous game where player A has a dominant strategy and player B has two strategies (none of which is a dominant strategy). How many pure strategy Nash equilibria will this game have? A) Exactly 1 B) Exactly 2 C) Either 1 or 2 D) None
1.a) If the three executives of a fraudulent organization report nothing to the authorities, each gets a payoff of 100. If at least one of them blows the whistle, then those who reported the fraud get 28, while those who didn’t get -100. Suppose they play a symmetric mixed-strategy Nash equilibrium where each is silent (does not report fraud) with probability p. What is p?A, 0.1B, 0.28C, 0.5D, 0.8 b) In a two-player game, with strategies and (some known and some unknown) payoffs as shown below, suppose a mixed-strategy equilibrium exists where 1 plays C with probability 3/4, and Player 2 randomizes over X, Y, and Z with equal probabilities. What are the pure-strategy equilibria of this game? A, (A, Y) and (B, X)B, (A, Z) and (C, Y)C, (B, X) and (C, X)D, (C, X) and (C, Y)
In a small town there are two pizza restaurants . If neither restaurant advertises, its revenue will not change. If only one firm advertises, the firm that advertises will double its revenue and the firm that doesn't advertise will see a decrease in its revenue, but if both firms advertise, their revenue will not change. What outcome would be predicted by game theory in this market? Both restaurants will advertise. Game theory would predict chat sometimes one restaurant would advertise, and the rest of the time both will advertise. Neither restaurant will advertise Game theory is only a theory and cannot predict real-world events. One restaurant will advertise.
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