4. Game theory terminology Select the term that best describes each definition listed in the following table. Dominant Strategy Tit-for- tat Strategy Prisoners' Dilemma Nash Payoff Matrix Definition Equilibrium Collusion Game A case in which individually rational behavior leads to a jointly inefficient outcome 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 The event that occurs when agents in a game form an agreement about which strategies to implement A strategy in which a player cooperates until the other player defects and then defects until the other player cooperates again

4. Game theory terminology Select the term that best describes each definition listed in the following table. Dominant Strategy Tit-for- tat Strategy Prisoners' Dilemma Nash Payoff Matrix Definition Equilibrium Collusion Game A case in which individually rational behavior leads to a jointly inefficient outcome 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 The event that occurs when agents in a game form an agreement about which strategies to implement A strategy in which a player cooperates until the other player defects and then defects until the other player cooperates again

Principles of Economics (MindTap Course List)

8th Edition

ISBN:9781305585126

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 5CQQ

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12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?
Consider the following coordination game: Player 2P1 Comedy Show Concert Comedy Show 11,5 0,0 Concert 0,0 2,2 a. Find the Nash equilibrium(s) for this game.b. Now assume Player 1 and Player 2 have distributional preferences. Specifically, both people greatly care about the utility of the other person. In fact, they place equal weight on their outcome and the other person’soutcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarianpreferences.c. Now consider the case where Player1 and Player2 do not like each other. Specifically, any positive outcome for the other person is viewed as anegative outcome for the individual, ρ = σ = -1. Find the Nashequilibrium(s) with these envious preferences.
3. Suppose that the various Balls of basketball or internet fame Lavar, Lamelo, Liangelo, Lonzo,and Spalding are considering playing in a 1-on-1 tournament. They get a payoff of 0 if theydecide not to participate. The following table illustrates their payoffs across the variousscenarios. 1 Player 2 Players 3 Players 4 Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 10 9 8 7 6 a. Find and describe all pure strategy Nash Equilibria.b. Suppose now Spalding, since it is in fact a literal basketball, gets a payoff of 0 in anycircumstance, being an inanimate object. The table is now as follows: 1 Player 2 Players 3 Players 4Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 0 0 0 0 0 Find and describe all pure strategy Nash Equilibria.
1) What are the Nash equilibria? Which one is unreasonable/non-credible threat? 2) What are the subgame perfect Nash equilibria? Does SPNE concept eliminate the unreasonable Nash equilibrium?
a Suppose you are given a choice between thefollowing options:A1: Win $30 for sureA2: 80% chance of winning $45 and 20% chance ofA2: winning nothing B1: 25% chance of winning $30B2: 20% chance of winning $45Most people prefer A1 to A2 and B2 to B1. Explainwhy this behavior violates the assumption that decisionmakers maximize expected utility.b Now suppose you play the following game: You havea 75% chance of winning nothing and a 25% chance ofplaying the second stage of the game. If you reach thesecond stage, you have a choice of two options (C1 andC2), but your choice must be made now, before youreach the second stage.C1: Win $30 for sureC2: 80% chance of winning $45 13.5 Bayes’ Rule and Decision Trees 767Most people choose C1 over C2 and B2 to B1 (from part(a)). Explain why this again violates the assumption ofexpected utility maximization. Tversky and Kahneman(1981) speculate that most people are attracted to thesure $30 in the second stage, even though the secondstage may never be…
Compare and contrast the Winning Strategy Theorem and the Equilibrium ExistenceTheorem Describe the hypotheses and the conclusions of each theorem. Whichresult (if either) has more demanding hypotheses? Which (if either) has more powerfulconclusions? Is one of these two theorems logically stronger than the other? Explain.What is the significance of each result, both for the application of game theory to realworld problems and for the historical development of the subject? Give one or moreoriginal examples to show how these theorems can be used in practice.
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Suppose that the University of Alabama and Clemson are making spending decisions for theupcoming year. Assume that Alabama is currently spending $15 million on their recruiting andfacilities, and Clemson is spending $10 million. Each team has an additional $5 million to spendor keep as profits. If they both choose to not spend the additional $5 million then Alabama hasa 60% chance of getting the highest quality quarterback recruit to commit to them (getting thecommitment of the player is the goal). However, if they both choose to spend the additional $5million then there is a 57% chance that Alabama gets the high quality quarterback to commit. IfAlabama spends the additional $5 million but Clemson doesn’t then there is a 67% chanceAlabama gets the recruit. However, if Alabama does NOT spend the additional $5million butClemson does then there is a 50% change either team gets the recruit’s commitment. Setup thepayoff matrix and label the players, their strategies, and their payoffs, and…
Refer to the Ultimatum Game in Figure 17.7. Recall that the payoffs are monetary payoffs. a. Suppose that players only care about monetary payoffs, with $1 = 1 util. Find the subgame– perfect equilibrium. b. Suppose that players are imperfectly altruistic. They receive 1 util for each dollar they earn but = util for each dollar the other player earns.Write down the extensive form reflecting the new payoffs. Find the subgame–perfect equilibrium. c. Suppose that players are perfectly altruistic, receiving 1 util for each dollar in the sum of their earnings. Write down the extensive form reflecting the new payoffs. Find the subgame– perfect equilibrium. d. Suppose that players are perfectly selfless, getting 1 util for each dollar the other player earns but no utility for their own earnings. Write down the extensive form reflecting the newpayoffs. Find the subgame–perfect equilibrium. Does player 1 end up choosing the outcome that player 2 prefers?…
8. Two states, A and B, have signed an arms-control agreement. This agreementcommits them to refrain from building certain types of weapons. The agreement is supposed tohold for an indefinite length of time. However, A and B remain potential enemies who wouldprefer to be able to cheat and build more weapons than the other. The payoff table for A (player1, the row player) and B (player 2, the column player) in each period after signing thisagreement is below. a) First assume that each state uses Tit-for-Tat (TFT) as a strategy in this repeated game.The rate of return is r. For what values of r would it be worth it for player A to cheat bybuilding additional weapons just once against TFT? b) For what values of r would it be worth deviating from the agreement forever to buildweapons? c) Convert both values you found in parts a and b to the equivalent discount factor dusing the formula given in lecture and section. d) Use the answers you find to discuss the relationship between d and r:…
2. Consider a game that game theory people refer to as the “ultimatum game.”We will refer to our two players as the “offerer” and the “decider”. How the gameworks is that the offerer proposes a way to split $1000 between the two players.While this could be done in a variety of ways, we will assume that the offerersonly has two possible proposals: Either a 50-50 split, or she offers the decider$50 and keeps the rest. The decider can either accept or reject the offer. If the offer is accepted, the money is split as proposed. If the offer is rejected, themoney spontaneously combusts and nobody gets anything. a) List the strategies for each player and write an extensive form version of thegame with payouts. b) List all the Nash equilibria of this game. c) Explain which, if any of the Nash equilibrium are not sub-game perfect. d) Write the game out in normal form and find the pure strategy Nashequilibrium. Explain how this matches with your answers to (b) and (c) . Alsoexplain why there…
Consider trade relations between the United States and Mexico. Assume that the leaders of the two countries believe the payoffs to alternative trade policies are shown in the image attached. a) What is the dominant strategy for the United States? For Mexico? Explain. b) Define Nash equilibrium. What is the Nash equilibrium for trade policy? c) In 1993, the U.S. Congress ratified the North American Free Trade Agreement, in which the United States and Mexico agreed to reduce trade barriers simultaneously. Do the perceived payoffs shown here justify this approach to trade policy? Explain.