9. Which of the following statements is true? a. A subgame perfect equilibrium need not be a Nash equilibrium. b. Subgame perfection requires players to always play optimally only on the equilibrium path of play in any game of perfect or imperfect information. c. A subgame of a game cannot include the game itself. d. Subgame perfection requires players to use strategies that constitute a best response or a mutual best response in every subgame of the larger game.

9. Which of the following statements is true? a. A subgame perfect equilibrium need not be a Nash equilibrium. b. Subgame perfection requires players to always play optimally only on the equilibrium path of play in any game of perfect or imperfect information. c. A subgame of a game cannot include the game itself. d. Subgame perfection requires players to use strategies that constitute a best response or a mutual best response in every subgame of the larger game.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Table 8. This table shows a game played between two players, A and B. The payoffs are given in the table as (Payoff to A, Payoff to B). A Select one: Up Middle Down Left (4,2) a. Middle-Center O b. Down-Center (3, 1) (1,3) B Center (2,5) (5, 3) (4,4) Refer to Table 8. This table shows a game played between two players, A and B. The payoffs in the table are shown as (Payoff to A, Payoff to B). Which of the following outcomes represents a Nash equilibrium in the game? Right (3, 3) (5,2) (6, 1) O c. Up-Left O d. More than one of the above is a Nash equilibrium in this game.
7. Which of the following is not true of the “Battle of the Sexes" Game? a. The predicted outcome demonstrates how independent and rational play by players can quickly reach an agreement or a convergence of expectations concerning which strategy will be played by each player in equilibrium. b. The Battle of the Sexes Game can be used to depict a variety of situations where the players' interests do not precisely coincide, except for the fact that they both want to avoid the outcomes that would result from choosing different actions from one another. c. Players do not have a dominant strategy but playing “Boxing" say, is a best response to the other playing "Boxing" even if it doesn't give the player the payoff associated with his or her preferred alternative. d. Played only once, the outcome where each goes to their preferred venue cannot be Nash Equilibrium.
5. Instead of choosing Game A or Game B in the first stage, player 1 chooses either game B or directly which action to play in game A. Game U D L (10,5) (5,10) R (0,0) (0,0) :Game B: L R U (6,6) (0,0) D (0,0) (0,0) (a) Write the game in extensive form. (b) Solve for all SPNEs of the modified game. (c) Do all the SPNEs give intuitively reasonable predictions? Why or why not? (Hint: think about what the modification of the payoff to game A entail for player 2 in that game and how the predictions contrast with the case where the game is chosen first, then the action.)
Question > Consider the following matrix game where Player 1 moves first then Player 2 observes player 1's move and responds. Draw the game tree for the sequential move game and then determine all the Nash equilibria. Player 1 Strategy A Strategy B Strategy C Strategy D -3, -2 10, 12 9, 20 Player 2 Please show each step on how to get the answer. Thank you! Strategy E 13,7 17, 17 12, 21 Strategy F 20,8 22, 16 19, 19
In your own words, and without using mathematical notation, provide an intuitive explanation of each of the following terms. a. A rationalizable strategy. b. A strategy in an extensive form game of perfect information. c. A Nash equilibrium in pure strategies. 20 S
5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…
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4. Sonia the Terrible lands her ship and crew of scurvy-pirate raiders onto a foreign beach. Up on the headland is a village, led by Jen the Brave. At this point, Sonia has a choice: she can SLASH her water barrels, eliminating her water supplies; or she can NOT SLASH, which keeps her water supplies completely intact. Having seen the action taken by Sonia, Jen can choose to CHARGE or to WAIT. The payoffs are as follows: if Sonia the Terrible chooses to SLASH and Jen CHARGES, the payoffs are (100, 20) to Sonia and Jen, respectively. If Sonia SLASHES and Jen WAITS, the payoffs are (10, 30). On the other hand, if Sonia chooses to NOT SLASH and Jen CHARGES, the payoff is (20, 15). If Sonia opts to NOT SLASH and Jen chooses to WAIT, the payoffs are (40, 10), respectively. What is the subgame perfect (or credible) equilibrium outcome? a. Sonia the Terrible chooses to SLASH; Jen the Brave chooses to CHARGE b. Sonia the Terrible chooses to NOT SLASH; Jen the Brave chooses to WAIT c. Sonia the…
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7. Solving for dominant strategies and the Nash equilibrium Suppose Gabriel and Nia are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Gabriel chooses Up and Nia chooses Down, Gabriel will receive a payoff of 6 and Nia will receive a payoff of 4. Gabriel Up Down Up 6,3 3,3 Nia Down 6, 4 7,4 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Gabriel chooses and Nia chooses