O 100.10 O 60.20 O 75.15 O 80.30 Question 26 Figure 1: Sequential Games) Use backwards induction to find the outcome of this game if Saudi Arabia goes first. Strategies for each player are choose a high or low level of oil output. Saudi Arabia high Nigeria Nigeria high low 100 75 60 Saudi Arabia Nigeria 80 10 15 20 30

O 100.10 O 60.20 O 75.15 O 80.30 Question 26 Figure 1: Sequential Games) Use backwards induction to find the outcome of this game if Saudi Arabia goes first. Strategies for each player are choose a high or low level of oil output. Saudi Arabia high Nigeria Nigeria high low 100 75 60 Saudi Arabia Nigeria 80 10 15 20 30

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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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?
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Consider the following sequential-move game: Player 1 Player 2 Player 3 Player 2 Player 3 R N LAF 3 E L 3 4 L R Player 1 Player 3 R EXE 5 L R L Pleaver g L Find the backward-induction equilibrium of this game. going 5 42" 5 44 Player 2 چلے Player 3 R O 5
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…
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Costco Spend $1B on advertising Spend $1.5B on advertising Spend $1B on advertising $3.5B; $2.7B $4.2; $2.2B Target Spend $1.5B on advertising $3.2B; $3.4B $4B; $3B
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Consider the following scenario to understand the relationship between marginal and average values. Suppose Crystal is a professional basketball player, and her game log for free throws can be summarized in the following table. Fill in the columns with Crystal's free-throw percentage for each game and her overall free-throw average after each game. Game Result Total Game Free-Throw Percentage Average Free-Throw Percentage Game 1 8/10 2 14/20 15/25 18/30 26/40 3 78°F Sunny 4 5 100 On the following graph, use the orange points (square symbol) to plot Crystal's free-throw percentage for each game individually, and use the green points (triangle symbol) to plot her overall average free-throw percentage after each game. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. (?) O 8/10 6/10 1/5 3/5 8/10 90 F2 -0- @ F3 -0+ # 80 F4 $ F5 H OL % F6 ba 80 A I C F8 & 357 * F10 FO F11 Ea F12 2 Fn Lock Prt Sc +-- F 10:23 A…
3. Consider the following two-player game: H L D T 2,3 0,2 4,0 1,1 (a) What are (pure- and mixed-strategy) Nash equilibria of this game? (b) Suppose the game is repeated twice, and each player's payoff is the sum of the payoffs they obtain in the two periods. What are the subgame perfect equilibria of the game? (c) Suppose the game is repeated indefinitely, and each player discounts his/her payoff with a discount factor 8 € (0, 1). Find a subgame perfect equilibrium in which (H, T) is played in every period on the equilibrium path. Compute the discount factor & needed for this equilibrium. (d) Suppose the game is repeated indefinitely, and each player discounts his/her payoff with a discount factor & € (0, 1). Find a subgame perfect equilibrium in which (H,T) and (L,T) are played alternately on the equilibrium path. Compute the discount factor & needed for this equilibrium. (e) Suppose the game is repeated indefinitely. Player 1 (the row player) discounts her payoff with a discount…
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