Determine which strategies are dominated in the following normal-form games.221LCR1LRU5,90.14,3A3,32,0Σ3,20,91,1B4,18,-1D2.80,18,4(b)(a)21WXYN2LRU3,64,105,00,8U1,10,0M2,63,3 4,101,1Ꭰ0,05,5D1,52,93,04,6(c)(d)

The question asks to determine which strategies are dominated in each of the given normal-form…

Answered: Determine which strategies are…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Two players play the following game for infinite times. For the player to continue to cooperate what would be the ranges of their discount factor, δ_1 and δ_2, respectively? cooperate betray cooperate (10,20) (-25,30) betray (15, -22) (-12, -18)
P1 P1 P2 P2 F F Y 3, 4 0,3 0,3 2,5 3,6 5, 2 Which of the following is a subgame perfect equilibrium of this game? (RDJ,FQY) (RMU,ZTH) (LDU,ZQY) (RDU,ZTY) O (LMJ,ZTY) (RMU,FTH)
In Homework 1, we saw that there is no strict dominant strategy equilibrium in an inspection game. Thus, the players must randomize and play a mixed strategy in equilibrium. Suppose the agent shirks with probability p₁ and works with probability (1 - p₁), while the principal inspects with probability p2 and does not inspect with probability (1-P2). Find the mixed strategy equilibrium for this game. I NI S (0, -k) (w, -w) W (w c, p-w-k)| (wc, p-w) Table 1: Payoff matrix for the inspection game
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Suppose 2 players play the following game infinite times in the future. What should be the minimum value of the time discount so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (10, 10) Defect (2, 12) (4,4) (12, 2)
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R (3,2) (0,0) (2,4) (5,4) (0,0) In the extensive form representation of the game between Player 1 and Player 2, Player 1 moves first and chooses L or R. If Player 1 chooses R the game ends, if Player 1 chooses L then Player 1 and 2 play a simultaneous move game. The game has strategy Subgame Perfect Nash Equilibria (SPNE). The maximum payoff Player 2 gets in a SPNE is pure strategy Nash equilibria and pure (Please, enter only numerical answers like: 1, 2, 3, ...)
(ii) A mixed strategy profile (p, q) is one in which p = (p,P2.... P) is the mixed strategy of player 1, and q- (g1, q2,..q4) is the mixed strategy of player 2. Show that if p, >0 in a Nash equilibrium profile (p*, q*), the player 2 must also play i with strictly positive probability q'; > 0. (State clearly any theorem you use to show this. You are not required to justify the theorem.) %3D
Individual A Cooperate Defect Individual B Cooperate 28, 28 34,8 Defect 8, 34 12, 12 Suppose individuals live in villages that are homogeneous by type and a fractions of their interactions takes place in their village, the rest occurring in the city where the types were mixed. The fraction of the population who are cooperators is a. a) Write the expected return functions for cooperate and defect as a function of s and a. b) Under which conditions does an interior equilibrium exist for the fraction of the population playing cooperate (a) c) If the interior equilibrium for a exists, is the interior equilibrium unstable or stable? d) Find the impact of higher s on the interior equilibrium for a. What intuitively does this outcome mean? Discuss your answer.
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Determine which strategies are dominated in the following normal-form games. 2 2 1 L C R 1 L R U 5,9 0.1 4,3 A 3,3 2,0 Σ 3,2 0,9 1,1 B 4,1 8,-1 D 2.8 0,1 8,4 (b) (a) 2 1 W X Y N 2 L R U 3,6 4,10 5,0 0,8 U 1,1 0,0 M 2,6 3,3 4,10 1,1 Ꭰ 0,0 5,5 D 1,5 2,9 3,0 4,6 (c) (d)