Consider the following Bayesian game. In this 2-player game, P2 observes Na-ture's move, but P1 does not.P2LRU1, 2 3, 4P1D2,3 5,51/32/3N1. Draw the extensive form of this game.2. Identify all the BNE(s).P2LRU8,6 0,4P1D5, 11.2

Part 1: Extensive Form of the GameIn the extensive form of this Bayesian game, we can visualize the…

Answered: Consider the following Bayesian game.…

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter16: Bargaining

Section: Chapter Questions

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8) Find the mixed strategy Nash equilibrium of the following normal form game. Player 2 T1 T2 T3 2, 3 3, 5 1, 1 Player 1 S2 1, 4 4, 3 0, 5 Player 1 attaches probability (S1, S2) = () and Player 2 attaches probability (T1, T2, T3) = ( ) Player 1 attaches probability (S1, S2) = (.) and Player 2 attaches probability (T1, T2, T3) = (qi, 42, 1 – q1 – 92) where q1 , and 0 < q2 S %3D Player 1 attaches probability (S1, S2) = (G,;) and Player 2 attaches probability (T1, T2, T1) = (qı.42, 1 – q1 – 42) where 0 < qi <, and q2 = 3. Player 1 attaches probability (S1, S) = (;, -) and player 2 attaches probability (T1, T2, T3) = (1.42, 1- q1- 42) where 0 s qı s and q2 =
B block allow 5,9 3, 11 high A 6,2 4,4 low In this normal form game, there is a Nash equilibrium where A chooses high; block high; allow low; block low; allow and B chooses
2. Army 1 of country 1 must decide whether to attack army 2 of country 2 which is occupying an island between the two countries (i.e. army 1 moves first). In the event of an attack, army 2 may fight or retreat over a bridge to its mainland. Each army prefers to occupy the island than not to occupy it; a fight is the worst outcome for both armies. (a) Model the situation as an extensive form game with perfect information. Find a Nash Equilibrium of this game which is not subgame perfect. (b) Find the only Subgame Perfect Nash Equilibrium and compare with the equilibrium in the previous question. (c) Assume now that army 2 has the possibility of burning the bridge to its mainland. If it does, army 2 would then not be able to retreat if army 1 attacked. i. Write down the extensive form of this game. Show that army 2 can increase its payoff in a Subgame Perfect Nash equilibrium in the new game. Interpret what this fact illustrates. ii. iii. Now assume that the attacking army cannot observe…
A small community has 10 people, each of whom has a wealth of $3,000. Each individual must choose whether to contribute $300 or $0 to the support of public entertainment for their community. The money value of the benefit that a person gets from this public entertainment is one half of the total amount of money contributed by all individuals in the community. This game has a Nash equilibrium in which 5 people contribute $300 and for public entertainment and 5 people contribute nothing. This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment. This game has no Nash equilibrium in pure strategies, but has a Nash equilibrium in mixed strategies. This game has a dominant strategy equilibrium in which all 10 citizens contribute $300 to support public entertainment. This game has two Nash equilibria, one in which everybody contributes $300 and one in which no- body contributes $300.
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Not Play 1 Play 11 2 1 Trust Distrust 1 Steal Share 0 2 10 0 55 5 5 Find all of the pure strategy Nash Equilibria of this game. There can be more than one equilibrium. [Here ((Not Play, Steal), (Trust)) indicates that player 1 chooses Not Play at the first decision node and Steal at the second decision node, and 2 chooses Trust at his unique decision node.] a) ((Play, Share), (Trust)) b) ((Not play, Share), (Distrust)) c) ((Not play, Steal), (Distrust)) d) ((Not play, Steal), (Trust)) ☐ e) ((Play, Steal), (Distrust))
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In this game, P1 observes Nature's move, but P2 does not. With probability p, q, and 1-p-q, such that both p, q = (0, 1) (i.e. neither p nor q can be exactly 0 or 1), two players, P1 and P2, play the following games: p Nature 1-p-q P2 P2 P2 L R L R L R U 3,2 1,0 U 3,0 4,1 U 5,0 3,1 P1 P1 P1 Ꭰ 1,0 3,2 D 2,0 1,1 D 6,0 4,1 1. Draw the extensive form of this game (no need to write down the payoffs). 2. Identify the set of rationalizable strategy profiles. 3. For which values of p does this game has two Bayesian Nash equilibrium in pure strategies?
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Consider the following Bayesian game. In this 2-player game, P2 observes Na- ture's move, but P1 does not. P2 L R U 1, 2 3, 4 P1 D 2,3 5,5 1/3 2/3 N 1. Draw the extensive form of this game. 2. Identify all the BNE(s). P2 L R U 8,6 0,4 P1 D 5, 1 1.2