Please answer step by step 3)Find pure and mixed strategy Nash Equilibria of the following games1) Matching Pennies game:Player B - headsPlayer B - tailsPlayer A - heads1, -1-1, 1Player A - tails-1, 11, -12) Bank bailoutBank-RiskyBank - SafeGovernment- BailoutGovernment- Let fail6,20,33,64,5

1. Matching Pennies Gamea) Pure Strategy Nash EquilibriumDefinition: A pure strategy Nash…

Answered: 3) Find pure and mixed strategy Nash…

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

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4. Two investors have each deposited 5 (all amounts are in $10,000s) with a bank. The bank has invested these deposits in a long-term project. If both investors make withdrawals at date 1 then each receives 3 and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives 5, the other receives 1, and the game ends. Finally, if neither investor makes a withdrawal at date 1 then the project matures and the investors make withdrawal decisions at date 2. If both investors make withdrawals at date 2 then each receives 7 and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 9, the other receives 5, and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns 7 to each investor and the game ends. Show the bi-matrix for dates 1 and 2.
1.1. What is a game in normal form? What is a strictly dominated strategy in a normal-form game? What is a pure-strategy Nash equilibrium in a normal-form game? 1.2. In the following normal-form game, what strategies survive iterated elimination of strictly dominated strategies? What are the pure-strategy Nash equilibria? L C R T 2.0 1,1 4,2 M 3,4 1,2 2,3 B 1,3 0,2 3,0
4. Consider the following model of a bank run. Depositors may either Hold or Withdraw their funds from a bank. Both players hold deposits of 6, which earn interest of 1 if kept in the bank. If either depositor withdraws then the bank fails. If both try to withdraw then each depositor can only recover half of their deposits. The payoffs for a two-player version of this game are given below: Player 2 Player 1 Hold Withdraw Hold 7,7 6,0 Withdraw 0,6 3,3
You and I play the following game. Hidden from you, I put a coin in my hand: with probability p it is a 10 pence coin and otherwise it is a 20 pence coin. You now guess which coin is in my hand: you guess it is 20 pence with probability s and otherwise you guess it is a 10 pence coin. You get to win the coin if you guess correctly and otherwise win nothing. What (in terms of p and s) is your expected gain in pence from playing this game once with me? Challenge: suppose we are going to play repeatedly and you want to maximise your gain and I wish to minimise my loss. What value of p should I choose and what value of s should you choose? (This question is somewhat ill-defined, but it does have an interesting possible answer.) (Note: anything labelled "challenge" will not be part of the hand-in.)
4. You have probably had the experience of trying to avoid encountering someone, whom we will call Rocky. In this instance, Rocky is trying to find you. It is Saturday night and you are choosing which of two possible parties to attend. You like Party 1 better and, if Rocky goes to the other party, you get a payoff 20 at Party 1. If Rocky attends Party 1, however, you are going to be uncomfortable and get a payoff of 5. Similarly, Party 2 gives you a payoff of 15, unless Rocky attends, in which case the payoff is 0. Rocky likes Party 2 better, but he is likes you. He values Party 2 at 10, Party 1 at 5, and your presence at either party that he attends is worth an additional payoff of 10. You and Rocky both know each others strategy space (which party to attend) and payoffs functions.
Consider the following two-player game. S; = [0, 1], for i = 1, 2. Payoffs are as follows %3D ( 100 if 81 if $1 + 82 = $2 u1 (81, 82) = u2 (81, s2) = 150 – [s2 – s1 -P. Part a: Describe B1. Explain. Part b: Describe B2. Explain. [Hint: it is not necessary that you use calculus to answer any part of this question.]
1. Each of two players simultaneously announces either Rock, Paper, or Scissors. Paper beats Rock, Rock beats Scissors, and Scissors beats Paper. The player who names the winning object receives $1 from her opponent. If both players make the same choice, no payment is made. Each players's preferences are represented by by the expected amount of money she receives. a) Formulate the situation as a strategic game and find all its mixed strategy equilibria. Make sure that you consider all different supports. b) Find all the mixed strategy equilibria of the modified game in which player 2 is prohibited from announcing Rock.
Does the game have a nash equilibrum and why/whynot
9. Find all of the Nash equilibria for the three-player game here. Player 1 a b Player 3: A Player 2 X y Z 1,1,0 2,0,0 2,0,0 3,2,1 1,2,3 0,1,2 2,0,0 0,2,3 3,1,1 Player 1 a b C Player 1 Player 3: C X Player 2 y 2,0,0 0,1,2 0,1,1 1,2,1 3,1,2 0,1,2 a b C Player 3: B Player 2 X 2,0,0 1,2,0 0,1,2 Z 0,1,2 0,1,2 1,1,2 y 0,0,1 1,2,1 2,2,1 Z 2,1,2 1,2,1 2,1,0
Please select the correct option and write clear. Thank you.
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))
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 =

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3) Find pure and mixed strategy Nash Equilibria of the following games 1) Matching Pennies game: Player B - heads Player B - tails Player A - heads 1, -1 -1, 1 Player A - tails -1, 1 1, -1 2) Bank bailout Bank-Risky Bank - Safe Government- Bailout Government- Let fail 6,2 0,3 3,6 4,5