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 1 Hold Withdraw Hold 7,7 6,0 Player 2 Withdraw 0,6 3,3 (a) Find any pure-strategy Nash equilibria of this game. (b) Find any mixed-strategy Nash equilibria of this game. (c) How do the concepts of 'payoff dominance' and 'risk dominance' apply in this context? Do they help us to predict which equilibrium is more likely to occur?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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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 1
Hold
Withdraw
Hold
7,7
6,0
Player 2
Withdraw
0,6
3,3
(a) Find any pure-strategy Nash equilibria of this game.
(b) Find any mixed-strategy Nash equilibria of this game.
(c) How do the concepts of 'payoff dominance' and 'risk dominance' apply in this
context? Do they help us to predict which equilibrium is more likely to occur?
(d) Suppose we now make this game sequential so that Player 2 moves first. Player 1
observes Player 2's action and moves second. What are the (pure strategy) Nash
equilibria and subgame perfect equilibria of this new game?
(e) Give one example of how the players or a third party could prevent a suboptimal
outcome from occurring in this game.
Transcribed Image Text: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 1 Hold Withdraw Hold 7,7 6,0 Player 2 Withdraw 0,6 3,3 (a) Find any pure-strategy Nash equilibria of this game. (b) Find any mixed-strategy Nash equilibria of this game. (c) How do the concepts of 'payoff dominance' and 'risk dominance' apply in this context? Do they help us to predict which equilibrium is more likely to occur? (d) Suppose we now make this game sequential so that Player 2 moves first. Player 1 observes Player 2's action and moves second. What are the (pure strategy) Nash equilibria and subgame perfect equilibria of this new game? (e) Give one example of how the players or a third party could prevent a suboptimal outcome from occurring in this game.
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