Mixed strategies
1.[2p] In a mixed equilibrium, why is a player indifferent between the pure strategies they mix over?
In a mixed equilibrium, why is a player indifferent between the pure strategies they mix over?
The answer is: Because otherwise shifting probability towards the better one would raise their expected payoff
The answer is: Because otherwise shifting probability towards the better one would raise their expected payoff
The answer is: Because otherwise shifting probability towards the better one would raise their expected payoff
2.[2p] Whose payoffs determine a player's own equilibrium mixing probabilities?
Whose payoffs determine a player's own equilibrium mixing probabilities?
The answer is: The other player's, through their indifference condition
The answer is: The other player's, through their indifference condition
The answer is: The other player's, through their indifference condition
3.[2p] In the audit game, evading pays the taxpayer -100 if audited and 50 if not, and declaring pays 0. What audit probability makes the taxpayer indifferent? Give a decimal.
In the audit game, evading pays the taxpayer -100 if audited and 50 if not, and declaring pays 0. What audit probability makes the taxpayer indifferent? Give a decimal.
4.[3p] The authority earns 80 from auditing an evader, -20 from auditing an honest return, -50 from missing an evader, and 0 otherwise. What evasion probability makes the authority indifferent? Give a decimal.
The authority earns 80 from auditing an evader, -20 from auditing an honest return, -50 from missing an evader, and 0 otherwise. What evasion probability makes the authority indifferent? Give a decimal.
5.[3p] In that same game the penalty for a caught evader is tripled from 100 to 300, with no change to the authority's payoffs. What is the new equilibrium probability of evasion? Give a decimal.
In that same game the penalty for a caught evader is tripled from 100 to 300, with no change to the authority's payoffs. What is the new equilibrium probability of evasion? Give a decimal.
6.[3p] A harsher penalty in an inspection game with no change to the enforcer's payoffs
A harsher penalty in an inspection game with no change to the enforcer's payoffs
The answer is: lowers the audit rate and leaves the offence rate where it was
The answer is: lowers the audit rate and leaves the offence rate where it was
The answer is: lowers the audit rate and leaves the offence rate where it was
7.[1p] Nash's theorem guarantees that every finite game has at least one equilibrium once mixed strategies are allowed.
Nash's theorem guarantees that every finite game has at least one equilibrium once mixed strategies are allowed.
The answer is: True
8.[3p] Player 1 wins 2 if both play Heads, 1 if both play Tails, and loses 1 otherwise; the game is zero-sum. With what probability does player 1 play Heads in equilibrium? Give a decimal.
Player 1 wins 2 if both play Heads, 1 if both play Tails, and loses 1 otherwise; the game is zero-sum. With what probability does player 1 play Heads in equilibrium? Give a decimal.
9.[3p] Match each reading of a mixed strategy to what it says.
Match each reading of a mixed strategy to what it says.
Literal randomisation
Population frequency
Harsanyi purification
a share of a large population plays each action
the player really does use a chance device
private payoff shocks make each player pure
Show the answer
Literal randomisation: the player really does use a chance device Population frequency: a share of a large population plays each action Harsanyi purification: private payoff shocks make each player pure