Yup. Though you don’t necessarily need to imagine the money “changing hands”—if both people get paid 2 extra pennies if they tie, and the person who bids less gets paid 4 extra pennies, the result is the same.
The point is exactly what it says in the title. Relative to the maximum cooperative payoff, the actual equilibrium payoff can be arbitrarily small. And as you change the game, the transition from low payoff to high payoff can be sharp—jumping straight from pennies to millions just by changing the payoffs by a few pennies.
Relative to the maximum cooperative payoff, the actual equilibrium payoff can be arbitrarily small.
Please be careful to specify “Nash equilibrium” here, rather than just “equilibrium”. Nash is not the only possible result that can be obtained, especially if players have some ability to cooperate or to model their opponent in a way where Nash’s conditions don’t hold.
In actual tests (admittedly not very complete, usually done in psychology or economics classes), almost nobody ends up at the Nash equilibrium in this style game (positive-sum where altruism or trust can lead one to take risks).
Yup. Though you don’t necessarily need to imagine the money “changing hands”—if both people get paid 2 extra pennies if they tie, and the person who bids less gets paid 4 extra pennies, the result is the same.
The point is exactly what it says in the title. Relative to the maximum cooperative payoff, the actual equilibrium payoff can be arbitrarily small. And as you change the game, the transition from low payoff to high payoff can be sharp—jumping straight from pennies to millions just by changing the payoffs by a few pennies.
Please be careful to specify “Nash equilibrium” here, rather than just “equilibrium”. Nash is not the only possible result that can be obtained, especially if players have some ability to cooperate or to model their opponent in a way where Nash’s conditions don’t hold.
In actual tests (admittedly not very complete, usually done in psychology or economics classes), almost nobody ends up at the Nash equilibrium in this style game (positive-sum where altruism or trust can lead one to take risks).