Doesn’t the existence of the rule that says that no money changes hands if there’s a tie alter the incentives? If we both state that we want 1,000,000 pounds, then we both get it and we both walk away happy. What incentive is there for either of the two agents to name a value that is lower than 1,000,000?
If your strategy remains unchanged, I can change my strategy to “999,999.99 please” and come away with 1,000,000.01 in total, so that’s not a Nash equilibrium.
The maximum theoretical payout is 1000000.01 pounds. And since both players know this, and for any given tie amount, a player’s net can be increased by a penny by reducing their bid by a penny, they will recursively calculate to 0.
Unless they have a theory of mind and can model ways to take risks in order to increase results in the cases where the other player ALSO takes risks. We call this “trust”. and it can be greatly increased with communication, empathy, and side-agreements.
I think it’s long been known that Nash equilibria are not necessarily optimal, only guaranteed that the other player’s choices can’t hurt you. It’s perfectly defensive in adversarial games. This is great for zero-sum games, where the other player’s increase is exactly your decrease. It’s nearly irrelevant (except as a lower bound) for cooperative (variable-sum) games.
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).
Doesn’t the existence of the rule that says that no money changes hands if there’s a tie alter the incentives? If we both state that we want 1,000,000 pounds, then we both get it and we both walk away happy. What incentive is there for either of the two agents to name a value that is lower than 1,000,000?
If your strategy remains unchanged, I can change my strategy to “999,999.99 please” and come away with 1,000,000.01 in total, so that’s not a Nash equilibrium.
I see. And from then it follows the same pattern as a dollar auction, until the “winning” bet goes to zero.
The maximum theoretical payout is 1000000.01 pounds. And since both players know this, and for any given tie amount, a player’s net can be increased by a penny by reducing their bid by a penny, they will recursively calculate to 0.
Unless they have a theory of mind and can model ways to take risks in order to increase results in the cases where the other player ALSO takes risks. We call this “trust”. and it can be greatly increased with communication, empathy, and side-agreements.
I think it’s long been known that Nash equilibria are not necessarily optimal, only guaranteed that the other player’s choices can’t hurt you. It’s perfectly defensive in adversarial games. This is great for zero-sum games, where the other player’s increase is exactly your decrease. It’s nearly irrelevant (except as a lower bound) for cooperative (variable-sum) games.
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).