I think your epistemic status is right. Nash is not a good guide to what happens in one-shot games.
You give a high bid in TD (assuming no one cares what the bags are worth, only EV) because your expected returns are higher when you bid high, given most others will either not get to the Nash logic, or get far enough to realize that many others won’t get there and therefore they shouldn’t use it, or realize that those who do get there will realize others won’t get there, or even just realize that even if everyone gets there some will choose to ignore it because even if a few others ignore it, you do better that way. And so on.
A thought experiment is, what is the right mixed strategy if your opponent will know what your exact mixed strategy is? I think of this as ‘asymmetric Nash.’
Is a mixed strategy enough in this case, or does it require communication and trust (in this case, “trust” is equivalent to changing the payout structure to include points for self-image and social cohesion)?
A mixed-strategy would be to bid between $2 and $100 in some probability distribution that gives some weight to each value, and adds up to 1. Assume 1.01% to each value 2..100 to start. The hypothetical counter to this never includes 100 (99 dominates it as a pure strategy, and as a sub-strategy), so either distributes 1.02% to 2..99 or 1.01% to 2..98 and 2.02% to 99, unsure which, but it doesn’t matter because we’re going to iterate further. The obvious response to this counter-strategy is to never bid 99 or 100, redistributing those probabilities. Continue until you’re 100% $2 bids.
Nash is Nash, there’s no asymmetry available. The only way to win is to play a different game—communication allows you to change the payoff matrix by getting your opponent to consider future interactions and image considerations as valid parts of the result.
″ in this case, “trust” is equivalent to changing the payout structure to include points for self-image and social cohesion ”
I guess I’m just trying to model trust in TD without changing the payoff matrix. The payoff matrix of the “vague” TD works in promoting trust—a player has no incentive breaking a promise.
You’re just avoiding acknowledging the change in payoff matrix, not avoiding the change itself. If “breaking a promise” has a cost or “keeping a promise” has a benefit (even if it’s only a brief good feeling), that’s part of the utility calculation, and is part of the actual payoff matrix used for decision-making..
“breaking a promise” or “keeping a promise” has no intrinsic utilities here.
What I state is that under this formulation, if the other player believes your promise and plays the best response to your promise, your best response is to keep the promise.
What utility do you get from keeping the promise, and how does it outweigh an extra $1 from bidding $99 (and getting $101) instead of $100?
If you’re invoking Hofstadter’s super-rationality (the idea that your keeping a promise is causally linked to the other person keeping theirs), fine. If you’re acknowledging that you get outside-game utility from being a promise-keeper, also fine (but you’ve got a different payout structure than written). Otherwise, why are you giving up the $1?
And if you are willing to go $99 to get another $1 payout, why isn’t the other player (kind of an inverse super-rationality argument)?
My assumption is that promises are “vague”, playing $99 or $100 both fulfil the promise of giving a high claim close to $100, for which there is no incentive to break.
I think the vagueness stops the race to the bottom in TD, compared to the dollar auction in which every bid can be outmatched by a tiny step without risking going overboard immediately.
I do think I overcomplicated the matter to avoid modifying the payoff matrix.
I think your epistemic status is right. Nash is not a good guide to what happens in one-shot games.
You give a high bid in TD (assuming no one cares what the bags are worth, only EV) because your expected returns are higher when you bid high, given most others will either not get to the Nash logic, or get far enough to realize that many others won’t get there and therefore they shouldn’t use it, or realize that those who do get there will realize others won’t get there, or even just realize that even if everyone gets there some will choose to ignore it because even if a few others ignore it, you do better that way. And so on.
A thought experiment is, what is the right mixed strategy if your opponent will know what your exact mixed strategy is? I think of this as ‘asymmetric Nash.’
Is a mixed strategy enough in this case, or does it require communication and trust (in this case, “trust” is equivalent to changing the payout structure to include points for self-image and social cohesion)?
A mixed-strategy would be to bid between $2 and $100 in some probability distribution that gives some weight to each value, and adds up to 1. Assume 1.01% to each value 2..100 to start. The hypothetical counter to this never includes 100 (99 dominates it as a pure strategy, and as a sub-strategy), so either distributes 1.02% to 2..99 or 1.01% to 2..98 and 2.02% to 99, unsure which, but it doesn’t matter because we’re going to iterate further. The obvious response to this counter-strategy is to never bid 99 or 100, redistributing those probabilities. Continue until you’re 100% $2 bids.
Nash is Nash, there’s no asymmetry available. The only way to win is to play a different game—communication allows you to change the payoff matrix by getting your opponent to consider future interactions and image considerations as valid parts of the result.
″ in this case, “trust” is equivalent to changing the payout structure to include points for self-image and social cohesion ”
I guess I’m just trying to model trust in TD without changing the payoff matrix. The payoff matrix of the “vague” TD works in promoting trust—a player has no incentive breaking a promise.
You’re just avoiding acknowledging the change in payoff matrix, not avoiding the change itself. If “breaking a promise” has a cost or “keeping a promise” has a benefit (even if it’s only a brief good feeling), that’s part of the utility calculation, and is part of the actual payoff matrix used for decision-making..
“breaking a promise” or “keeping a promise” has no intrinsic utilities here.
What I state is that under this formulation, if the other player believes your promise and plays the best response to your promise, your best response is to keep the promise.
What utility do you get from keeping the promise, and how does it outweigh an extra $1 from bidding $99 (and getting $101) instead of $100?
If you’re invoking Hofstadter’s super-rationality (the idea that your keeping a promise is causally linked to the other person keeping theirs), fine. If you’re acknowledging that you get outside-game utility from being a promise-keeper, also fine (but you’ve got a different payout structure than written). Otherwise, why are you giving up the $1?
And if you are willing to go $99 to get another $1 payout, why isn’t the other player (kind of an inverse super-rationality argument)?
My assumption is that promises are “vague”, playing $99 or $100 both fulfil the promise of giving a high claim close to $100, for which there is no incentive to break.
I think the vagueness stops the race to the bottom in TD, compared to the dollar auction in which every bid can be outmatched by a tiny step without risking going overboard immediately.
I do think I overcomplicated the matter to avoid modifying the payoff matrix.