I love the probabalistic rejection idea—it’s clever and fun. But it depends a LOT on communication or repetition-with-identity so the offerer has any clue that’s the algorithm in play. And in that case, the probabalistic element is unnecessary—simple precommitment is enough (and, in strictly-controlled games without repetition, allowing the reponder to publicly and enforceably precommit just reverses the positions).
I think our main disagreement is on what to do when one or more participants in one-shot (or fixed-length) games are truly selfish, and the payouts listed are fully correct in utility, after accounting for any empathy or desire for fairness. Taboo “fair”, and substitute “optimizing for self”. Shapley values are a good indicator of bargaining power for some kinds of game, but the assumption of symmetry is hard to justify.
Totally! One of the most impressive results I’ve seen for one-shot games is the Robust Cooperation paper studying the open-source Prisoners’ Dilemma, where each player delegates their decision to a program that will learn the exact source code of the other delegate at runtime. Even utterly selfish agents have an incentive to delegate their decision to a program like FairBot or PrudentBot.
I think the probabilistic element helps to preserve expected utility in cases where the demands from each negotiator exceed the total amount of resources being bargained over. If each precommits to demand $60 when splitting $100, deterministic rejection leads to ($0, $0) with 100% probability. Whereas probabilistic rejection calls for the evaluator to accept with probability slightly less than $40/$60 ≈ 66.67%. Accepting leads to a payoff of ($60, $40), for an expected joint utility of slightly less than ≈ ($40, $26.67).
I think there are also totally situations where the asymmetrical power dynamics you’re talking about mean that one agent gets to dictate terms and the other gets what they get. Such as “Alice gets to unilaterally decide how $100 will be split, and Bob gets whatever Alice gives him.” In the one-shot version of this with selfish players, Alice just takes the $100 and Bob gets $0. Any hope for getting a selfish Alice to do anything else is going to come from incentives beyond this one interaction.
I love the probabalistic rejection idea—it’s clever and fun. But it depends a LOT on communication or repetition-with-identity so the offerer has any clue that’s the algorithm in play. And in that case, the probabalistic element is unnecessary—simple precommitment is enough (and, in strictly-controlled games without repetition, allowing the reponder to publicly and enforceably precommit just reverses the positions).
I think our main disagreement is on what to do when one or more participants in one-shot (or fixed-length) games are truly selfish, and the payouts listed are fully correct in utility, after accounting for any empathy or desire for fairness. Taboo “fair”, and substitute “optimizing for self”. Shapley values are a good indicator of bargaining power for some kinds of game, but the assumption of symmetry is hard to justify.
Totally! One of the most impressive results I’ve seen for one-shot games is the Robust Cooperation paper studying the open-source Prisoners’ Dilemma, where each player delegates their decision to a program that will learn the exact source code of the other delegate at runtime. Even utterly selfish agents have an incentive to delegate their decision to a program like FairBot or PrudentBot.
I think the probabilistic element helps to preserve expected utility in cases where the demands from each negotiator exceed the total amount of resources being bargained over. If each precommits to demand $60 when splitting $100, deterministic rejection leads to ($0, $0) with 100% probability. Whereas probabilistic rejection calls for the evaluator to accept with probability slightly less than $40/$60 ≈ 66.67%. Accepting leads to a payoff of ($60, $40), for an expected joint utility of slightly less than ≈ ($40, $26.67).
I think there are also totally situations where the asymmetrical power dynamics you’re talking about mean that one agent gets to dictate terms and the other gets what they get. Such as “Alice gets to unilaterally decide how $100 will be split, and Bob gets whatever Alice gives him.” In the one-shot version of this with selfish players, Alice just takes the $100 and Bob gets $0. Any hope for getting a selfish Alice to do anything else is going to come from incentives beyond this one interaction.