Reading Clarifications 1, 2, and 3 seems to imply that it would not be useful or applicable in this scenario.
Clarification 1: Yes, utilities are invariant up to a positive affine transformation so there’s no canonical way to split utilities evenly. Hence the part about “Assume a magical solution N which gives us the fair division.” If we knew the exact properties of how to implement this magical solution, taking it at first for magical, that might give us some idea of what N should be, too.
Clarification 2: The way this might work is that you pick a series of increasingly unfair-to-you, increasingly worse-for-the-other-player outcomes whose first element is what you deem the fair Pareto outcome: (100, 100), (98, 99), (96, 98). Perhaps stop well short of Nash if the skew becomes too extreme. Drop to Nash as the last resort. The other agent does the same, starting with their own ideal of fairness on the Pareto boundary. Unless one of you has a completely skewed idea of fairness, you should be able to meet somewhere in the middle. Both of you will do worse against a fixed opponent’s strategy by unilaterally adopting more self-favoring ideas of fairness. Both of you will do worse in expectation against potentially exploitive opponents by unilaterally adopting looser ideas of fairness. This gives everyone an incentive to obey the Galactic Schelling Point and be fair about it. You should not be picking the descending sequence in an agent-dependent way that incentivizes, at cost to you, skewed claims about fairness.
Clarification 3: You must take into account the other agent’s costs and other opportunities when ensuring that the net outcome, in terms of final utilities, is worse for them than the reward offered for ‘fair’ cooperation. Offering them the chance to buy half as many paperclips at a lower, less fair price, does no good if they can go next door, get the same offer again, and buy the same number of paperclips at a lower total price.
Can you show how this would lead to a ‘jerk’ never gaining in the aforementioned scenario?
Reading Clarifications 1, 2, and 3 seems to imply that it would not be useful or applicable in this scenario.
Can you show how this would lead to a ‘jerk’ never gaining in the aforementioned scenario?