UDT as a Nash Equilibrium

I re­al­ized to­day that UDT doesn’t re­ally need the as­sump­tion that other play­ers use UDT. In any game where all play­ers have the same util­ity func­tion, “ev­ery­one us­ing UDT” is a Nash equil­ibrium that gives ev­ery­one their high­est pos­si­ble ex­pected util­ity. So you can just use it unilat­er­ally.

That cov­ers such cases as Ab­sent-Minded Driver, Psy-Kosh’s prob­lem, Wei’s co­or­di­na­tion prob­lem. Notably it doesn’t cover the Pri­soner’s Dilemma, be­cause the play­ers as­sign differ­ent util­ities to the same out­come.

(Also this shows how Von Neu­mann-Mor­gen­stern ex­pected util­ity max­i­miza­tion is ba­si­cally a re­stric­tion of UDT to sin­gle player games with perfect re­call. For im­perfect re­call (AMD) or mul­ti­ple play­ers (Psy-Kosh) you need the full ver­sion.)

You can ac­tu­ally push game the­ory a bit fur­ther, and al­low games where play­ers have differ­ent util­ity func­tions, as long as some sub­set of play­ers can jointly en­force their high­est pos­si­ble ex­pected util­ities. UDT doesn’t sup­port that kind of de­ci­sion-mak­ing, but re­ally it should be a no-brainer too...?

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