A Series of Increasingly Perverse and Destructive Games

Re­lated to: Higher Than the Most High

The linked post de­scribes a game in which (I fudge a lit­tle), Omega comes to you and two other peo­ple, and ask you to tell him an in­te­ger. The per­son who names the largest in­te­ger is al­lowed to leave. The other two are kil­led.

This got me think­ing about vari­a­tions on the same con­cept, and here’s what I’ve come up, tak­ing that game to be GAME0. The re­sults are sort of a fun time-waster, and bring up some in­ter­est­ing is­sues. For your en­joy­ment...

THE GAMES:

GAME1: Omega takes you and two strangers (all com­pe­tent pro­gram­mers), and kid­naps and se­dates you. You awake in three rooms with in­struc­tions printed on the wall ex­plain­ing the game, and a com­puter with an op­er­at­ing sys­tem and pro­gram­ming lan­guage com­piler, but no in­ter­net. Food, wa­ter, and toi­letries are pro­vided, but no ex­ter­nal com­mu­ni­ca­tion. The par­ti­ci­pants are al­lowed to write pro­grams on the com­puter in a lan­guage that sup­ports ar­bi­trar­ily large nu­mer­i­cal val­ues. The pro­grams are taken by Omega and run on a hy­per­com­puter in finite time (this hy­per­com­puter can re­solve the halt­ing prob­lem and in­finite loops, but pro­grams that do not even­tu­ally halt re­turn no out­put). The per­son who wrote the pro­gram with the largest out­put is al­lowed to leave. The oth­ers are in­stantly and painlessly kil­led. In the event of a tie, ev­ery­one dies. If your pro­gram re­turns no out­put, that is taken to be zero.

GAME2: Iden­ti­cal to GAME1, ex­cept that each pro­gram you write has to take two in­puts, which will be the text of the other play­ers’ pro­grams (as­sume they’re all writ­ten in the same lan­guage). The re­ward for out­putting the largest num­ber ap­ply nor­mally.

GAME3: Iden­ti­cal to Game2, ex­cept that while you are se­dated, Omega painlessly and im­per­cep­ti­bly up­loads you. Ad­di­tion­ally, the in­struc­tions on the wall now spec­ify that your pro­gram must take four in­puts—black­box func­tions which rep­re­sent the up­loaded minds of all three play­ers, plus a simu­la­tion of the room you’re in, in­dis­t­in­guish­able from the real thing. We’ll as­sume that play­ers can’t mod­ify or in­ter­pret the con­tents of their op­po­nents’ brains. The room func­tion take an ar­gu­ment of a string (which con­trols the text printed on the wall, and out­puts what­ever num­ber the per­son in the simu­la­tion’s pro­gram re­turns).

In each of these games, which pro­gram should you write if you wish to sur­vive?

SOME DISCUSSION OF STRATEGY:

GAME1: Clearly, the triv­ial strat­egy (im­ple­ment the Ack­er­man or similar fast-grow­ing func­tions and gen­er­ate some large in­te­ger), gives no bet­ter than ran­dom re­sults, be­cause it’s the bare min­i­mal strat­egy any­one will em­ploy, and your rank­ing in the re­sults, with­out knowl­edge of your op­po­nents is en­tirely up to chance /​ how long you’re will­ing to sit there typ­ing nines for your Ack­er­mann ar­gu­ment.

A few al­ter­na­tives for your con­sid­er­a­tion:

1: if you are aware of an ex­is­tence hy­poth­e­sis (say, a num­ber with some prop­erty which is not con­clu­sively known to ex­ist and could be any in­te­ger), write a pro­gram that brute-force tests all in­te­gers un­til it ar­rives at an in­te­ger which matches the re­quire­ments, and use this as the ar­gu­ment for your rapidly-grow­ing func­tion. While it may never re­turn any out­put, if it does, the out­put will be an in­te­ger, and the ex­pected value goes to­wards in­finity.

2: Write a pro­gram that gen­er­ates all pro­grams shorter than length n, and finds the one with the largest out­put. Then make a sep­a­rate stab at your own non-meta win­ning strat­egy. Take the length of the pro­gram you pro­duce, tetrate it for safety, and use that as your length n. Re­turn the re­turn value of the win­ning pro­gram.

On the whole, though, this game is sim­ply not all that in­ter­est­ing in a broader sense.

GAME2: This game has its own amus­ing quirks (pri­mar­ily that it could prob­a­bly ac­tu­ally be played in real life on a non-hy­per­com­puter), how­ever, most of its salient fea­tures are also pre­sent in GAME3, so I’m go­ing to defer dis­cus­sion to that. I’ll only say that the ob­vi­ous strat­egy (sum the out­puts of the other two play­ers’ pro­grams and re­turn that) leads to an in­finite re­cur­sive trawl and never halts if ev­ery­one takes it. This holds true for any sim­ple strat­egy for adding or mul­ti­ply­ing some con­stant with the out­puts of your op­po­nents’ pro­grams.

GAME3: This game is by far the most in­ter­est­ing. For starters, this game per­mits acausal ne­go­ti­a­tion be­tween play­ers (by par­ties simu­lat­ing and con­vers­ing with one an­other). Fur­ther­more, an­thropic rea­son­ing plays a huge role, since the player is never sure if they’re in the real world, one of their own simu­la­tions, or one of the simu­la­tions of the other play­ers.

Play­ers can ne­go­ti­ate, barter, or threaten one an­other, they can at­tempt to send sig­nals to their simu­lated selves (to in­di­cate that they are in their own simu­la­tion and not some­body else’s). They can make their choices based on coin flips, to ren­der them­selves difficult to simu­late. They can at­tempt to brute-force the sig­nals their simu­lated op­po­nents are ex­pect­ing. They can simu­late copies of their op­po­nents who think they’re play­ing any pre­vi­ous ver­sion of the game, and are un­aware they’ve been up­loaded. They can simu­late copies of their op­po­nents, ob­serve their meta-strate­gies, and plan around them. They can to­tally ig­nore the in­puts from the other play­ers and play just the level one game. It gets very ex­cit­ing very quickly. I’d like to see what strat­egy you folks would em­ploy.

And, as a fi­nal bonus, I pre­sent GAME4 : In game 4, there is no Omega, and no hy­per­com­puter. You sim­ply take a friend, chlo­roform them, and put them in a con­crete room with the in­struc­tions for GAME3 on the wall, and a linux com­puter not plugged into any­thing. You leave them there for a few months work­ing on their pro­gram, and watch what hap­pens to their psy­chol­ogy. You win when they shrink down into a dead-eyed, ter­mi­nally-para­noid and en­tirely in­sane shell of their former selves. This is the eas­iest game.

Happy play­ing!