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cousin_it comments on A simple game that has no solution - Less Wrong Discussion
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Let's say player 1 submits a computer program that will receive no input and print either A, B or C. Player 2 submits a computer program that will receive a single bit as input (telling it whether P1's program printed A), and print either X or Y. Both programs also have access to a fair random number generator. That's a simultaneous move game where every Nash equilibrium leads to payoffs (3,0). Hopefully it's not too much of a stretch to say that we should play the game in the same way that the best program would play it.
If additionally each program receives the other's source code as input, many better Nash equilibria become achievable, like the outcome (4,1) proposed by Eliezer. In this case I think it's a bargaining problem. The Nash bargaining solution proposed by Squark might be relevant, though I don't know how to handle such problems in general.
Should we (humans) play like the best program that don't have access to each other's source code play it, or play like the best programs that do have access to each other's source code play it? I mean, figuratively we have some information about the other player's source code...
I think that if we know about one another that we believe in playing like programs with access to each other's source when playing against opponents about which we know [QUINE], then we are justified to play like programs with access to each others source. :)