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Nisan Stiennon

Towards higher-order game theory​

If you're playing a game, you need to form counterfactual beliefs, like:

"If you believed I will do P, then you would do Q."

If you're playing a game with agents who are good at modeling other agents, you may need to form iterated counterfactuals, like:

"If you believed (if I believed you will do P, then I would do Q), then you would do R."

In this talk I'll formalize such "higher-order" beliefs and the agents that use them. As applications, we'll see "prudent" agents who try to cooperate, solutions to some coordination games, and the infinite-order limit. This is a work in progress, and I haven't worked out all the proofs. The formalism will involve reflective oracles and domain theory, and I'll explain those concepts briefly in the talk.

Keywords​

  • Game theory
  • Domain theory