Game Theory seminars

How can people coordinate their actions or make joint decisions? One possibility is that each person attempts to predict the actions of the other(s), and best-responds accordingly. But this can lead to bad outcomes, and sometimes even vicious circularity. An alternative view is that each person attempts to work out what the two or more players would agree to do, if they were to bargain explicitly. If the result of such a "virtual" bargain is "obvious," then the players can simply play their respective roles in that bargain. I suggest that virtual bargaining is essential to genuinely social interaction (rather than viewing other people as instruments), and may even be uniquely human. This approach aims to respect methodological individualism, a key principle in many areas of social science, while explaining how human groups can, in a very real sense, be "greater" than the sum of their individual members.

Aram Harrow connects the Unique Games conjecture, especially small-set expansion, with the quantum separability problem. The Lasserre hierarchy used for Unique Games and the k-extendible relaxation of quantum separability turn out to be closely equivalent algorithmic approaches. The talk examines how quantum-information conjectures could yield quasipolynomial algorithms or hardness results for Unique Games, and discusses promising research directions. It introduces the necessary quantum mechanics, Unique Games, and hierarchy background rather than presupposing it. The presentation draws partly on the papers arXiv:1205.4484 and arXiv:1210.6367.