oops, you are right. I’ll fix it. thanks.

]]>Thanks for the fascinating post. A comment regarding communication complexity of correlated equilibria: although every game has a correlated equilibrium with polynomial-sized support, in general there are also correlated equilibria with exponential-sized supports. In particular, if you run the ellipsoid method directly on the LP, the generated candidate solutions will have exponential-sized supports. Then communicating these vectors to the individual players becomes problematic.

Perhaps what you had in mind was Papadimitriou’s (STOC 2005) algorithm, which applies the ellipsoid method on the dual LP. Although the dual problem has exponential number of constraints, a separation oracle can be constructed that only requires each player to compute certain expected utilities and submit a short vector. (As an aside, this separation oracle has interesting connections to swap-regret-minimizing learning algorithms.)

]]>thanks. done.

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