🔖 Subjectivity and Correlation in Randomized Strategies by Robert J. Aumann | Journal of Mathematical Economics

Subjectivity and Correlation in Randomized Strategies by Robert J. Aumann (Journal of Mathematical Economics 1 (1974) 67-96. North-Holland Publishing Company)
(.pdf download) Subjectivity and correlation, though formally related, are conceptually distinct and independent issues. We start by discussing subjectivity. A mixed strategy in a game involves the selection of a pure strategy by means of a random device. It has usually been assumed that the random device is a coin flip, the spin of a roulette wheel, or something similar; in brief, an ‘objective’ device, one for which everybody agrees on the numerical values of the probabilities involved. Rather oddly, in spite of the long history of the theory of subjective probability, nobody seems to have examined the consequences of basing mixed strategies on ‘subjective’ random devices, i.e. devices on the probabilities of whose outcomes people may disagree (such as horse races, elections, etc.).

Suggested by In Game Theory, No Clear Path to Equilibrium by Erica Klarreich (Quanta Magazine)

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🔖 Communication complexity of approximate Nash equilibria | arXiv

Communication complexity of approximate Nash equilibria by Yakov Babichenko, Aviad Rubinstein (arXiv)
For a constant ϵ, we prove a poly(N) lower bound on the (randomized) communication complexity of ϵ-Nash equilibrium in two-player NxN games. For n-player binary-action games we prove an exp(n) lower bound for the (randomized) communication complexity of (ϵ,ϵ)-weak approximate Nash equilibrium, which is a profile of mixed actions such that at least (1−ϵ)-fraction of the players are ϵ-best replying.

Suggested by In Game Theory, No Clear Path to Equilibrium by Erica Klarreich (Quanta Magazine)

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