Fair Distribution Protocols or How the Players Replace Fortune
- 1 May 1992
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 17 (2) , 327-340
- https://doi.org/10.1287/moor.17.2.327
Abstract
There are n ≥ 2 players P1, P2, …, Pn, each of them having a finite alphabet A1, …, An, and there is a probability distribution p on A = A1 × ⋯ × An. The players want to choose a ∈ A according to p in such a way that Pk knows only the kth component, ak, of a. This can be done with the help of an impartial person or “fortune” who chooses a ∈ A according to p and informs Pk on ak only. But what happens if no such person is available? Can the players find a procedure that replaces fortune? It is proved here that the answer is yes when n ≥ 4. As an application it is shown that a correlated equilibrium of a noncooperative n-person game (n ≥ 4) coincides with a Nash equilibrium of an extended game involving, in addition, plain conversations only.Keywords
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