Multi-Party Games

Abstract

The rich mathematical theory of two-party communication naturally invites us to consider scenarios involving k > 2 players. In the simplest case, we have some function f(x)whose input x is decomposed into k equally-sized parts $\rm x=\rm (x_{1},\,.\,.\,.\,,x_{k})$. There are k players who wish to collaboratively evaluate a given function f on every input x. Each player has unlimited computational power and full knowledge of the function. As in the case of two players, the players are not adversaries—they help and trust each other. Depending on what parts of the input x each player can see, there are two main models of communication: