On communication games with more than two players

A k-player game is a communication game between k parties, each of which has an access to a half of input bits. 2-player games were introduced by Yao (1981) and are known as best-partition two-party games. We first describe a lower bounds argument for this case, based on computing the term-rank and clique-number of communication matrices. Using this argument we exhibit an explicit function on n variables such that any 2-players protocol for it requires #OMEGA#(#sq root#(n)) bits of communication, whereas 3 players need to communicate only constant number of bits. We then consider another restriction: we allow any number of players but require that every singular input bit is accessable to < k of these players. We prove that, for small values of k, no such protocol can recognize codewords of some linear codes of length n using less than #OMEGA#(#sq root#(n)) bits of communication. (orig.)SIGLEAvailable from TIB Hannover: RR 1843(95-11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman