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In this paper we deal with the problem of sharing one communication wire among a (possibly large) number of communication stations. The fact that all communication stations are considered identical and that they share one objective of using the communication wire as efficiently as possible leads to the concept of symmetric team problems. For symmetric team problems we define a symmetric solution by the restriction that all decision makers must have identical decision rules. In the first section of this paper the concepts of symmetric team problems and symmetric solutions are developed and motivated. A theorem is given that relates symmetric solutions to randomized decision rules. An example is given which illustrates that the concept of symmetric solutions explains some everyday phenomena. In the second section the access problem in multi-access wire communication is considered as a symmetric team problem. It is shown that the symmetric solution, which corresponds to randomized access rules, tends to give as good performance as the unrestricted solution when the number of stations becomes large (asymptotic optimality). The solutions are also determined numerically, giving quantitative information on the asymptotic behavior.