We propose in this paper a new mechanism for selecting a most suitable partner in a cooperative wireless communication system, using a type of game called the Bidding game. In this game, in which the conventional theories of economic bidding are applied, the cooperative communication network is modeled as a single-user, multi-relay system in which the source acts as the auctioneer while the relays or partners act as the bidders in the game. The resource being auctioned here is power, and the relay which offers the highest bid in terms of price is selected and allocated power by the source node. Our findings show that there is a linear relationship between the utility achievable by a source node and the selection of a suitable partner for the cooperative process by that node. Our simulation also shows that the proximity of a relay node to the source node has an effect on the selectability of the node prior to the bidding.