Auctioning off a non-rivalrous good with interference

Auctions are a prevalent way to exchange goods and are well-studied for the exchange of rivalrous goods, but are less studied for non-rivalrous goods. I examine an auction framework where the good sold can be used simultaneously by multiple bidders if their use does not conflict with others; this simultaneous use directly affects the efficiency of the auction. A timely example includes the auctioning off of a radio spectrum by a licensed primary user to unlicensed secondary users who can use the spectrum simultaneously if they are located far enough apart to not cause interference. I examine a uniform price auction over non-conflicting groups and examine how non-rivalry impacts both efficiency and collusion. Conditions are given under which an auction over groups generates higher social welfare than an individual auction. Additional conditions are given under which collusion in a group auction results in higher prices.