Contagious Matching Games

Abstract

This paper explores a simple class of matching games in which individuals meet pairwise, unwittingly passing along a bad in a contagion fashion. It may be a private “bad”, like a counterfeit money or stolen art. Or it may be a collective “bad”, like a disease or a computer virus. Either way, individuals expend effort to avoid acquiring the “bad”. With a private “bad”, these efforts are complements, and the game is submodular. With a collective “bad”, they are substitutes, and the game is supermodular. The symmetric equilibria of these games share a common feature, that the marketplace often produces fewer “infections” as the bad grows more prevalent. One cannot, for instance, infer that counterfeiting is less severe when there is less passed counterfeit money.