Hidden passing games

We introduce random encounter matching games, where a hidden trait is sometimes unwittingly passed—either private and bad (like counterfeit money), or collective and bad (a disease), or hidden and good (rare coin), or collective and good (information). One optimally expends effort to avoid acquiring bad traits or trying to acquire good ones. The game shifts from strategic complements to substitutes changing from private to collective, or good to bad traits. A unique equilibrium exists in all cases, and coincides for collective bad and private good traits, and collective good and private bad traits. Equilibrium incidence can be a misleading signal of prevalence for bad traits at high prevalence: one cannot infer that counterfeiting is less severe when there is less passed counterfeit money, or prevalence is higher with more infections.