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Selling diversity
We provide a general yet tractable model to derive revenue-optimal mechanisms in settings with allocation-dependent externalities. Such externalities are present in settings ranging from concerts and parties to fashion items and software to college and workplace experiences. Our framework allows for transfers and for screening through ordeals like waiting in line, joining a fan club, or completing lengthy applications. We elucidate when and how such seemingly wasteful actions enhance price discrimination in the presence of externalities. Ordeals effectively filter out undesirable customers or members in some settings. In other settings, ordeals can be leveraged to allocate to desirable consumers who may have low purchasing power. We find conditions under which optimal mechanisms create two classes of customers: those who pay with money and those who pay with effort (effort discrimination). We find separate conditions under which those who pay also engage in the ordeal (certification).