On the impossibility of protecting risk-takers

Risk-neutral sellers can extract high profits from risk-loving buyers by selling them lotteries. To limit this problem, gambling is heavily regulated in most countries. I show that protecting risk-loving buyers against profit-maximizing sellers is essentially impossible. Even if buyers are risk-loving in the weakest sense, the seller can construct a nonrandom winner-pays auction that ensures unbounded profits. The result holds even if the seller cannot use any mechanism that resembles a lottery and only requires that buyers are asymptotically risk loving. This condition is satisfied, for example, when preferences satisfy Savage’s axioms or with prospect theory preferences.