Auctions vs. fixed pricing: competing for budget constrained buyers

We investigate price mechanism selection in a setting where sellers compete for budget constrained buyers by adopting either fixed pricing or auctions (first or second price). We show that first and second price auctions are payoff equivalent when some bidders are financially constrained, so sellers are indifferent to adopt either format. We characterize possible equilibria and show that if the budget is high, then sellers compete via fixed pricing, if it is low then they compete via auctions, and if it is moderate then they mix, so both mechanisms coexist. The budget constraint becomes less binding if sellers use entry fees. Interestingly an improvement of the budget---e.g. letting customers pay in installments---may lead to fewer trades and a loss of efficiency