The Optimal Bribe: Price Versus Quantity Competition in Oligopolies

ABSTRACT We analyze an entry deterrence model between an incumbent firm and a potential entrant, where the incumbent strategically offers bribes to local officials to raise entry barriers. Our focus is a three‐stage Bertrand game under incomplete information in a differentiated goods market. Unlike prior research assuming implicit entry costs, we explicitly model bribery as a strategic decision in an oligopolistic setting and compare the optimal bribe between Bertrand and Cournot competition. We find that the optimal bribe decreases sharply under Bertrand competition as product substitutability increases and remains lower than in Cournot competition, while for complementary goods, bribery is higher under Bertrand. We establish and prove a zero net cross‐effects property, showing that price responsiveness to market size and marginal cost both vary with competition intensity but perfectly offset each other. These results highlight how entry deterrence strategies depend on the nature of competition and type of goods, helping policymakers to design effective regulations and anti‐corruption policies that promote fair market entry.