This paper studies the patent licensing decision of an insider patentee when two firms engage in a mixed (Cournot-Bertrand or Bertrand-Cournot) competition where one firm adopts the quantity strategy while the other uses the price strategy and vice versa. If either the fixed fee or royalty is applied, then the licensor prefers the fixed fee when the licensor takes the quantity strategy, while the licensee uses the price strategy (Cournot-Bertrand). If the two-part tariff is applied, then the two-part tariff is more likely to be adopted by the licensor under Cournot-Bertrand than under Bertrand-Cournot competition.