Entry game models are often used to study the nature of firms' profits and the nature of competition among firms in empirical studies. However, when there are multiple players in an oligopoly market, the resulting multiple equilibria have made it difficult in previous studies to estimate the payoff functions of players in complete information, static and discrete games without using unreasonable assumptions. To overcome this difficulty, the present paper proposes a practical estimation method for an entry game with three players using a Bayesian approach. Some mild assumptions are imposed on the payoff function, and the average competitive effect is used to capture the entry effect of the number of firms. Our proposed methodology is applied to Japanese airline data from the year 2000, when there were three major airline companies, ANA, JAL and JAS. The model comparison is conducted to investigate the nature of strategic interaction among these Japanese airline companies.