This paper proposes a Bayesian estimation of the payoff functions in entry games using Markov chain Monte Carlo simulation. In order to deal with the multiple Nash equilibria, we describe the econometric model with a latent variable that represents the player's choice of an equilibrium among the multiple equilibria. The statistical incoherency problem considered in previous studies is also discussed for our entry game model, and we provide an alternative justification for the previous estimation procedures. Our proposed methodology is applied to Japanese airline data, and model selection based on the marginal likelihood is conducted to investigate the nature of the strategic interaction between two major Japanese airline companies. Finally, we predict the entry probabilities of two airline companies for the Shizuoka airport that is currently under construction.