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In this letter, uncertainty in users' network selection is modeled by a Markov chain. In the presence of such uncertainty, the price competition game of wireless local area network (WLAN) service providers (SPs) is analyzed and the existence of Bayesian Nash equilibrium is proved. Using the price of anarchy as a metric of efficiency for social welfare maximization, it is shown that an increase in competition does not result in significant losses in efficiency. Compared to a monopoly, an unregulated duopoly of WLAN SPs is recommended as it results in a more equitable distribution of surplus amongst the SPs and the users.