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Mobile handset manufacturers are introducing new features that allow a user to configure the same handset for seamless operation with multiple wireless network providers. As the competitiveness in the wireless network service market intensifies, such products will deliver greater freedom for the mobile users to switch providers dynamically for a better price or quality of experience. For example, when faced with an unexpected wireless link quality problem, the user could choose to physically switch the provider, or she could be more strategic and use her freedom of switching provider as a `psychological weapon' to force the current provider upgrading the link quality without delay. In this paper, we explore the latter option where users threaten to quit the current provider unless he (the provider) takes immediate actions to improve the link quality. By threatening the provider, the user will have to accept the risk of having to disconnect from the current provider and reconnect to another in the middle of a communication session, should the provider defies the threat. The user therefore will have to carefully assess the merit of issuing such threats. To analyze the dynamics of this scenario, we formulate the problem as a brinkmanship game theory model. As a function of user's and provider's payoff or utility values, we derive conditions under which the user could expect to gain from adopting the brinkmanship strategy. The effect of uncertainties in payoff values are analyzed using Monte Carlo simulation, which confirms that brinkmanship can be an effective strategy under a wide range of scenarios. Since user threats must be credible to the provider for the brinkmanship model to work, we discuss possible avenues in achieving threat credibility in the context of mobile communications.