Our paper investigates the effects of introducing performance-based incentives in a competitive healthcare market. We consider a market in which a payer applies a performance-based compensation contract to two competing hospitals. We use G/G/m queueing dynamics to describe the patient care process and include information asymmetry between the payer and the hospitals regarding the hospital operating costs. Our paper is the first to study the performance-based contracting problem in a healthcare market in the presence of competition on both the quality of and the access to care and the cost information asymmetry between the payer and care providers. We analyze the socially optimal and Nash equilibrium outcomes under bonus compensation where each of the competing hospitals is rewarded based on patient benefits delivered at that hospital. We show that both the stronger competition among hospitals and the introduction of bonus incentives can enhance patient benefits. Furthermore, we demonstrate that, in the presence of information asymmetry between the payer and the hospitals regarding hospitals' operating costs, the social welfare loss generated by the fee-for-service compensation as well as by the optimal bonus contract can be partially mitigated by increasing the degree of competition for patients. Such mitigation effect is amplified when the potential cost differential between the hospitals is sufficiently high and, simultaneously, the correlation between their cost parameters is not too negative.