Competition and Incentive in Healthcare System: Pricing, Quality and Accessibility

Abstract

In this thesis, we study competition and incentive management in healthcare markets. First of all, we consider a service market where capacitated providers compete on prices for price- and access-sensitive patients. Stochastically arriving patients choose service providers to maximize their random utilities, which can be calibrated with a discrete choice model. Assuming that patients cannot observe queue lengths but possess structural knowledge of the market, the choice probabilities are specified as functions of prices and perceived expected waiting times, which forms a rational expectations equilibrium (REE) in steady state. We first show that there exists a unique REE under which the arrival rates are implicit functions of prices. We then analyze the structural properties of REE which allow us to develop a provably efficient fixed-point algorithm to compute the REE arrival rates. We next leverage the structural properties to characterize the equilibrium pricing decisions under REE in monopoly, duopoly, and oligopoly settings, subsequently. Furthermore, we perform a simulation study to examine the effects of misspecifying the true arrival rate model under REE as explicit logit functions of prices. Interestingly, the results show that the misspecified models, which result in suboptimal pricing decisions, may increase the profitability under competition. Lastly, the analysis is extended to the settings with observable sample average waiting times and queue lengths.

In the second part of this thesis, we study quality competition in a healthcare market under regulated prices and imperfect quality information. Each hospital is modeled as a single server and stochastically arriving patients choose hospitals (or leave if outside option is allowed) based on their perceived quality and waiting times. In particular, we formulate each patient’s perceived quality as an additive form of the true quality and a random noise and use the variations of the random noise to measure the accuracy of quality information. By assuming that patient utility functions are linear and letting the random noise follow independent and identically distributed Gumbel distributions, the discrete choice behavior of patients is represented by a multinomial logit (MNL) model. We first show that there exists a unique REE and then characterize the optimal quality decisions under regulated prices in monopoly, duopoly, and oligopoly settings, respectively. Our results show that, in general, more accurate quality information leads to better quality. However, in the presence of outside options, improvement in quality information may lead to lower quality when the quality information is sufficiently precise. Interestingly, we find that better quality information may in fact lower patient ex-ante surplus. Moreover, our results imply that the regulator should improve quality information accuracy only when the service cost and the marginal cost of improving information accuracy are both low and the current information accuracy is neither too high nor too low. Lastly, if both the quality information accuracy and payments to hospitals can be controlled, the regulator had better adjust the payments only and maintain the current quality information accuracy.

In the third part of this thesis, we investigate how to design performance-based incentives in a competitive healthcare market with imperfect quality information. We adopt a three-stage stackelberg game to model the system: the payer first designs a performance-based payment contract, hospitals then set their quality of care under the performance-based payment contract and last patients choose hospitals through utility maximization. We first characterize the optimal quality decisions under a given bonus contract, and also characterize the optimal contracting decision in a class of bonus contracts in the market without outside options. We find that in the absence of outside options, the fee-for-service reimbursement should be set as small as possible and improving quality information accuracy can lower bonus reimbursement. Moreover, the system under the optimal bonus contract can reach the social optimum when the treatment cost is small or the quality information is sufficiently noisy. Our results also show that competition intensity and performance-based incentives are substitutes to each other. For the market with outside options, we use numerical studies to show that fee-for-service reimbursement should also be set as small as possible and improving quality information accuracy can increase (decrease) bonus reimbursement when quality information is initially sufficiently precise (noisy).