Dynamic hospital competition under rationing by waiting times.

We develop a dynamic model of hospital competition where (i) waiting times increase if demand exceeds supply; (ii) patients choose a hospital based in part on waiting times; and (iii) hospitals incur waiting time penalties. We show that, whereas policies based on penalties will lead to lower waiting times, policies that promote patient choice will instead lead to higher waiting times. These results are robust to different game-theoretic solution concepts, designs of the hospital penalty structure, and patient utility specifications. Furthermore, waiting time penalties are likely to be more effective in reducing waiting times if they are designed with a linear penalty structure, but the counterproductive effect of patient choice policies is smaller when penalties are convex. These conclusions are partly derived by calibration of our model based on waiting times and elasticities observed in the English NHS for a common treatment (cataract surgery).