EURO 2024 Copenhagen
Abstract Submission

EURO-Online login

2882. Competition between hospitals with age-structured patients and negative congestion effects: a differential game approach

Invited abstract in session MD-33: Optimal control in organizations, stream Optimal Control Theory and Applications.

Monday, 14:30-16:00
Room: 42 (building: 303A)

Authors (first author is the speaker)

1. Dominika Machowska
Institute of Applied Mathematics and Mechanics, University of Warsaw
2. Michael Kuhn
Vienna Institute of Demography
3. Andrzej Nowakowski
Mathematics & Computer Sciences, University of Lodz
4. Agnieszka Wiszniewska-Matyszkiel
Institute of Applied Mathematics and Mechanics, University of Warsaw
5. Stefan Wrzaczek
Economic Frontiers, Institute for Applied Systems Analysis (IIASA)

Abstract

We explore a noncooperative game framework involving two hospitals, where treatment quality suffers under congestion. Recognizing that healthcare demand is significantly influenced by patient age, we incorporate a continuous age distribution into our model. Each hospital aims to determine the optimal treatment(age-structured) intensity that maximizes its objective: for a public hospital, this involves enhancing the cross life-expectancy as measure for the number and quality of treated patients (public hospital); for a private hospital, the goal is to maximize profits based on public payments for treatment. The resulting problem leads to the introduction of differential games with the closed-loop information structure. The paper formulates conditions for verifying whether a given strategy profile constitutes a Nash equilibrium with the dual closed-loop information structure. The verification theorem is then used to develop a numerical algorithm for determining Nash equilibria in a finite number of steps. The numerical simulations demonstrate how the Nash equilibrium can shift in response to varying socio-economic factors.

Keywords

Status: accepted

Back to the list of papers