A MAXIMUM PRINCIPLE APPROACH TO A DETERMINISTIC MEAN FIELD GAME OF CONTROL WITH ABSORPTION

Paulwin Graewe, Ulrich Horst, Ronnie Sircar

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study a deterministic mean field game on finite and infinite time horizons arising in models of optimal exploitation of exhaustible resources. The main characteristic of our game is an absorption constraint on the players' state process. As a result of the state constraint the optimal time of absorption becomes part of the equilibrium. Using Pontryagin's maximum principle, we prove the existence and uniqueness of equilibria and solve the infinite horizon models in closed form. As players may drop out of the game over time, equilibrium production rates need not be monotone nor smooth.

Original languageEnglish (US)
Pages (from-to)3173-3190
Number of pages18
JournalSIAM Journal on Control and Optimization
Volume60
Issue number5
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Keywords

  • maximum principle
  • mean field game
  • optimal exploitation
  • stochastic control

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