EURO 2024 Copenhagen
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3515. Self enforcing agreements, delayed information and taxes in a differential game modelling extraction of common renewable resources

Invited abstract in session TA-33: Heterogeneity in optimal control problems, stream Optimal Control Theory and Applications.

Tuesday, 8:30-10:00
Room: 42 (building: 303A)

Authors (first author is the speaker)

1. Agnieszka Wiszniewska-Matyszkiel
Institute of Applied Mathematics and Mechanics, University of Warsaw
2. Rajani Singh
Department of Digitalization, Copenhagen Business School

Abstract

We analyse a differential Fish Wars game with n players and the infinite time horizon. We calculate the social optimum, a Nash equilibrium and partial cooperation equilibria. The Nash equilibrium always leads to depletion of fish, while the social optimum results in sustainability for a whole interval of parameters. Partial cooperation is in between, with the chance for sustainability growing with the number of cooperators, but only a coalition of size 2 is stable, which makes sustainability unlikely also in this regime. This is "the tragedy of the commons" in its most drastic form due to logarithmic payoff. We solve "the tragedy" by two frameworks to: either by an environmental agreement or by a tax-subsidy system. In the first framework, we analyse agreements in which each signatory reduces fishing to the social optimum level until they detect that another signatory has defected. We also assume it takes time to detect a defection. We are interested in the maximal detection time for which the agreement still remains self-enforcing. Counter-intuitively, it turns out that the more players, the higher this maximal detection time, so the more stable the agreement. Concerning the second framework, besides solving our specific "tragedy", we also propose a general algorithm for finding financial incentives enforcing the optimal profile in a large class of differential games and a large class of financial incentives or proving that such an incentive does not exist.

Keywords

Status: accepted

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