Feedback Nash equilibria for non-linear differential games in pollution control. (English) Zbl 1181.91252
Summary: Dynamic problems of pollution and resource management with stock externalities often require a differential games framework of analysis. In addition they are represented realistically by non-linear transition equations. However, feedback Nash equilibrium (FBNE) solutions, which are the desired ones in this case, are difficult to obtain in problems with non-linear-quadratic structure. We develop a method to obtain numerically non-linear FBNE for a class of such problems, with a specific example for shallow lake pollution control. We compare FBNE solutions, by considering the entire equilibrium trajectories, with optimal management and open-loop solutions, and we show that the value of the best FBNE is in general worse than the open-loop and optimal management solutions.
MSC:
| 91B76 | Environmental economics (natural resource models, harvesting, pollution, etc.) |
| 91A23 | Differential games (aspects of game theory) |
| 91A80 | Applications of game theory |
Keywords:
differential games; pollution control; non-linear feedback Nash equilibrium solution; Abel equation; open-loop; optimal managementReferences:
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