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Game theoretical model of harvesting two species of fish. (English) Zbl 0874.90215

We consider a nonlinear model of harvesting two species of fish, the dynamics of which is described by a Lotka-Volterra system of state equations. The problem of minimizing the cost functions of the players is solved in two ways using as principles of optimality the Nash equilibrium and the Stackelberg equilibrium, applying Pontryagin’s maximum principle. To compare the two different ways of solution we include an example of calculating Nash and Stackelberg equilibrium with equal initial data. It is shown that the Stackelberg equilibrium gives a more accurate result and it seems to be more correct to use for the calculation of the strategies of the players. But in this case we faced the problem of time inconsistency. To overcome it we used a regularization method (see Zakharov, 1994) which supposes to consider differential games with payoffs being transferable during the time.

MSC:

91A23 Differential games (aspects of game theory)
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
91A65 Hierarchical games (including Stackelberg games)
91B62 Economic growth models
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