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Numerical versus analytic calculation of optima and equilibria in Fish Wars model with finite time horizon
- Speaker(s)
- Rajani Singh
- Date
- March 16, 2016, 2:15 p.m.
- Room
- room 4050
- Seminar
- Seminar of Biomathematics and Game Theory Group
In our research, we analyse a model of Fish Wars, first introduced by
Levhari and Mirman, restricted to finite time horizon. In this models, dynamic games of extraction of common fishery by n>2 countries is studied, with logarithmic instantaneous and terminal payoffs and exponential function of regeneration of the biomass. We are interested in Nash equilibria and a profile resulting from maximization of aggregate payoff. We study it both by analytic and numerical methods and compare results. Since for this model, analytic results can be easilty calculated, comparison of numerical and analytic results is possible. However, if the model is seriously modified, then analytic calculation of optima and equilibria ceases to be feasible. In such a case, only numerical methods can be used. Therefore, analysis of dynamic games of this type using numerical methods is really needed.
Although we study a specific model, one of more general objectives of the presentation is to answer the question, whether using numerical methods in a dynamic game model with a singularity in payoff, which results from considering instantaneuous and terminal payoffs with logarithmic part, can result in reasonable oucomes. Suprisigly, in this study, the answer is positive.
Levhari and Mirman, restricted to finite time horizon. In this models, dynamic games of extraction of common fishery by n>2 countries is studied, with logarithmic instantaneous and terminal payoffs and exponential function of regeneration of the biomass. We are interested in Nash equilibria and a profile resulting from maximization of aggregate payoff. We study it both by analytic and numerical methods and compare results. Since for this model, analytic results can be easilty calculated, comparison of numerical and analytic results is possible. However, if the model is seriously modified, then analytic calculation of optima and equilibria ceases to be feasible. In such a case, only numerical methods can be used. Therefore, analysis of dynamic games of this type using numerical methods is really needed.
Although we study a specific model, one of more general objectives of the presentation is to answer the question, whether using numerical methods in a dynamic game model with a singularity in payoff, which results from considering instantaneuous and terminal payoffs with logarithmic part, can result in reasonable oucomes. Suprisigly, in this study, the answer is positive.
