Research of the problem of fair distribution of fishing quotas by the methods of game theory

Game theory emerged as a science in the second half of the 20th century. It managed to prove itself well in the analysis of economic situations involving several subjects of economic activity (players), whose interests are completely or partially opposite. At the same time, in a number of cases, the solution of the game satisfied all players, but was not the most profitable (there was a Nash equilibrium), and in a number of other cases, it was possible to take into account the interests of all parties to the maximum (there was a Pareto optimal solution). The transfer of the principles of game theory to other areas turned out to have a number of difficulties associated, among other things, with the correct interpretation of strategies and gains of the parties in a conflict situation. For this reason, despite the obvious benefit from the possible application of game theory methods to problems of a fair distribution of quotas for catching fish and other seafood, this step has not been taken until recently.
In this paper, we consider a scheme for applying the algorithms of the theory of bimatrix and cooperative games on the example of solving the problem of finding the percentage of the allowable catch of the black halibut in the Barents Sea for two countries participating in the catch and give a meaningful interpretation of the results. The basis for the calculations was real data collected by the Russian–Norwegian Fisheries Commission in recent decades to determine the proportions of the catch of the indicated fish species in the respective sea zones. Since not all components of the payoff matrices of the players are uniquely determined, it became possible to perform a parametric analysis of the mathematical model of the conflict situation both in the search for an equilibrium solution and in the implementation of the arbitration scheme.
The work is an extended and supplemented version of the report [2].