Application of bargaining schemes for equilibrium determination in dynamic games

Владимир Викторович Мазалов; Vladimir Mazalov; Анна Николаевна Реттиева; Anna Rettieva

doi:10.17076/mgta_2023_2_76

Владимир Викторович Мазалов Institute of Applied Mathematical Research KarRC RAS; Saint Petersburg State University
Vladimir Mazalov Institute of Applied Mathematical Research KarRC RAS; Saint Petersburg State University
Анна Николаевна Реттиева Institute of Applied Mathematical Research KarRC RAS; Saint Petersburg State University
Anna Rettieva Institute of Applied Mathematical Research KarRC RAS; Saint Petersburg State University

DOI: https://doi.org/10.17076/mgta_2023_2_76

Keywords: dynamic games, asymmetric players, multicriteria games, cooperative equilibrium, bargaining scheme

Abstract

Cooperation plays an important role in dynamic games related to resource management problems. To construct the cooperative behavior in asymmetric (when players possess different discount factors) and multicriteria (when players have vector payoff functions) dynamic games the standard approaches are not applicable. The paper presents the methods based on bargaining schemes to determine the cooperative equilibria in such games. The cooperative strategies and payoffs in asymmetric dynamic games are obtained via the Nash bargaining scheme, while for the multicriteria dynamic games the modified bargaining schemes are applied. To illustrated the presented approaches, dynamic bioresource management problems (fish wars problem) with asymmetric players and vector payoff functions is investigated.