Cooperative game theoretic results from the tuna fishing problem

Abstract Bergantiños et al. (2023) introduce cooperative tuna fishing games. We prove that the core of this game is not empty. We give an explicit formula for the $$\tau $$ -value. We also study the distance game associated with tuna fishing games and prove that it is a generalized big boss game. In most practical cases, the number of vessels is two or three. In these cases, the core and the core cover coincide. Moreover, we provide an explicit formula for the nucleolus.