A Coalitional Great Fish War Model with Quasi-Hyperbolic Discounting

This paper studies the coalitional great fish war model in a setting with βδ-preferences (or quasi-hyperbolic discounting). We derive the equilibrium strategies and payoffs in this coalition game under non-cooperation, full cooperation, and partial cooperation, under simultaneous moves and with first-mover advantage for the coalition. We focus on the effects of the short-run discount factor β on the sustainability of cooperation. We find that the introduction of quasi-hyperbolic discounting can have a significant impact on the existence of stable coalitions. In particular, in contrast with the standard case of exponential discount functions, in which the coalitions of more than two players are always unstable under simultaneous moves, the grand coalition can be stable if the bias towards the present is sufficiently high (i.e., for small values of β). In addition, we show that, under simultaneous moves, there can be up to three sustainable coalitions, including the grand coalition, and larger coalitions are better from an ecological perspective, since total harvesting is lower. Thus, the consideration of quasi-hyperbolic discounting offers a promising avenue to address the challenge posed by small coalitions.