In this paper, we present a simple framework to study competition, cooperation and bargaining options among fisheries when they operate under financial and technological constraints. Competition within constraints leads to a particular type of mathematical game in which the strategy choice by one player changes the strategy set of the other. By studying the equilibria and bargaining space of this game when players maximize either profit or yield, we show that differences in financial constraints among players lead to a tougher play, with a reduced bargaining space as the least constrained player can readily exclude another from the competition. The exacerbating effects of constraints on competition are particularly strong when players maximize yield. We discuss the significance of our results for fisheries management in a current context of financialization and technological development. We suggest that in order to maximize the chances of fruitful negotiations and aim towards a fair sharing of sea resources, it would be helpful to focus on leveling current differences in the constraints faced between competing fishing systems, notably by supporting local financial systems and technological control.