This paper aims at explaining the recent rise in profits in the French Guiana shrimp fishery (FGSF) despite the overall fall in activity observed between 1990 and 2009. We develop a stochastic search‐matching version of the usual Cobb–Douglas bioeconomic fishery model. In this version catch per unit effort becomes endogenous, decreasing in the ratio of empty vessels to escaped fish, which we call “anthropic pressure” and which is determined by standard profit maximization. We first estimate the stochastic harvest function, which exhibits nearly constant returns to scale. We then show that a decrease in equilibrium anthropic pressure and congestion between vessels may be more than compensated by the consecutive rise in catch per unit effort. This leads to a fall in average harvesting costs and thus, to a rise in profits. In addition, we identify the condition under which a search‐matching fishery, working under open access, could reach a maximum economic yield equilibrium, which corresponds to a very particular case. Finally, the model makes it possible to evaluate the actual catch per unit effort and explain how the FGSF changed over the period considered with the help of the open access and maximum economic yield frameworks.