Evolutionary oligopoly models of commercial fishing with heterogeneities

n this paper we provide an overview of some recent dynamic models of commercial fisheries. Our starting points are the papers by Okuguchi (Keio Econ Stud 35: 9-17, 1998) and Okuguchi and Szidarovszky (Seoul J Econ 11(3): 321330, 1998) and Szidarovszky and Okuguchi (Seoul J Econ 13: 471-476, 2000) on oligopoly competition in international fisheries, which are based on the assumptions of homogeneous fish population, homogeneous space and continuous time. Following also insightful hints given in Okuguchi (Keio Econ Stud 21: 37-44, 1984) and Erjaee and Okuguchi (Keio Econ Stud 41: 61-71, 2006), we describe how some heterogeneities can be introduced in fishery models. The examples provided in this paper include bioeconomic models of fisheries with several species and with different time scales, ranging from continuous-time to discrete-time dynamic models and also addressing hybrid models, where some variables evolve in continuous time whereas other ones change in (event-driven) discrete time. Fishery models where the aquatic environment is subdivided into adjacent patches, characterized by different fishing policies including, as a particular case, Marine Protected Areas, are also described. Finally, we describe a fishery models with cooperators and defectors and punishment policies to encourage cooperation. All the models described in this overview include an evolutionary mechanism, based on imitative behavior, through which fishers are allowed to change their harvesting strategy over time. Some of these models have been motivated by projects or management experiences performed in the Adriatic Sea by Italian fishing authorities.