Applied Maths Seminar: Ewald -- A Stochastic Differential Fishery Game for a Two Species Fish Population with Ecological Interaction

Applied Maths Seminar 

Christian-Oliver Ewald, University of Sydney 

A Stochastic Differential Fishery Game for a Two Species Fish Population with Ecological
Interaction 

Wednesday 26th Aug 14:05-14:55pm, Eastern Avenue Lecture Theatre.  

We combine and extend two existing lines of research in game theoretic studies of
fisheries.  The first line of research is the inclusion of the aspect of predation and
the consideration of multi-species fisheries within classical game theoretic models of
fisheries and goes back to Quirk and Smith (1977), Anderson (1975) and most recently
Sumaila (1996).  The models developed in this line are either static or discrete time
and do not include ecological uncertainty.  The second line of research includes
continuous time and uncertainty, but focuses on single species models and does not
capture any features of ecological interaction, see for example Jorgensen and Yeung
(1996).  In this article we develop a continuous time framework, where ecological
interaction is described by a stochastic dynamics, including the cases of predator prey
and competition.  We obtain a stochastic differential game and derive feedback
Nash-equilibrium strategies in semi-analytic form.  Furthermore we compare the results
with the case where fisheries regulations restrict each fishery as to only being allowed
to fish one particular species and study the inefficiencies which arise from this.  In
addition to that, we also consider the case where fisheries cooperate.  Here we observe
quite different effects on the ecosystem, depending on whether the system is competitive
or predator prey.  

This is joint work with Wen-Kai Wang for St.Andrews.