Fish are an extremely important resource worldwide, for nutritional and economic reasons. However, many fish stocks are being exploited at an ecologically unsustainable level. It is thus of importance that fisheries’ management strategies can be found which will allow signif- icant amounts of fishing to occur, while protecting these renewable resources for the future. In this thesis we are particularly concerned with situations where individual economic inter- ests and environmental concerns coincide. We use behavioral models of individual fishers to investigate how individual profit motivation leads to aggregate fishing behavior. These are coupled with a variety of fish population models, in order to obtain a picture of how this exploitation impacts the fishery. We pay consideration to the economic value of the fishery, as well as using population abundance as a proxy for ecological health. This approach is viewed through the lens of game theory.

In Chapter 2 we consider a dynamic size spectrum PDE model of a single fish popula- tion, which is supported by a producer spectrum of plankton on which the juvenile fish prey. This size spectrum model gives the abundance of the fish population by the size of its con- stituent members, by tracking the transfer of biomass that occurs throughout the population due to predation, mortality, and reproduction. This size spectrum model is paired with an individual based model of many fishers exploiting the population in a small scale open ac- cess fishery. We allow individual agents to change their own size-selectivity behavior, and to make the choice of whether or not to fish in order to meet profit expectations. We find that the aggregate size-selective harvesting behavior reaches a Nash equilibrium, in which

we also observe balanced harvesting of the fish stock. Furthermore, the number of active agents in the fishery converges over time. Results from this chapter have been submitted for publication.

In Chapter 3, we consider the classic Gordon-Schaefer bioeconomic model of a fishery from a non-cooperative game theory perspective. We frame exploitation as a symmetric 2-player game in which fishers take action by selecting a harvesting intensity. For a fish population at equilibrium, we find a level of fishing effort that strictly dominates all other actions, as well as a Pareto optimal frontier where the total exploitation is equivalent to that of a monop- olist. Consequently, this game is structurally equivalent to an Iterated Prisoners Dilemma. We extend our analysis to non-equilibrium populations using numerical simulations, and evaluate the relative performance of well-known strategies for an IPD (such as tit-for-tat) in these conditions.

In Chapter 4, we use a Markov decision process framework to find an optimal exploitation policy for a monopolist in a noisy environment. Optimal policies map from the population biomass to the level of fishing effort which will maximise the current and future value of the fish stock. Fish populations were modelled using a Beverton-Holt process to allow for the inclusion of noise in the stock recruitment relationship. Increasing stochasticity in the population was found to reduce the optimal fishing intensity with respect to biomass. This analysis was then extended in Chapter 5 to a Markov game situation in which there are two independent fishers acting to maximize profit. A combination of fishing policies that was a Nash equilibrium was obtained.

The thesis concludes with Chapter 6, where we summarise the thesis and present some directions for future research.