The literature on game theory and fisheries is reviewed, beginning with the initial papers from the late 1970s on cooperative and noncooperative games. Later developments considered repeated games and trigger strategies as well as the stability of coalitions. It is argued that the latter literature is overly pessimistic in that it does not pursue breakdown of successive coalitions to its ultimate end, which may provide a worse outcome than an apparently unstable coalition. The choice of strategic variable is considered at some length, but in the existing literature this choice is seldom explicitly motivated. Similarly, the spatial distribution of fish is seldom analyzed in the existing literature, but it could make a difference. This article looks at fishing in a common pool, fishing in separate pools with interacting substocks, and sequential fishing. Fishing on the high seas is discussed and the enforcement issue identified as an underresearched problem. Imperfect information on fish stocks and their migrations is also underresearched.

The sharing of the Northeast Atlantic mackerel (Scomber scombrus) stock is analysed as a game between four parties: the European Union, Norway, the Faroe Islands, and Iceland. Consideration is given to how the outcome depends on the nature of the stock's migrations. Two types of migrations are considered: (i) density-dependent, where the mackerel migrates into the Icelandic economic zone only if it exceeds 3.5 million t, and (ii) stochastic migrations, where the said migrations are stochastic. It is determined that the Faroe Islands would never accept a cooperative solution wherein they can only fish with the globally optimal fishing mortality within their own zone. This is also true for Iceland when the migrations into her zone are stochastic, but not if they are density-dependent. In the latter case, the other players have incentives to retaliate to Icelandic overfishing by fishing harder, which greatly reduces the number of years when mackerel are available in the Icelandic zone. It is assumed that the objective is maximization of the catch volume over a time-horizon of 50 years.