Nash equilibrium can resolve conflicting maximum sustainable yields in multi-species fisheries management

The current fisheries management goals set by the European Commission states that fish stocks should be harvested to deliver maximum sustainable yields (MSY) and simultaneously, management should take ecosystem considerations into account. This creates unsolved trade-offs for the management of the stocks. We suggest a definition of a multi-species-MSY (MS-MSY) where no alternative fishing mortality (F) can increase yield (long term) for any ecologically interacting stock, given that the other stocks are fished at constant efforts (Fs). Such a MS-MSY can be solved through the game theoretic concept of a Nash equilibrium and here we explore two solutions to this conflict in the Baltic Sea. We maximize the sustainable yield of each stock under two constraints: first, we harvest the other stocks at a fixed F (FNE); second, we keep the spawning stock biomasses of the other stocks fixed [biomass Nash equilibrium (BNE)]. As a case study, we have developed a multi-species interaction stochastic operative model (MSI-SOM), which contains a SOM for each of the three dominant species of the Baltic Sea, the predator cod (Gadus morhua), and its prey herring (Clupea harengus), and sprat (Sprattus sprattus). For our Baltic Sea case, MS-MSYs exist under both the FNE and the BNE, but there is no guarantee that point solutions exists. We found that the prey species' spawning stock biomasses are additive in the cod growth function, which allowed for a point solution in BNE. In the FNE, the herring MSY was found to be relatively insensitive to the other species' fishing mortalities (F), which facilitated a point solution. The MSY targets of the BNE and the FNE differ slightly where the BNE gives higher predator yields and lower prey yields.