WELFARE MEASUREMENT AND COST-BENEFIT ANALYSIS IN NASH AND STACKELBERG DIFFERENTIAL FISH GAMES

ABSTRACT. This paper develops welfare measures and cost-benefit rules in Nash and Stackelberg differential fish games. The model consists of two fisheries competing on a common fishing ground, but the results are valid in more general settings. Under steady state conditions, the present value of the fisheries' future profit is directly proportional to the current profit plus the value of the net investments in the fish population (the Hamiltonian). Outside the steady state, the rule must, under a Nash game, be modified by adding the present value of the marginal harm done to the fishery by the competitor's future catches to the Hamiltonian. Under a Stackelberg game the present value of the leader's future profit remains proportional to the value of his Hamiltonian.