Lobbying as a multidimensional tug of war

We analyze lobbying as contest in which lobbyists exert effort to pull a policy outcome in a multidimensional space in their preferred directions. We prove existence and uniqueness of equilibrium and perform comparative statics on the cost of effort and policy utility of the lobbyists. As cost of effort increases, the equilibrium policy outcome and inefficiency (i.e., total effort expended) are constant. Assuming power utility, the equilibrium policy minimizes a social loss function that depends on curvature of utilities. As lobbyists become less tolerant of larger losses, the equilibrium policy outcome converges to the Rawlsian policy, which maximizes the payoff of the worst-off lobbyist, and inefficiency may become large or go to zero, depending on the configuration of ideal points. As lobbyists become less tolerant of smaller losses, the equilibrium outcome converges to the mean of the lobbyists’ ideal points, and inefficiency goes to zero.