Vessel sharing agreements under nonlinear costs

We examine a game-theoretic model of vessel sharing agreements in industries endowed with a general class of price functions and classes of convex cost functions. We study the equilibrium structure thereof—in particular, the existence of a unique equilibrium global aggregate as well as the existence of a unique equilibrium—and we provide a comparative statics analysis of consumer welfare with respect to an ordinal measure of concentration of the industry. We show that the a “high degree" of convexity of the cost functions can generate anti-competitive effects. In the presence of linear costs, the model satisfies a weak aggregative form in the sense of aggregative games. By allowing for the nonlinearity of variable cost functions, we further weaken the aggregative nature of the games considered. We provide a refined technique for treating these games in which both the equilibrium structure and the comparative statics analysis are based on the comparison of the equilibrium conditions of the players who strictly decrease their equilibrium strategies within the groups that strictly decrease the group’s equilibrium aggregate from an equilibrium with a smaller global aggregate associated with a less concentrated industry to an equilibrium with a (weakly) larger global aggregate associated with a more concentrated (but possibly identical) industry.