Relative Profitability of Dynamic Walrasian Strategies

The advantage of price-taking behavior in achieving relative profitability in oligopolistic quantity competition has been much appreciated recently from economic dynamics and evolutionary game theory, respectively. The current research intends to provide a direct economic interpretation as well as intuitive justification and further to build a linkage between different perspectives. In particular, a detailed illustration of an arbitrary oligopoly that produce a homogenous product is presented. So long as the outputs of other firms are fixed and the residual demand is downward sloping, for any two identical firms whose cost functions are convex, their output space can be divided symmetrically into mutually exclusive relatively profitability regimes. Furthermore, there exist infinitely many relative-profitability reactions for each firm in such residual duopoly, all of which intersect at the residual Walrasian equilibrium. This suggests that sticking to this dynamical equilibrium output constantly (i.e., the static Walrasian strategy) turns out to be a relative-profitability strategy at each period. On the other hand, regardless of what strategies its rival may take, a firm adopting price-taking strategy or more generally defined dynamic Walrasian strategies can achieve the relative profitability if an intertemporal equilibrium is reached. The methodology adopted and the conclusions arrived clarify the confusions and misunderstandings due to the different usages of same terminologies under different frameworks and generalize the previous available results in the literature to a higher level and a broader context.