Limit-pricing as Bertrand equilibrium

Summary. We consider a Bertrand duopoly model with increasing returns to scale where one of the firms have a cost advantage and prices vary over a grid. We find that typically more than one equilibria exist. However, there are only two perfect equilibria. Moreover, as the size of the grid becomes small, both these equilibria converge to the limit-pricing outcome. Received: February 25, 2000; revised version: January 9, 2001     

Heterogeneous duopoly with isoelastic demand function

In this paper we analyze a duopolistic market with heterogeneous firms when the demand function is isoelastic (Puu, T., 1991. Chaos in duopoly pricing. Chaos, Solitons and Fractals 1, 573–581.). We consider the same heterogeneous firms of Zhang et al. (Zhang, J., Da, Q., Wang, Y., 2007. Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling 24, 138–148.) introducing a nonlinearity in the demand function instead of the cost function. Stability conditions of the Nash equilibrium and complex dynamics are studied. In particular we show two different routes to complicated dynamics: a cascade of flip bifurcations leading to periodic cycles (and chaos) and the Neimark-Sacker bifurcation which originates an attractive invariant closed curve. Comparisons with respect to the Puu model and the model of Zhang et al. are performed.     

Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty

We provide new results for two-stage games in which firms make capacity investments when demand is uncertain, then, when demand is realized, compete in prices. We consider games with demand rationing schemes ranging from efficient to proportional rationing. In all cases, there is a subgame perfect equilibrium outcome coinciding with the outcome of the Cournot game with demand uncertainty if and only if (i) the fluctuation in absolute market size is small relative to the cost of capacity, or (ii) uncertainty is such that with high probability the market demand is very large and with the remaining probability the market demand is extremely small. Otherwise, equilibria involve mixed strategies. Further, we show under efficient rationing that condition (i) is sufficient for the unique equilibrium outcome to be an equilibrium outcome of the Cournot game with demand uncertainty.     

Stakeholders’ relationships and product market competition

In this article, we study the relationships between main stakeholders (shareholders, consumers and employees) when firms are consumer oriented (CO) in the sense of caring about consumers’ interests in the objective function. We let these firms first bargain with labour union over their employees’ wages and then compete either in the quantity space (Cournot competition) or in the price space (Bertrand competition). Our model shows that taking care of the consumers’ interests when determining product market strategies may reverse the traditional ranking between Cournot and Bertrand equilibria. This implies that if shareholders in a CO firm can choose either a quantity or a price strategy, they will surprisingly choose the latter. Moreover, we show that the conflicting interests between main stakeholders are attenuated under Bertrand competition compared to Cournot competition.     

International duopoly with overseas production and strategic trade policies

This paper examines the strategic export policies in a reciprocal market model of an international Cournot duopoly where two firms in domestic and foreign countries reciprocally supply their products to other countries through overseas production as well as export. It also considers the fact that the firms must incur export costs in addition to production costs. Thus, this paper shows, among others, that the effects of export policies on firms' output and export choices do not depend on the slopes of firms' reaction curves. It is also shown that firms' total outputs are independent of the export policies, and the optimal domestic and foreign export subsidies are zero (laissez-faire).     

Competition,strategic delegation and delay in technology adoption

This paper examines how strategic managerial delegation affects firms' timing of adoption of a new technology under different modes of product market competition. It demonstrates that strategic delegation has differential impacts on adoption dates under Cournot and Bertrand competitions. Strategic delegation with ‘own-performance’-based incentive schemes always leads to early adoption in markets with Bertrand competition compared to that under no-delegation, but not necessarily so in markets with Cournot competition. It also shows that under strategic delegation with ‘own-performance’-based incentive schemes, adoption occurs earlier (later) in markets with Cournot competition than in markets with Bertrand competition, if the degree of product differentiation is high (low). In contrast, under strategic delegation with ‘relative-performance’-based incentive schemes, adoption dates do not differ across markets with different modes of competition. It also analyses implications of firms' choice over types of managerial incentive schemes on the speed of diffusion of new technology.