Endogenous Timing and Strategic Choice: The Cournot‐bertrand Model

Abstract

Cournot establishes a Nash equilibrium to a duopoly game under output competition; Bertrand finds a different Nash equilibrium under price competition. Both treat the strategic choice variable (output versus price) and the timing of play as exogenous. We investigate Cournot-Bertrand models where one firm competes in output and the other competes in price in both static and dynamic settings. We also develop a general model where both the timing of play and the strategic choice variables are endogenous. Consistent with the conduct of Honda and Scion, we show that Cournot-Bertrand behaviour can be a Nash equilibrium outcome.

Union Bargaining in an Oligopoly Market with Cournot-Bertrand Competition: Welfare and Policy Implications

“…Because one firm competes in price, efficient bargaining is not possible with the Cournot-Bertrand model. 9 Operationally, the inverse demand Equations (1) and (2) Consistent with the analysis of the Cournot-Bertrand model without a union (Tremblay and Tremblay [16] and Tremblay, et al [8]), our model generates an asymmetric equilibrium where the Cournot-type firm has the strategic advantage (as long as d > 0). Given the high degree of heterogeneity in firm behavior, bargaining costs may be substantially higher in the Cournot-Bertrand model, an issue we take up in the next section.…”

“…As discussed in the introduction, the Kreps and Scheinkman [9] model reflects the idea that firms will prefer price competition when prices are inflexible relative to production. In addition, Tremblay, et al [8] show that the mix of Cournot-Bertrand behavior can be supported when there are suitable demand or cost asymmetries to induce just one firm to behave as a Bertrand competitor. In furniture manufacturing, for example, capacity may adjust relatively slowly for mass-producers, causing them to behave as Cournot competitors.…”

“…In an industry with a relatively fixed-proportion technology, efficient bargaining forces firms to compete in output (as in Cournot). From the firm's perspective, however, there are market conditions under which Bertrand or Cournot-Bertrand competition is preferred to Cournot competition (Kreps and Scheinkman, [9]; Tremblay, et al [8]). If the cost of switching from price to output competition is sufficiently high, these firms will reject Cournot competition and efficient bargaining.…”

“…In models with the demand and cost structures described above, the dominant strategy is to compete in output (Singh and Vives [14]; Tremblay, et al [8]). This result holds when a union is added.…”

“…This produces the following demand function for firm i: (8) where subscript i identifies Firm 1 or 2 and subscript j identifies the other firm. In each model, we calculate the SPNE, using backwards induction.…”