We analyze a Bertrand-Edgeworth game in a homogeneous product industry, under efficient rationing and constant (and identical across firms) marginal cost until full capacity utilization. We solve for the unique equilibrium in a subset of the no pure strategy equilibrium region of the capacity space in which differences in individual capacities are sufficiently small.
DasguptaP.MaskinE. (1986). The existence of equilibria in discontinuous economic games, I: Theory. Review of Economic Studies, 53(1), 1–26.
2.
DavidsonC.DeneckereR. (1984). Horizontal mergers and collusive behavior. International Journal of Industrial Organization, 2(2), 117–132.
3.
De FrancescoM.A.SalvadoriN. (2010). Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly. MPRA working paper No. 24087.
4.
HirataD. (2009). Asymmetric Bertrand-Edgeworth oligopoly and mergers. The B.E. Journal of Theoretical Economics. Topics, 9(1), 1–23.
5.
KrepsD.ScheinkmanJ. (1983). Quantity precommitment and Bertrand competition yields Cournot outcomes. Bell Journal of Economics, 14(2), 326–337.
6.
OsborneM.J.PitchikC. (1986). Price competition in a capacity-constrained duopoly. Journal of Economic Theory, 38(2), 238–260.
7.
VivesX. (1986). Rationing rules and Bertrand-Edgeworth equilibria in large markets. Economics Letters, 21(2), 113–116.