François Salanié

In the canonical partial equilibrium setting, firms with arbitrary cost functions sell an homogenous good to the demand side. Consider an allocation for which all trades take place at the same price, and balance demand exactly. This allocation is said to be robust to undercutting if a firm cannot increase profits by undercutting its competitors. We fully characterize the set of these allocations. This set includes the set of competitive equilibria, but it may also include other allocations with higher prices, for which the First Welfare Theorem fails. We also show that the set of these allocations coincides with the set of equilibrium outcomes of a simple competitive game in which firms compete in limit orders. Hence, these allocations have a strategic foundation with non-negligible firms, in contrast to competitive allocations.