Oligopolistic Entry Deterrence under Incomplete Information
Recent work has investigated the effects of asymmetric information between an incumbent firm and a potential entrant. This study extends the analysis to allow the initial market structure to be a noncooperative oligopoly. We show that there is a Bayesian Nash equilibrium in which the incumbent firms, although unable to collude, strategically deter entry that would have occurred under complete information. In contrast to the past limit-pricing literature, it is a high price that deters entry as it signals to the potential entrant that this is a high-cost industry. Extending the model to allow for multiple potential entrants, we find that increasing the degree of potential competition raises the preentry price and reduces the likelihood of entry.
Given ?>0 andp?(0,1), we consider the following problem: findu such that $$\begin{gathered} - \Delta u + \lambda [u]_ + ^p = 0in\Omega , \hfill \\ u = 1on\partial \Omega , \hfill \\ \end{gathered} $$ whereΩ??2 is a smooth convex domain. We prove optimalH 1 andL ? error bounds for the standard continuous piecewise linear Galerkin finite element approximation. In addition we analyse a more practical approximation using numerical integration on the nonlinear term. Finally we consider a modified nonlinear SOR algorithm, which is shown to be globally convergent, for solving the algebraic system derived from the more practical approximation.