Collusion and heterogeneity of firms

Abstract

We examine the impact of heterogeneous discounting on collusion in dynamic Bertrand competition. We show exactly when collusion can be sustained and how collusion would be organized efficiently with heterogeneous discounting. First, we show that collusion is possible if and only if the average discount factor exceeds a certain threshold, with or without capacity constraints. Next, we identify a dynamic pattern of market share that characterizes efficient collusion and obtain the unique long‐run prediction despite the presence of multiple equilibria. In the long run, the most patient firm and the most impatient firm tend to dominate the market.

Self-Enforcing Price Leadership

“…The described setting is a special case of Obara and Zincenko [13]. They consider a Bertrand oligopoly with complete information in which firms can have different discount factors.…”

“…The discount factor threshold, δ s l ,s h , is equal to 1/2 when the ratio s l /s h is below 1 − 1/ √ 2 ≈ 0.293, and it is increasing on s l /s h when the ratio is above 1 − 1/ √ 2. Obara and Zincenko [13] show that δ ≥ 1/2 is a necessary and sufficient condition for having a collusive outcome in an infinitely-repeated Bertrand duopoly with complete information. 4 Therefore, in the limit case (when φ = 0), no collusion of any type could be possible when δ < 1/2.…”

“…Based on this result, we should expect that result to hold as φ approaches 0. In that case, if the ratio s l s h is sufficiently small and the shocks become sufficiently persistent, price leadership is an equilibrium whenever a collusive equilibrium is possible (more precisely, the discount factor threshold δ s l ,s h is the same as the minimum threshold in Obara and Zincenko [13]).…”