Tacit collusion with price-matching punishments

Abstract

JEL classification: L11 L12 L13 L41Keywords: Collusion Intertemporal reaction functions Kinked demand curve Tacit collusion is explored under a strategy in which, loosely speaking, firms match the lowest price set by any firm in the previous period. Conditions are provided under which this strategy supports collusive outcomes in a subgame perfect equilibrium. In contrast to traditional results, the highest collusive price is always lower than the monopoly price. It corresponds to the unique Nash equilibrium price when upward and downward price deviations are matched. Our paper provides a game theoretic interpretation of the old kinked demand curve theory which unlike earlier attempts does not depart from standard timing assumptions to do so.

Collusive price rigidity under price-matching punishments

“…If it deviated to Z, however, then Z is matched in future low-cost states, otherwise p N (c, n) is set. Departing slightly from the kinked demand curve but consistent with Lu and Wright (2010), firms do not match prices below p N (c t , n) in period t because doing so seems unreasonable. This assumption is not crucial in determining the range of rigid prices for which collusion is sustainable or the parameter space where the best collusive prices are rigid.…”

“…Drawing on the insights of Lu and Wright (2010), we assume that firm i's price-matching punishment strategy profile for all t is of the form:…”

“…Since it is less profitable to deviate in a period of high costs than one of low costs, the (constrained) optimal 'deviation' price from the best rigid price in a period of high costs also equals the best rigid price. 8 The best rigid price is equivalent to the best collusive price analysed by Lu and Wright (2010) as c → 0, and it is strictly increasing in the level of high costs. The reason is that a given rigid price is easier to support in a period of low costs when the high-cost level is closer toĉ than when it is close to zero, because the long-term loss from a small deviation increases with c. In contrast to Lu and Wright (2010), the monopoly price of the low-cost state may be supportable.…”

“…This provides game theoretic support for the results of the kinked demand curve. We derive this result by extending Lu and Wright (2010) who analyse an infinitely repeated game where, similar to the kinked demand curve, firms match lower deviation prices (provided they are above the oneshot Nash equilibrium price) but do not match higher deviation prices. They show that collusive prices are sustainable under such "pricematching punishments" when products are symmetrically differentiated and when market conditions do not vary over time.…”

Collusion in two models of spatial competition with quantity-setting firms

“…See alsoLu and Wright (2010) for a "price-matching" punishment mechanism instead of the traditional grim trigger punishment mechanism. 3 The only exception we are aware of is the forthcoming paper byAndaluz (2010), where Cournot competition is also discussed.…”