The Kinked Demand Model and the Stability of Cooperation

This paper focusses on a particular behaviour for firms competing in imperfect competitive markets firstly theorized in the late 30s by a number of well known economists (Robinson (1933), Sweezy (1939)). This is the well known model of kinked demand curve, basically predicting an asymmetric behaviour of every firm in response to a price change: each firm expects its rivals to be more reactive in matching its price cuts than its price increases. Although this theory has been often criticized as not theoretically grounded, we show that this is not the case. In particular, in a symmetric and monotone market, we prove that, if every firm accepts a simple kinked-demand norm of behaviour (KD), the perfectly collusive outcome (monopoly pricing) constitutes an equilibrium. We show that this result is rather robust and can be extended to all symmetric strategic form games in which players are allowed to deviate either individually or in a coordinated manner as coalitions of players: a KD norm of behaviour always makes the efficient outcome (the one maximizing the sum of all players' utility) stable. Also, we show that a slightly stronger norm of behaviour (implicitly implying a norm of reciprocity) makes the efficient outcome the only stable outcome of the game. Finally, the KD norm of behaviour can also be considered rational whenever players' actions are strategic complements in the sense of Bulow et al. (1982).