Kinked norms of behaviour and cooperation
Research Highlights
► Firms’ behaviour in the kinked demand model is interpreted as a behavioural rule. ► We show that this rule possesses strong stability properties. ► It makes a symmetric efficient strategy profile stable in all symmetric games. ► A symmetric social norm makes the efficient profile the unique stable profile.
Introduction
This paper focusses on the postulated behaviour of firms competing in imperfect competitive markets, first theorized in the late 30s by a number of well known economists (Robinson, 1933, Sweezy, 1939), and best known as the “kinked demand model”. This basically predicts an asymmetric behaviour of firms in response to a price change, each expecting its rivals to be more reactive in matching its price cuts than its price increases. This prediction has been empirically tested by Hall and Hitch (1939) and later by Bhaskar et al. (1991), extensively criticized as not grounded in rational behaviour by Stigler, 1947, Domberger, 1979, Reid, 1981 and more recently analyzed in a dynamic settings by Marschak and Selten, 1978, Maskin and Tirole, 1988, Bhaskar, 1988.
In this paper we add to this debate by showing that this behavioural rule possesses strong stability properties and, therefore, may sustain firms' collusion. In particular, in a symmetric and monotone market, we prove that, if every firm adopts and expects a simple kinked demand social norm of behaviour (KSN), the symmetric collusive outcome (i.e. monopoly pricing) constitutes an equilibrium. We show that this result is rather robust and can be extended to all n-person symmetric strategic form games: a KSN always makes the symmetric efficient strategy profile (the one maximizing the sum of all players' utility) stable. Moreover, we show that under some additional standard assumptions on players' payoff functions, a slightly stronger norm of behaviour (implicitly implying a norm of reciprocity) makes the efficient outcome the only stable outcome of the game.
The paper is organized as follows. The next section introduces a game-theoretic setting. Section 3 concludes.
Section snippets
A general setting
We first introduce a class of games in which players are endowed with the same strategy space and perceive symmetrically all strategy profiles of the game. Moreover, players' payoffs possess a monotonicity property with respect to their opponents' choices. Although very specific, this setting still covers many well known economic applications (as Cournot and Bertrand oligopoly, public goods games and many others). We denote a monotone symmetric n-player game in strategic form as a triple G = (N, (X
Concluding remarks
In this paper we have shown that, for all symmetric and monotone strategic form games, the behaviour postulated by the classical model of kinked demand possesses strong stability properties. Such a result holds even stronger when players expect a fully symmetric norm of behaviour by all remaining players in the event of an individual deviation. In this case, the perfectly cooperative (collusive) outcome becomes the only stable outcome of the game, As a consequence, firms may implicitly adopt
Acknowledgments
We wish to thank Gani Aldashev, Tom Kirchmaier, Jorn Rothe and all participants to seminars at the London School of Economics, University of Venice and University of Urbino.
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