# Repeated Games and Price Wars

## Abstract

This paper is an attempt to reconcile the – at first sight different – views on the determinants of collusion and price wars expressed in Rotemberg and Saloner (1986), Green and Porter (1984), and Stigler (1964). We first argue that the logic of Rotemberg and Saloner (1986) presupposes two determinants for collusion, namely (1) market shares are publicly observable, and (2) volatility of market shares due to exogenous factors is limited. We make our arguments in a model in which firms repeatedly play a Bertrand type price competition game, while market shares are determined by a stochastic process, conditional on current market shares and prices. Following Rotemberg and Saloner (1986), we show under the two conditions of public observability and limited volatility of market shares that firms can collude using dynamic price adjustment strategies. We show that when the first condition (public observability) is violated, we revert to the logic of Green and Porter (1984). When the second condition (limited volatility of market shares) is violated, for example when consumer loyalty has decreased, we also observe that collusion can no longer be sustained, in line with the arguments in Stigler (1964).

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