Apparent collusion and conjectural variations in differentiated oligopoly

The conjectural variations model has become the standard exposition of oligopoly theory, although rivals' assumed behaviour is not profit-maximising. One response has been models with consistent conjectures, developed from rational expectations concepts. This paper adopts another approach, based on Stigler's famous (1964) paper. Collusion is enforced by the threat of retaliating to price cuts, but is imperfect because of their imperfect knowledge, which limits the probability of retaliation, or retaliation lags. Three models of imperfect collusion incorporating these features, separately and in combination, demonstrate the formal equivalence between the results of imperfectly policed collusion and proportional conjectural variations.