Review of Industrial Organization
13: 333–345, 1998.
1998 Kluwer Academic Publishers. Printed in the Netherlands.
Sustaining Collusion via a Fuzzy Trigger
RACHAEL E. GOODHUE
Department of Agricultural and Resource Economics, University of California at Davis, CA, U.S.A.
Abstract. Probability theory is the standard economic representation of uncertainty, although it is not
always an accurate one. Fuzzy logic is an alternative representation that does not require individual
beliefs regarding the explicit functional form of uncertainty. This paper applies fuzzy logic to an
oligopoly trigger pricing game. The fuzzy trigger pricing game reverses the standard cyclical price
war prediction; collusion-sustaining price wars are most likely to occur during times of high demand.
The fuzzy model also predicts that markets with relatively volatile prices are more likely to undergo
collusion-sustaining price wars. The predictions are consistent with available empirical evidence.
Key words: fuzzy logic and economics, uncertainty and information, trigger prices, collusion.
The representation of information and uncertainty underlies conclusions derived
from economic analysis. The neoclassical economic framework uses random vari-
ables to represent uncertainty and people’s beliefs over outcomes, so that pre-
dictions regarding economic behavior under uncertainty are based on probability
theory. The profession has adhered to this analytical framework in spite of exper-
imental evidence, such as the well-known Allais paradox, that people’s choices
under uncertainty do not always follow the laws of probability. This paper con-
siders an alternative possibility-based representation of uncertainty, applies it to
sustaining collusion in an oligopoly using a trigger price, and compares the results
obtained in this framework to those from the standard approach. Fuzzifying the
trigger price game reverses Green and Porters’ (1984) conclusion regarding the
cyclical nature of price wars; in the fuzzy trigger game, price wars are more likely
to occur during an expansionary period.
For many years, economists regarded price wars as prima facie evidence of
competitive behavior or the breakdown of collusive behavior. When trigger strate-
gies were ﬁrst formally modeled, price wars were never observed in a collusive
equilibrium (Friedman, 1971). Green and Porter (1984) reversed the convention-
al wisdom. They demonstrated that price wars can be evidence of sustainable
collusion over a long period of time in the presence of demand uncertainty. In equi-
I would like to thank Jill McCluskey, Gordon Rausser, Leo Simon, Lotﬁ Zadeh, two anonymous
referees and the editor of this journal for their comments on this paper, and the National Science
Foundation for the support provided by a NSF Graduate Fellowship. Responsibility for any remaining
mistakes or omissions is my own.