|
Description
Previous literature has shown that demand fluctuations affect the scope for tacit collusion. I study whether discount factor fluctuations can have similar effects. I find that collusion depends not only on the level of the discount factor but also, and more surprisingly, on its volatility. Collusive prices and profits increase with a higher discount factor level, but decrease with its volatility. These results have important implications for empirical studies of collusive pricing, the role that collusive pricing may play in economic cycles and the study of cooperation in repeated games.
1. Introduction
* It is well known that oligopolies can use the threat of future price wars to sustain prices above competitive levels if firms care enough about the future (Friedman, 1971). The extent to which firms care about the future depends primarily on the interest rate if the firms' objective is to maximize the present value of profits. The firms' discount factor may also depend on other forces, such as the probability that the product may become obsolete and the time needed for cheating to be detected. Given that the interest rate and other variables that affect the discount factor are constantly changing, it is important to study tacit collusion under discount factor fluctuations.
I characterize collusive prices and profits when the discount factor changes over time and show that collusive prices and profits increase with both present and future levels of the discount factor but decrease with its volatility. These results have important implications not only for the study of collusion but also for repeated game theory in general.
Oligopoly games are one example among many of an environment in which it is natural to assume that the discount factor changes over time. Another example would be that of a partnership, where the probability that the partnership might end varies over time. Thus, the volatility of the discount factor may be an important determinant of cooperation for many kinds of repeated games, not just oligopoly.
The environments I study and the specific results I find are as follows. I consider the case in which the discount factor, identical for all firms, is randomly and independently drawn every period. I characterize the maximum symmetric tacit collusion prices and profits that can be supported in an environment in which firms are identical and compete repeatedly on price. The three main results derived from this characterization are as follows. (1)
First and more interestingly, I show that the higher the volatility of the discount factor, the lower the collusive prices and profits that can be supported in equilibrium. The reason for this is twofold. First, given that the combination of the incentive compatibility and feasibility constraints results in a concave collusive profit function (as a function of the discount factor), an increase in volatility leads to a decrease in expected profits. Second, this decrease in expected profits reduces the size of future punishment and hence results in a decrease in equilibrium profits and prices.
Second, the higher the discount factor in a given period, the higher the collusive prices and profits that can be supported in equilibrium in that period. The intuition behind this is straightforward: the higher the discount factor, the stronger the threat of future price wars and the higher prices and profits can be without firms deviating.
Third, a shift in the distribution function toward higher discount factors would result in an increase in the profits and prices that can be supported in equilibrium for each discount factor. Again, the intuition is straightforward. From the previous result, we know that the higher the realization of the discount factor, the higher collusive prices and profits will be. Hence, a shift in the distribution function toward higher discount factors would result in an increase in the expected value of collusive profits and an increase in the threat of future punishment, allowing higher equilibrium prices and profits.
The rest of the article is organized as follows. In Section 2, I relate this article to the previous literature. In Section 3, I study the optimal tacit collusion solution and provide comparative statics results. In Section 4, I conclude.
2.... |
More articles from RAND Journal of Economics
Free entry and social efficiency under vertical oligopoly., June 22, 2007
Looking for additional articles?
Click here
to search our database of over 3 million articles.
|
%20%20&position=1)