Abstract
The ability of oligopolistic firms tacitly to exploit their potential market power and achieve better outcomes than the non-cooperative Nash equilibrium was first analyzed by Friedman (1971). Friedman argued that in an infinitely repeated game, the threat of future punishment can be used to enforce cooperative behavior. Starting from a collusive output level, duopolists may define future reactions to deviation from that output level (trigger or grim strategies), by which both the deviating and the punishing firm are hurt. Following Friedman, the sustainability of the collusive equilibrium can then be measured by calculating the critical discount factor that equalizes the long term gains from a collusive strategy with the gains from a deviating strategy. In a seminal article, Bernheim / Whinston (1990) claim that multimarket contact may help firms to sustain collusive outcomes whenever firms or markets differ from each other. They consider firms that compete in several markets. It is shown, that the opportunity these firms have to punish deviation from a cooperative equilibrium in every “contact” market may relax binding incentive constraints in a wide range of circumstances. Furthermore, whenever firms differ in their production costs or when scale economies are present, multimarket contact allows the development of “spheres of influence”, which enables firms to sustain higher levels of profits and prices. Bernheim and Whinston assume that markets are independent of one another. The mechanism driving their result is that the ability for multimarket firms to “pool” their incentive constraints across markets allows them to export “slack enforcement power” from one market to the other.
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References
Alexander (1985) was the first who hinted at this implicit assumption. Lee / Tang (1994) developed the idea further, claiming that firms must pursue a corporate strategy if multimarket contact is to be effective and assuming a correlation between lateral diversification and corporate strategy.
Recent work about the importance of the organizational structure was done, however, in a one market context, by Spagnolo (1998), who examines the strategic use of managerial low-powered incentives as a means of sustaining one market collusion.
In accordance with most of the models dealing with (multimarket) collusion, the focus in this analysis will be on stationary equilibria.
This approach will be followed in the subsequent analysis.
This peculiarity resulting from the joint cost term has not been considered so far in the literature.
See Appendix E.1. Only if g is positive and very high, might efficient collusive outcomes where one firm monopolizes the collusive market and the other firm concentrates on the other market be possible.
The critical discount factors are equal for both firms, as output is allocated evenly to each firm.
See Appendix E.2.
The separation of incentive constraints for both markets can never be optimal. As two market punishment is a more severe punishment for deviation than one market punishment, it relaxes the incentive constraint of firms for each single market. See Appendix E.3 for a proof.
This assumption implies a fair allocation of market shares and equalizes and minimizes the critical discount factors of both firms (min s max min i {δ** i , δ** j }).
See chapter 3 for efficient output shares in case of joint profit maximization and Appendix E. 4 for output shares that minimize deviation profits.
See Appendix E.4.
MATH (see also Appendix E.4).
As firms and divisions symmetrical, it is assumed that both the percentage of divisional profits and the fixed part of managers’ salary are the same in both firms and both divisions.
As divisions do not participate in profits of the other division, a division being allocated a low output share cannot alleviate its disadvantage in its own market by concentrating on a second market. The monopolization of one market by one division is therefore never feasible: punishment profits are alway higher than collusive profits. The minimal discount factor for both firms (for one or two market collusion), min s maxi is obtained for symmetrical output shares. See also Appendix E.5.
Again, this assumption can be made only because s = 1/2.
This is consistent with the approach to ask for the most collusive outcome (see chapter 7.1).
See Appendix E.6
See Appendix E.6
See also Appendix E. 6.
See Appendix E.6.
However, as mentioned in chapter 7.2, we do not expect to observe one market collusion in centralized firms if they face diseconomies of scope. Comparing the critical discount factor for two market collusion in centralized firms (δ ** (ŝ)) with the discount factor for one market collusion in decentralized firms (δΦ*) for g > 0 would lead to the result, that collusion in one market in decentralized firms is always more difficult than collusion in (at least) one market in centrailized firms.
See appendix for λ crit>(g)
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© 2001 Deutscher Universitäts-Verlag GmbH, Wiesbaden
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Neubauer, S. (2001). Collusion and multimarket contact in a repeated game. In: Multimarket Contact and Organizational Design. Beiträge zur betriebswirtschaftlichen Forschung, vol 97. Deutscher Universitätsverlag, Wiesbaden. https://doi.org/10.1007/978-3-663-05979-0_7
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DOI: https://doi.org/10.1007/978-3-663-05979-0_7
Publisher Name: Deutscher Universitätsverlag, Wiesbaden
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