Strategic Competition in Oligopolies with Fluctuating Demand
Dynamic oligopolistic competition has implications both for the strategic management of firms and for the design of an effective competition policy. Consequently, the present book considers the issue from a private and social perspective. It discusses the
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In the following, a firm index is omitted where no information is lost.
(4.2)
74
4 Fluctuating Demand
is positive. Therefore, the inequahty (4.2) states the condition for collusion that yields periodic profits TTA- The discounted additional profit stream from the participation in the collusive agreement, given by the first term on the right hand side above, increases in the discount factor S. The additional profit from defection, TTD — TTA, is independent of S. A firm's incentive to collude, V{7rA,S), thus increases in its valuation of future profits. If it places a low value on future profits, corresponding to a low value of the discount factor, perfect collusion by joint monopolization of the market is impossible. Then, the firms must decrease the incentive to defect, given by the last two terms above. As the one-shot gain from cheating on an implicit agreement is smaller, the lower the current profit from collusion is, the firms then restrict competition to a lesser extent. In the case of quantity competition, the participants in the implicit agreement produce a larger output and realize a lower market price than in the monopoly equilibrium. In order to gain the highest possible profits from such imperfect collusion they set the smallest output that makes the implicit agreement viable. To the same end, they set the highest price that yields a nonnegative incentive to collude (4.2) and produce the corresponding quantity if they compete in prices instead. In principle, per-period profits could also be reduced by agreeing on a collusive output that is even smaller than the share monopoly output or a collusive price above the monopoly price. Since an extreme output restriction or very high market price rises suspicion in the competition authorities, colluding firms will not use this strategy. By solving for the threshold of the discount factor, that fulfills condition (4.2) with equality, we obtain ^ ^ ^crit. =
—
(4.3)
as an alternative formulation of the condition for collusion that yields a periodic profit of TTA for each participant. It shows that a firm takes part in the implicit agreement if it values future profits more than is indicated by the threshold ^QXXX.- Since the level of collusive profits may be any amount between the ATas/i-competitive and the share of the monopoly profit, the condition (4.3) applies to all collusive equilibria between the Nash and the mo
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