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Strategic Management II
1. Dynamics in oligopolistic industries - Slides & Chapter 7
The main topic here is to study how firms can discipline competitors that undercut prices,
such that high prices can be sustained by competitors that interact.
Cooperative Pricing In the Bertrand competition model, the final outcome yields equilibrium prices equal to marginal costs. Firms would benefit from sustaining higher prices, but how can this be achieved? - Firms can Collude in a tacit form or explicit form.
- Importantly, this agreement must be self-binding.
- Note that explicit contracts to sustain collusion are anticompetitive and are thus deemed illegal in many countries.
- Cooperative pricing: every firm acts in its own self-interest (non-cooperative decision making), and the outcome is equivalent to what would be obtained under formal collusion.
What are the mechanisim that allow firms to sustain cooperative pricing? - Repeated interaction: firms should employ pricing strategies that discipline the prices of competitors. If competitors deviate from the cooperation price, they should be punished.
- Sufficient punishments: the profits obtained by a deviating firm, given the punishment that will follow, should be inferior to the profits obtained by not deviating.
- Credible punishments: punishment strategies need to induce equilibrium. That is, firms that apply punishments should not benefit from deviating by ceasing to do so.
Bertrand with multiple periods To analyze dynamics, we need to add more than one period to the model (repeated game).
Assume: - N>2 firms - Homogeneous products - No capacity constraints - Firms set prices simultaneously in every period - Demand and cost functions: D(p)=6-p and C(q)=2q With only one period, it’s clear that the final outcome is the Bertrand paradox, with prices equal to MC (p=MC=2) and zero profits.
1 With multiple periods, firms would like to sustain the monopoly cooperation price and each firm would obtain , profits per period. This last result requires that firms adopting pricing strategies that punish deviators that undercut that monopoly cooperation price.
- Grim Trigger Strategy 1.
Quote =4 If any of the other firms have deviated so far, keep the same price If there is any deviator, thus, set p=MC=2 Here, the punishment is marginal cost pricing Finite Horizon Cooperation Consider a game of 2 periods and solve by backward induction. Cooperation in both periods with grim trigger strategies requires all firms to quote p=4. But, in the last period, it always pays off for a firm to unilaterally deviate (given that it’s the last period and there is no punishment after that time).
Grim trigger strategies don’t induce equilibrium in this case, with finite horizon. This is because there is no credible punishment if a firm deviates in the last period. Thus, the unique subgame perfect equilibrium with finite horizon involves repetition of the Bertrand outcome (setting p=MC and zero profits).
Infinite Horizon Cooperation Cooperation is sustainable under infinite horizon and additional conditions. But, since there is no last period, we cannot use backwards induction. Instead, subgame perfection requires we consider all possible subgames. First, we show punishment is credible.
Consider the case in which a firm has not cooperated. The remaining firms will quote a price equal to marginal cost thereafter. Since a punishing firm cannot benefit from deviating given that all other punishing firms are charging marginal cost, the grim trigger strategy is credible.
Next, we show that punishment is not only credible, but also sufficient.
Let r>0 be the discount rate. The present value of cooperation yields: ( ) ∑ ( ) On the other hand, the payoff for a deviating firm when all firms have charged the cooperation price in the past in the current period, and thereafter.
2 The punishment is sufficient if and only if the following holds: , which is equivalent to Thus, cooperative pricing is sustainable with grim trigger strategies only if the discount rate is low enough (that is, if firms are patient enough).
Consider an other case: ( ) Cooperation can be maintained only if: ( ) 3 Misreads or Misinterpretations Grim trigger strategies illustrate how cooperation may be sustained. Otherwise, misreads or misunderstanding when observing the prices of competitors can preclude the opportunity for future cooperation.
Competitor responses and tit-for-tat Suppose two firms are currently charging a price somewhere between the Bertrand price and the monopoly price. Firm A is considering raising its price to the monopoly level. If firm B doesn’t follow firm A pricing, it will capture 100% of the market. Although it’s in the collective interest to charge the monopoly price, firm B is better off undercutting firm A’s price.
Now suppose that prices can be changed every week, so firm A can reduce price the next week if sees that firm B doesn’t follow. Thus, firm A’s decision to raise price carries little risk, because it sacrifices at most one week’s profit. In addition, firm A knows that firm B has a lot to win by following A and increase price. This means that it makes a lot of sense for firm A to raise its price.
The desirable properties of the winning tit-for-tat strategy are: - Niceness: facilitates cooperation, never first to defect.
Provocability: punishes defection Forgiveness: willing to cooperate again after defections Market structure and cooperative pricing The ease of achieving cooperative pricing may depend on certain aspects of market structure: - Concentration Conditions that affect reaction speeds and detection lags Asymmetries among firms Factors that make cooperation difficult - Fragmented market structure: Individual share of the joint profit decreases with number of colluding firms n, so both deviating becomes more attractive and punishment becomes less harsh for firms. In the condition for sustainable cooperating pricing, as n decreases, the numerator increases and the denominators decreases, making it easier for the condition to hold.
( ) 4 - Slow reaction speed and detection lags: it increases the incentives to deviate because they extend the period of gains before the punishment arrives. The determinants of the reactions speed are: o Frequency of interactions with the rival (Infrequent sales): When orders are lumpy, the frequency of competitive interactions in reduced. Lag between orders makes the gain from price cutting more valuable relative to the cost imposed by rival’s retaliation.
o Availability of information about a rival’s price cut (Scarcity of information about transactions): Deviations from cooperative pricing is easier to detect when the transactions are public than when they are private. Deviations from cooperative pricing are harder to detect when the products are custom made individual buyers than when they are standardized (Complex transactions may make misreading more likely compared with simple transactions).
o Difficulty in distinguishing changes in volume of sales due to changes in demand as opposed to changes in rival’s price (Market volatility): If marginal cost changes with output, cooperative pricing involves chasing a moving target.
If the price cuts can be matched instantaneously, cooperative pricing can be maintained for any discount rate.
As the time interval for the short term gain for the deviator is reduced, the present value of benefits from cooperation is more likely to exceed this short term gain. In the condition, as the time interval goes to zero, so does the interest rate r.
- - Asymmetries among firms: if firms differ in their cost structures or in the quality of their products, cooperation requires that firms set different prices and the complexity of sustaining cooperation increases. Significant asymmetries in the size of firms can also difficult the credibility of punishments. (Firms differ in the incentives they face for cooperative pricing due to different costs; different capacities and different product qualities).
o Asymmetries in cost: The marginal costs are different for the firms and so are the monopoly prices preferred by each of the firms. Without a single monopoly price to serve as a focal point, coordination becomes difficult.
Differences in product quality can create similar obstacles to coordination.
o Asymmetries in capacity: Small firms have stronger incentives to defect from cooperative pricing than their larger rivals. This is because larger firms get a larger share of the benefits of cooperative pricing and may have weak incentives to punish small deviators. On the other hand, small firms have a large set of potential customers to attract by price cutting.
Regulatory policies: strength of competition authorities, fine sizes on anti-competitive behavior, and specific policies enacted (Leniency policies).
Factors that facilitate cooperation - Price leadership: price leader in the industry announces price changes ahead of others and others match the leader’s price. The system of price leadership can break 5 - - - - down if the leader does not retaliate if one of the follower firms defects. Sometimes, the price leader may simply act as a barometer of market conditions. Even without collusion, firms follow the price leader because they face the same changes in market conditions.
Preannouncement of price changes: facilitates coordination among firms. Advance announcement reduces the uncertainty that the rival will undercut the firm, and also gives the firms the possibility to roll back the changes if the rival deviates from cooperative pricing.
Most favored customer clauses: if a firm commits to match its lowest price across its customer base, it reduces its own incentives to deviate. Most favored customer clause allows the buyer to pay the lowest price charged by the seller. While this clause appears to benefit the buyer (a price cut to any one customer lowers the price for the most favored customer) it also inhibits price competition.
Price matching policies: if a firm commits to match the lowest price of competitors, it reduces their incentives to deviate.
Staggered contracts: intertemporal rigidities in demand can facilitate collusion. If consumers have long-term contracts with staggered expiration dates, the opportunity to attract all the demand at any given point in time dissipates.
Multimarket contact: if firms collude in several markets, the threat of punishment becomes harsher if it can be applied across all markets.
Cooperation in booms and busts Industries are subject to cyclical fluctuation in demand: - Booms: The optimal prices are well above the marginal cost.
Busts: The margins are nearly zero.
Facilitating practices and antitrust Pricing decisions should be made unilaterally. It must have a legitimate justification for price increases, price cuts, and other pricing policies (clauses, audits). Do not be overly aggressive with price cuts, it could be interpreted as a punishment strategy. Do not preannounce price changes without a legitimate justification. Limit the audience and control the content of the announcement (It could be interpreted as a coordination signal).
Explicit Collusion Consists on the communication among players in order to avoid coordination failures (Firms form a cartel in order to increase their profits by coordinating their activities rather than acting independently). Anti-cartel laws prohibit firms from explicitly agreeing to take actions that reduce competition, such as jointly setting price.
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