Chapter 9 Flashcards
Two equilibria with a Bertrand game with infinite series of periods
Nash-Bertrand equilibrium, ignoring at each stage what the previous history of the industry was.
Grim strategy, both firms set price at the monopoly level, and share monopoly profits equally. Firm 1 sets the price at the monopoly level as long as firm 2 does too. However, only an equilibrium if the no-deviation constraints are statisfied.
No-deviation constraint
V = 0.5pi^m * (1/(1-delta)
Since future payoffs are not a function of what the deviation was, but only whether there was a deviation at all, it follows that the best strategy for firm 1 is the one that maximizes short-run profits. V’ = pi^M
equilibrium if V => V’. Delta => 0.5!!!!!!!!!
When is there an equilibrium with grim strategies?
If the discount factor is sufficiently high, then there is a Nash equilibrium of the repeated game where the price = monopoly price for every period
Under the threat that if any firm ever deviates from the price level, then both firms revert to the standard Nash-Bertrand equilibrium
The discount factor - two uses
- Measures how much $1 one period into the future is worth compared to now.
delta = 1/(1+r)
if f = the frequency with which firms change their prices –> delta = 1 / (1+(r/f)) - Probability that the payoff next period will be received at all. h = the probability that the industry ceases to exist –> delta = (1-h) / (1+(r/f))
if g = constant grothw rate of demand –> delta = (1+g)(1-h) / (1+(r/f))
Succes of Collusion
Collusion is normally easier to maintain when firms interact frequently and when the probability of industry continuation and growth is high.
Why don’t firms collude more often?
- Antitrust policy is a binding constraint on the firms’ actions –> cartel agreements are illegal.
- If a firm expects to exit the industry with a high probability (h), then its incentives to deviate from collusive agreements are also very high as there is little to lose –> delta is decreasing in h.
- The mentioned collusive agreements are not really an equilibrium, they form a nash equilibrium.
- In a world of imperfect observability, not all prices are observed with precision and the possibility of secrete price cuts must be taken into account.
Tacit agreement
When firms agree to or approve something without saying it or putting it in writting
Customer markets
Industries where each customer is sufficiently large that prices are negotiated on a case by case basis –> collusive agreements are difficult to monitor
Price wars
Suppose that demand fluctuates and that this cannot be perfectly observed –> unexpected low demand leads to a guessing problem and often a price war
Price wars
Suppose that demand fluctuates and that this cannot be perfectly observed –> unexpected low demand leads to a guessing problem and often a price war
Although price wars occur in equilibrium no firm cheats in equilibrium. If price cuts are difficult to observe, then occasional price wars must be necessary to discipline collusive agreements.
Demand fluctuations and collusive agreements
Suppose that demand fluctuates over time, but that in each period, the state of demand is observed by all firms. The difference between future collusive profits and future profits under price war must be sufficiently large to deter the firm to cheat and pursuing short-term gains.
Firm heterogeneity and price wars
Asymmetry between firms causing a price war. A firm that is in a difficult situation has a lower discount factor (delta 2) than a firm that is doing well (delta 1). If the difference between delta 1 and delta 2 is sufficiently high, it may be that collusion is possible for the patient (wealthy) firms but not among impatient (poor) firms.
In equilibrium, no firm can have an incentive to deviate if a higher price is maintained.
Market structure and collusion
- Collusion is more likely in concentrated industries than in fragmented ones –> easier to establish and maintain collusive agreement with fewer competitors. Consequently, the temptation to cut prices is relatively greater when there are more competitors, and collusion is more difficult to sustain.
- It is easier to maintain collusion among similar forms than asymmetric ones –> Otherwise there are different cost and efficient prices that maximize profits, so one firm could undercut the other. Constraint: agreement on profit distribution.
Multimarket contact
Firms that compete with each other in several markets have a great propensity to collude and so to a greater extent. Firm 1 might convince firm 2 not to undercut its monopoly price in market 1 with the threat it would under cut firm 2 in the latter’s market if it were to happen.
Most-favoured-customer base clause
bind firms not to offer a discount to a particular customer without offering the same discount to every other customer within a period of time –> lower incentive to price aggressively –> collusive pricing agreements are more stable than if no clause is imposed
