Avoiding the Bertrand Trap

Slide 1:Avoiding the Bertrand Trap

Part I: Differentiation and other strategies

Slide 2:Administrative Matter

In section this Friday, the GSI will go over Exercises #2, #3, #4, #5 (parts (a)-(c) only), #6, and #7 from �Introduction to Game Theory & The Bertrand Trap.� This information is also posted on the course web site.

Slide 3:The Bertrand Trap

Recall the model�s assumptions: they produce a homogeneous product they have unlimited capacity they play once (alternatively, myopically, or w/o ability to punish) customers know prices. customers face no switching costs the firms have the same, constant marginal cost

Slide 4:Bertrand Model

Slide 5:An �Easier� Bertrand Model

Q P D pmin firm demand mkt. demand v

Slide 6:Avoiding the Bertrand Trap

Avoiding the trap means altering these assumptions; that is, doing at least one of the following: don�t produce a homogeneous product don�t have unlimited capacity don�t play myopically (facilitate tacit collusion) make it difficult for customers to learn prices make it difficult for customers to switch from one firm to the other lower your costs

Slide 7:Avoiding the Trap: Method 1

Lowering your costs. Lower your MC to k < c, where c is your rival�s MC. Equilibrium: you charge po = c - ?, where ? is a very small amount and your rival charges pr = c. Proof: An equilibrium p > c would lead to Bertrand undercutting, so p ??c in equilibrium. Your rival will never charge less than c, so you can get away with charging c - ?.

Slide 8:Potential Problems with Method 1

Question is sustainability of cost advantage: Could fail the �I� test in VRIO. Care that cost-cutting today does not result in negative long-run consequences. Could make firm vulnerable to fluctuations in trade policy (if cost advantage gained by �exporting� jobs).

Slide 9:Avoiding the Trap: Method 2

Limiting capacity Let K1 and K2 be the capacities of the two firms. For convenience, assume a flat demand curve (i.e., easier model). If K1 + K2 ? D, then no problem: equilibrium is p = v (i.e., monopoly pricing); there is no danger of undercutting on price because neither rival can handle the additional business.

Slide 10:Limiting Capacity

If K1 + K2 > D, but Kt < D for t = 1,2; then monopoly price (i.e., v) cannot be sustained because of undercutting. However, each firm is guaranteed a profit of at least (D - Kr)(v - c) > 0, where Kr is the rival�s capacity. Equilibrium in this simple model involves complicated mixed strategies. But positive profits made!

Slide 11:Choosing Capacities

It turns out that the game in which firms first choose their capacities and then play a Bertrand-like game is equivalent to Cournot competition.

Slide 12:Cournot Competition

Firms simultaneously choose quantity (capacity). If Q is total quantity, then price is such that all quantity just demanded; that is, so D(p) = Q. Note we are abstracting away the firms ability to set their own prices, but this turns out to be without consequence in equilibrium and it vastly simplifies the analysis.

Slide 13:Cournot Competition continued �

Assume two identical competitors. Each has a constant marginal cost of c. If you think rival will produce qr , then your demand curve is D(p)-qr .

Slide 14:Your Best Response

Quantity Price Market demand qr Your demand c MR qo p

Slide 15:If Rival Produces More

Quantity Price Market demand qr Your demand c MR qo p ? Your quantity goes down ? Price falls

Slide 16:Insights

Despite competition, you make a positive profit (price > unit cost). You produce less if you think rival will produce more (have less capacity if you think rival will have more). Your profits decrease with the output (capacity) of rival.

Slide 17:Equilibrium of Cournot Game

Quantity Price Market demand qr Your demand c MR qo p In equilibrium, must play mutual best responses. Given assumed symmetry, this means qo = qr .

Slide 18:Comparison with Monopoly

Quantity Price Market demand c qo Monopolist�s MR Qm Monopoly price

Slide 19:More Insights

Relative to monopoly, Cournot competition results in more output and lower prices. That is two means a lower price and more output than one. Logic continues: Three Cournot competitors results in a lower price and more output than with two. In general, prices and firm profits fall as the number of Cournot competitors increases. Again, the danger of entry and emulation.

Slide 20:Further on Cournot

On the class web site there is an additional reading on Cournot.

Slide 21:Summary of Method 2

Limiting capacity is a way to escape or avoid the Bertrand Trap. Competition in capacity is like the Cournot model. Lessons of the Cournot model: Firms charge lower price than monopoly, so still room for improvement through tacit collusion or other strategies. The more competitors, the lower will be price.

Slide 22:Avoiding the Trap: Method 3

Raise consumer search costs Return to basic assumptions, except assume that it costs a consumer s > 0 to �visit� a second firm (store). Let pe be the equilibrium price. That is, the price consumers expect to pay. Then each firm can charge p = min{pe + s,v}, because a customer would not be induced to visit a second store.

Slide 23:Raise Consumer Search Costs

Since customers expect both firms to charge pe, customers are evenly divided between the firms. There is no benefit to undercutting on price, since if rival is not charging more than min{pe+s,v}, you won�t attract any of its customers. Pressure now is to raise prices. Equilibrium is pe = v; i.e., the monopoly price.

Slide 24:Issues with Implementation

How to keep search costs high? Must prevent price advertising. Must ensure comparison shopping hard (or pointless). Preventing price advertising. Lobby gov�t to make illegal (liquor stores) �Gentlemen�s agreement� (a form of tacit collusion) Have professional association prohibit (generally found to be violation of antitrust laws)

Slide 25:Making Comparison Shopping Hard

Limit store hours Detroit automobile dealers Closing laws (more gov�t lobbying) Do not readily supply price information automobile dealers again use multiple prices (extras on cars, supermarkets) Make it pointless guarantee lowest price meeting competition clauses

Slide 26:Avoiding the Trap: Method 4

Raise consumers switching costs Return to assumptions of basic model, except now consumers are initially allocated equally to the two firms and must pay w to switch to another firm. Consumers know the prices at both firms.

Slide 27:Raising Switching Costs

Consider �easier� model of Bertrand. Assume, first, that w ? �(v - c). An equilibrium exists in which both firms charge monopoly price, v: To steal rival�s customers must charge v � w � e. Profits from stealing: (v � w � e � c)D . Profits from not stealing: (v � c)D/2, which is greater.

Slide 28:Raise Consumers Switching Costs

If w < �(v - c), then complicated equilibrium in mixed strategies. We know, however, that each firm can charge at least c + 2w (which is less than v): To profitably undercut a price of c + 2w, a firm would have to drop price to below c + w. But (c + 2w � c ) D/2 > (c + w - e - c)D Although equilibrium difficult to calculate, we thus know positive profits made in it.

Slide 29:Method 5: Product Differentiation

Two firms with identical, constant MC = c. Customers differ in their preferences. Imagine that customers are uniformly distributed along the unit interval with respect to taste. E.g., Assume customers each want one unit. Technical details: See the product differentiation handout on the website.

Slide 30:Equilibrium with Great Differentiation

0 0 Firm 0�s price Firm 1�s price Firm 0�s quantity Firm 1�s quantity MC D0(p0|p*) D1(p1|p*) p* MR0 MR1

Slide 31:Equilibrium with Modest Differentiation

0 0 Firm 0�s price Firm 1�s price Firm 0�s quantity Firm 1�s quantity MC D0(p0|p*) D1(p1|p*) p* MR0 MR1

Slide 32:Equilibrium with Even Less Differentiation

0 0 Firm 0�s price Firm 1�s price Firm 0�s quantity Firm 1�s quantity MC D0(p0|p**) D1(p1|p**) p* MR0 MR1 p**

Slide 33:An Experiment

In this experiment, you need to decide where to locate in a differentiated market. The market works as follows: Consumers are located on a number line from 1 to 63. There is one consumer at each location. Every consumer will pay $1 to buy one unit of the product, but only from the nearest store. If there is a tie, then a consumer buys fractional units from all the equally distant stores. A monopolist can locate anywhere and make $63 because all consumers will buy from the monopolist and pay $1 each. Costs: Entry costs $20. Marginal cost is $0.

Slide 34:Experiment continued

Rules I will invite people (as individuals or teams of 3 or fewer) to enter. You must choose a location that is a counting number between 1 and 63 inclusive (i.e., 3.5 is not a valid location). When people cease to be willing to enter, I will collect the entry fees and return profits according to location.

Slide 35:Where to �Locate�

Basically you want to locate far-away from your rivals�remember this is driving not football. Caveats If population is concentrated in �one place,� may need to get close to that place. When entering, sometimes pays to enter where the trade is (e.g., near other restaurants).

Slide 36:Where to locate (continued �)

Note that product differentiation is not a panacea if there is no market discipline. Brand proliferation. If can�t block entry or emulation. How would we evaluate differentiation strategy in Cramer?

Slide 37:Conclusions

You can avoid or escape the Bertrand Trap if You can achieve a cost advantage (Method�1) You can limit capacity (Method 2) Cournot competition You can raise search costs (Method 3) Sneaky benefits to price matching guarantees You can raise switching costs (Method 4) You can differentiate your product (Method 5)

Slide 38:But �

Some of these solutions can be vulnerable to lack of market discipline or entry/emulation: Others may be able to cut costs too. Others may attempt to capture business by lowering search or switching costs. Others may not be disciplined about capacity. Entry can erode benefits of limited capacity. Others may not be disciplined about maintaining brand distinctions. Entry can erode benefits of differentiation.

Slide 39:� which points to

Importance of maintaining discipline: Topic for next time � Method 6 � tacit collusion. Importance of deterring entry: Topic for later in term.