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Lecture 10: Game Theory/ Oligopoly
Managerial Economics BSP 1005 D2 November 2011

Sanjeev Mohta

Oligopoly
Small number of firms Great deal of interdependence Interdependence leads to strategic behavior Conditions may promote collusion No single model of oligopoly Many models depending on circumstances

Conclusions from some Oligopoly models
 The oligopoly firms will conspire and collaborate to charge the monopoly price and get monopoly profits.  The oligopoly firms will compete on price so that the price and profits will be the same as those of a Perfectly competitive industry.  The oligopoly price and profits will be somewhere between the monopoly and Perfectly competitive ends of the scale.  Oligopoly prices and profits are "indeterminate." That is, they may be anything within the range, and are unpredictable.

Applying Game Theory to Oligopoly
Price Competition (Bertrand) Location (Differentiation) : Hotelling

Capacity Competition : Simultaneous (Cournot) Capacity Competition : Sequential (Stackleberg)

The Setting
Key Assumptions:  2 Firms Same Marginal Cost Homogeneous product

Price Competition
Bertrand model
Sellers with unlimited capacity compete on price  Suppose one of the two firms charges price p, above marginal cost  The other firm has three choices: price > p: lose all customers price = p: split the market in half price < p: gain the whole market, even marginally below p  The same logic would apply to the other firm

Bertrand Model : Strategies
Firm 1’ action P > MC P < MC P = MC Firm 2’s best response Undercut Firm 1 Get out of the market P = MC, or get out of the market

In the case 1, if Price is greater than the monopoly price, the best response would be for Price to be the Monopoly price.

Nash Equilibrium
For each firm's response to be a best response to the other's each firm must undercut the other as long as P> MC Where does this stop? P = MC (!)

8

Avoiding Bertrand Paradox

Repeated Game
Example : Tit for Tat Strategy  Price High  Observe Competitors Pricing  Cut price only if the competitor cuts price  This could avoid price wars and achieve tacit cooperation

Variation of the Bertrand Model : I
Firms with Different Marginal Costs (with no capacity constraint) Equilibrium

In general the lowest cost firm(s) will keep the higher cost firms out / or leave them with little profits

Variation of the Bertrand Model :II
Firms with Differentiated Product ( example Customer Loyalty) Equilibrium Prices can sustain above marginal cost

Pricing: Differentiated Products

 Two Stores, Ajax and Bacchus, located on a linear road selling identical product with identical marginal cost of c.  The total distance between the two firm is 1  100% of the consumers are uniformly located on this road  The differentiation arises from the location  consumers , who is willing to pay Reservation price R for the product, prefers to buy from firm which is located closer to them as it involves transportation cost ( t ) to travel.

 Consider a consumer located at X from Ajax and (1-X) from Bacchus

Finding the reaction Function
 Step 1: For a consumer located at X, find the function that makes consumer indifferent between buying from Ajax and Bacchus  Step 2 : Derive the Demand function facing Ajax (X*) and for Bacchus (1-X*)  Step 3 : Find the profit maximization price for Ajax (PA) for every given price of Bacchus (PB) Result : reaction functions: PA = (PB +c+t)/2 and PB = (PA + c +t)/2 The equilibrium prices are PA* = c+ t and PB *= c+t

Pricing: Differentiated Products

Differentiated sellers: best response price functions

Hotelling conclusions
 If the two sellers set equal price they would get half the market demand  If Ajax increases its price, it does no lose the entire demand.  The Price exceeds marginal cost, thus the solution is better than Bertrand.  Higher the “ t “ less elastic the demand, higher...
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