Lecture 10: Game Theory/ Oligopoly
Managerial Economics BSP 1005 D2 November 2011
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)
Key Assumptions: 2 Firms Same Marginal Cost Homogeneous product
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.
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 (!)
Avoiding Bertrand Paradox
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
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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