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Employability and Careers Centre International Careers Week book online at 27 January – 31 January Postgraduate Study in the US with the Fulbright Commission Employability Skills for International Careers Paid Work Experience in the US with Parenthese International Talent Search with Universum Webinar International Volunteering Skills Talks Working in the UK after study Careers in EU Institutions and the Foreign and Commonwealth Office Chinese CV Masterclass International Teaching Opportunities Open to all International, EU and home students
EC930 Theory of Industrial Organisation Week 3: Game Theory Review – Nash Equilibrium Product Differentiation I – Representative Consumer Models , spring term
4 Outline Review of Game Theory Nash Equilibrium – Cournot/Bertrand Subgame Perfect Nash Equilibrium -- Capacity Game/ Stackelberg Product Differentiation I: Representative Consumer Models Derivation of Demand/Basic Assumptions Cournot/Bertrand Equilibria Comparison Example 1: Exam Question Example 2: Unilever/Sara Lee Reading: Lecture notes 2 Problem Set 3: Q1, 2 Discussion and Support: Cabral ch 12, Tirole ch 7. (Game Theory Appendix)
5 Taxonomy of solution concepts
6 Example of Nash equilibrium (1) “Prisoners’ dilemma” (payoffs: Andy, Bob) Andy Unique Nash equilibrium: (defect, defect) The Pareto dominant outcome (collude, collude) does not occur in equilibrium Bob Collude Defect Collude Defect 2, 2 -1, 3 3, -1 1, 1
7 Example of Nash equilibrium (1) Bertrand example (a=10, c=0, b=1 in earlier case) Nash equilibrium: (defect, defect) The Pareto dominant outcome (collude, collude) does not occur in equilibrium Firm 2 Firm 1 Collude Defect Collude Defect 100/8, 100/8 0, 100/4 100/4, 0 0, 0
8 Example of Nash equilibrium (1) Cournot example (a=10, c=0, b=1 in earlier case) Nash equilibrium: (defect, defect) The Pareto dominant outcome (collude, collude) does not occur in equilibrium Firm 2 Firm 1 Collude Defect Collude Defect 100/8, 100/8 300/32, 900/64 900/64, 300/32 100/9,100/9
9 Example of Nash equilibrium (2) “Battle of the sexes” 2 Nash equilibria in pure strategies (football, football), (opera, opera)
10 Example of SPE Entry game
11 Example of SPE Entry game 2 NE: (enter, accom), (stay out, fight) One of these seems more reasonable than other, though. Payoffs: (incumbent, entrant) Entrant incumbent Fight Accom Enter Stay Out -1, -1 2, 0 1, 1 2, 0
12 Example of SPE Entry game 2 NE: (enter, accom), (stay out, fight) Latter involves incredible threat and is not a SPE Only (enter, accom) is SPE
13 Example of SPE Stackelberg game: Incumbent chooses output…then entrant reacts to maximise profit. We solve this backwards: first, we obtain the best response to any output chosen by the incumbent…then we choose the best output for the incumbent, knowing what will follow. Q4 (2012 exam): P = 1-Q, MC = 0; 2 firms, homogeneous products. a.Firms choose quantities simultaneously. Obtain Nash equilibrium quantities/profits b. Firm A commits to quantity before firm B. Obtain subgame perfect Nash equilibrium. Are firms better/worse off than in (a)? c. Firm A chooses, but does not commit before B. What is the SPNE now?
14 Example of SPE Capacity/price game: Firms first choose capacities simultaneously…then firms then choose price to maximise profit simultaneously. We solve this backwards: first, we obtain the best response to any price chosen by the rival for any capacity level… then we choose the best capacity, knowing what will follow.
15 Product Differentiation (horizontal) Recall: At same price, some of both/all products purchased. Representative Consumer Models: Each consumer buys a single variety, all consumers have the same preferences (we model the “typical” consumer). Address Models: Each consumer buys a single variety, consumers differ (we model brand positioning in characteristics space). Eg: consumer products (shampoo, deodorant, toothpaste…) breakfast cereals petrol stations pubs
23 Reaction function of firm 2 Reaction function of firm 1 equilibrium
24 Reaction function of firm 2 Reaction function of firm 1 p Profit increases along reaction function Profit rises
26 Comparing the two, for substitutes, Bertrand prices lower and quantities higher in equilibrium than Cournot, and consumer surplus higher in Bertrand (except where markets independent, where all these are equal) Profits lower in Bertrand than Cournot. Opposite holds for complements case. So what if firms can choose which they compete in (p or q)? Think of a two stage game: Firms non-cooperatively choose whether they compete in p or q Firms compete non-cooperatively, as above. If the goods are substitutes, it is a dominant strategy to select Cournot (compete on quantities), whereas if the goods are complements, it is a dominant strategy to compete in prices.
27 Firm 2 Firm 1 Price Quantity Price Quantity Bertrand CournotPr QP Pr PQ And PR QP > Bertrand Profit; Cournot profit > Pr PQ Why? A Bertrand firm raises price against a rival assumed to keep (lower) price fixed raising price cuts sales a lot. A Cournot firm assumes, implicitly, that rival will raise price when I do in order to keep sales constant raising price cuts sales much less.
28 How to interpret this result and this model? Not clear that firms “choose” which game they are in or strategic variable: this may be determined by technology of industry. Not clear that representative consumer model is a good representation of reality, as it assumes all products compete with each other equally In most markets, some substitutes are closer than others. For this, we would need a different type of model…
31 Example: Unilever acquisition of Sara Lee Sara Lee Unilever EC concerned about effect in market for deodorants
32 Example: Unilever acquisition of Sara Lee Main relevant brands: Sara Lee – Sanex Deodorant Unilever – Rexona, Dove Deodorants Various formats (stick, roll on, spray) gender appeal (male, female, unisex) health appeal (skin-friendly, “no comment”) National markets Differentiated product within national markets. Market share of combined Sara Lee/Unilever brands = 35-70%, depending on national market. 4-5 other competitors in general.
33 Nested logit model using customer panels, switching analysis: deodorants malenon-maleoutside good Skin-friendly No comment Single nested model Sub-nest Individual products
34 Nested logit used to estimate demands for the goods, including own and cross price elasticities. Merger simulation then conducted, removing Sara Lee as a separate firm in a Bertrand, differentiated product model. Find approximately 5% price increase, with higher effect in non-male segment. Compensating efficiencies in wide range depending on country (5-25%) Remedy: require divestment of Sanex brand
35 Critique: Much of the model is reasonable: Nested logit assumes same elasticities (cross and own) within categories. While nesting is somewhat arbitrary, good checks used beforehand. Statistical testing of nesting is possible, but only eliminates models: cannot identify a single “best” nest (and did not in this case). Clearly, parties choose “best for them”. The acquisition was based on expected development (growth) of market, not on static effects – but modelling purely static. In other words, not only is competition static in Bertrand model, but no changes in demand parameters occur over time in this simulation – only ownership of brands changes (number of firms decreases by 1). Results indicated a 40% price rise for Sara Lee brand in static model: but acquisition was specifically for the purpose of growing the brand! Final decision was the Unilever abandoned the acquisition, as the remedy completely eliminated the original reason for the acquisition.
36 Summary: Nash equilibrium and Subgame Perfect Nash Equilibrium are flexible concepts to be used to characterise games of the type we have discussed until now. Cournot, Bertrand – examples of Prisoner’s Dilemma class Stackelberg, Capacity Choice – examples of SPNE (Horizontal) Differentiation: Representative Consumer Model Works well for goods where a “typical” consumer choosing among a set of goods that are equally substitutable is a good description of reality. These are static models so miss any dynamics