Competitive Strategy: Week 2. Bargaining

Transcription

1 Competitive Strategy: Week 2 Bargaining Simon Board Eco380, Competitive Strategy 1 2 Person Bargaining: Nash Solution 2 person bargaining game Outside option (u 1, u 2 ). Convex utility possibility set U Nash Solution [see picture] (u 1, u 2) is solution to max (u 1,u 2 ) U (u 1 u 1 )(u 2 u 2 ) Satisfies number of attractive axioms. Properties: efficiency and symmetry. Eco380, Competitive Strategy 2

2 Outside Options 2 Agents bargain over $1k. Nash bargaining implies agents share the pie 50:50. Increasing u 1 by $100 u i = 1 2 [1000 u 1 u 2 ] + u i Increases u 1 by $50. Decreases u 2 by $50. Lesson 1: Investing in outside option (e.g. alternative supplier) can increase bargaining strength. Increasing pie by $100 increases u i by $50. Lesson 2: Can t capture all investment in pie. Lesson 3: Investment inefficient. Better to contract than bargain. Eco380, Competitive Strategy 3 Ultimatum Game 2 players bargain over $1k. Outside option (u 1, u 2 ) = (0, 0). The Ultimatum Game: Agent 1 offers split (u 1, u 2 ) to player 2. Agent 2 accepts or rejects. If reject both get (0, 0) Solving the game: Backwards Induction. Agent 2 accepts if u 2 > $50. Agent 1 can thus offer (u 1, u 2 ) = ($950, $50) Lesson 4: Put yourself in opponents shoes Lesson 5: Rules matter Eco380, Competitive Strategy 4

3 Alternating Offers 2 players bargain over $1k. Outside option (u 1, u 2 ) = (0, 0). Alternating Offers Game: 1. Agent 1 makes offer. Agent 2 accepts/rejects. 2. If reject, A2 makes offer. A1 accepts/rejects, and so on. Agents are impatient: Discount factors are (δ 1, δ 2 ) Solving the game: Suppose û i is minimum Agent i will accept. When A1 makes offer A2 can guarantee herself δ 2 (1 û 1 ). Hence û 2 = δ 2 (1 û 1 ) and û 1 = δ 1 (1 û 2 ). Implying, Lesson 6: Patience is rewarded. û 1 = δ 2(1 δ 1 ) 1 δ 1 δ 2 and û 2 = δ 1(1 δ 2 ) 1 δ 1 δ 2 Eco380, Competitive Strategy 5 N Person Bargaining: The Card Game The Card Game I have 26 black cards. You have 26 red cards. $100 for pair How is $2600 split? What if I destroy 3 cards. How is $2300 split? Lesson 7: Be on the short side of the market. Eco380, Competitive Strategy 6

4 Example: NFL Franchise Added Values Raiders went (back) to Oakland. Rams went to St Louis. Fewer teams than interested cities. NFL teams get $300 million stadiums built for them. Fast food restaurants. Have Coke or Pepsi. Leads to competition. Your added value = Pie when you in game Pie when your out. General principal: Return in game depends on your added value. When I have 26 cards, your added value is $100. When I have 23 cards, your added value is $0. Eco380, Competitive Strategy 7 Bargaining and Perceptions Firm and supplier bargaining over contract. Everyone knows the supplier s cost is $100. The firm values contract at $150. But this information is private. Suppose firm offers the Nash solution $125. Now the supplier know the firm s value exceeds $125! Supplier now pushes for $135. Lesson 8: Private information is valuable. If in weak position: don t give info away. If in strong position: prove it! Week 11: Signaling. Eco380, Competitive Strategy 8

5 Perceptions: Examples Car Dealerships Suppose you are want to buy a 2 year old VW. Negotiation consists of you making series of offers. Dealer never makes offer: doesn t give away information. Artistic Differences In middle of picture director quits. The screenplay writer is willing to take over for $300k. The studio is is willing to pay $2m. First offer to be $750k. Writer s agent asks for $300k. Agree at $250k. Lesson 4 (reprise): Look at the game from opponent s perspective (Allocentrism). Eco380, Competitive Strategy 9 Threats Suppose you are negotiating with your employer Suppose you threaten looking for another job? How will your employer react? It is dangerous to make explicit threats. You provoke an emotional reaction. You encourage opponent to investigate their outside option. A better strategy is to help your employer see for herself that you may quit. Eco380, Competitive Strategy 10

6 War of Attrition 2 firms in market. When both in lose $c per period. Last firm wins market worth $1k. If both exit split prize. Examples: exit in declining industry, patent race, stags, NHL strike. Solution Each player drops out with probability p = 1 1 2c Expected profit equals p/2 which increases in c. War may last a long time. Even winner may lose money. Eco380, Competitive Strategy 11 Case Study: Texaco Pennzoil Jan 1984: Pennzoil agreed to acquire 3/7 of Getty oil. One week later: Texaco bought all of Getty. Pennzoil sued for breach of contract. Nov 1985: jury awarded Pennzoil $12 billion. Feb 1987: Appeals Courth lowered this to $10 billion. Apr 1987: Texaco went into bankruptcy to stop a liens on assets. Dec 1987: Texaco and Pennzoil eventually agreed a settlement of $3 billion. These shocks reduced the combined values of the companies by $3.4 billion. See Cutler and Summers (Rand, 1988). Eco380, Competitive Strategy 12

7 Inefficient Bargaining When bargaining you have two aims: 1. Maximise the size of the pie (cooperation) 2. Obtain a large share for yourself (competition) Bargaining may be inefficient: Investment in outside options Insufficient investment in pie (since only obtain half) Delay Lawyers fees A mediator can help reduce waste. Find more efficient way of bargaining. Settlement escrow Final offer arbitration Merger Eco380, Competitive Strategy 13 Summary Design protocols to maximise the pie. Look at the game from your opponents perspective Above all, your slice of pie depends upon value added. Raise your value added Lower your opponents value added Eco380, Competitive Strategy 14