Managerial Economics: Topic 4 Multiple-person bargaining

1. Managerial Economics: Topic 4Multiple-person bargaining Core bargaining Added value The range of possible prices Splitting the range?

2. Review:Efficiency= Maximising the Surplus Under specific conditions we�ve outlined: 1. The players meet and agree to take the actions that maximize surplus (�make the pie as large as possible�). bargaining is efficient (surplus maximised = no wasted surplus). 2. The players bargain over payments only = dividing the pie

3. �CORE� Bargaining Basic idea of Core Bargaining = Multi-person bargaining is like a �trading pit� for contracts if you are about to sign a contract with a group, specifying what everyone gets, people can shout out alternative offers of contracts if any of those offer are more attractive, you change. RULE = NO group or individual will ever accept less payoff than their outside option (=what the group could get if they split off & went on their own)

4. CORE bargaining rule for 2 people? With 2 people: You will never get less payoff than your outside option (= your BATNA), otherwise you�ll give up on negotiations and take your BATNA Depending on bargaining skill and the other factors described, you�ll get more or less of the surplus. If you are evenly matched in skill, delay costs, and risks of breakdown, you�ll get half the surplus. But that is less certain than that you should never accept less than your BATNA.

5. The Core Consider ALL the players at once: An allocation refers to a split of the total payoff available to all players An allocation is blocked if some individual or subgroup is better off separating and going their own way (i.e. the allocation does not give them their outside option) An allocation is in the core if it cannot be blocked by any individual or coalition

6. Example Three firms, A, B and C are negotiating a joint venture (JV). If any firm does not join the JV then it receives nothing. Firm B is critical to the JV. If firms A and C just set up the JV alone then they get nothing. Neither A nor C is critical to the JV. If A and B work together then they get $220m. Similarly if B and C work together then they get $200m But if all three work together then they get $300m in total

7. Example What is the �range of likely bargaining outcomes� (i.e. the core)? Is an equal split blocked? Yes! Under an equal split, A, B and C each get $100m. So B and C together get $200m. But if A and B leave C out of the JV, then they get $220m. So the coalition of A and B will block an even split. To be in the core we need a split so that each player gets a positive payoff; A and B together get at least $220m; B and C together get at least $200m; and the total $300m is divided up. e.g. A gets $90m, B gets $160m, C gets $50m.

8. Questions on the example: Is there a maximum that A can get? (How do I figure it out?) whatever I give A, the rest of the $300m is for B and C�. If I give A $250m, then B and C get $50m� Is there a maximum that B can get? Is there a maximum that C can get? Based on the above, Is there a minimum that A can get? (try an example) Is there a minimum that B can get? Is there a minimum that C can get? How are the minimum and maximum related?

9. Example A cannot get more than $100m, otherwise B and C will leave and earn $200m C cannot get more than $80m, otherwise A and B will leave and earn $220m There is no maximum on what B could get: the whole $300m could go to B, and A and C could get $0. The �cap� on A and C implies a minimum for B: If A and C can�t get more than $100m and $80m, then B can�t get less than $120m!

10. Lessons on multi-party bargaining The core sets the range of bargaining outcomes No player or sub group gets less than their outside alternative ASIDE: In some cost-sharing negotiations, the core may not exist (see handout): leads to unstable bargaining But we are concentrating on simple buying-selling problems. In buying-selling problems with constant or increasing production costs, the core always exists!

11. Added Value = contains all the necessary information about the core, in a simple buying-selling problem

12. Surplus and Added Value Remember: To find the actions that maximise surplus, think of the bargaining players as a big team or a family, doing what�s best for the group. Your Added Value = roughly, the economic profit from you cooperating with the rest of the group maximize the pie, cooperate (Group & you) a new option! Others cooperate, but you don�t cooperate with rest of group

13. What is Total Surplus? Total Surplus = (And we assume that when you cooperate, you take the action that creates the largest total payoff for the group.)

14. What is your Added Value? Your Added Value = If you leave the group (right-hand box), the rest of the group keeps maximizing their payoff without you. Careful!! Your added value is NOT what you get from bargaining; it�s the MAXIMUM you could get.

15. Property 3 of bargaining: You can�t get more than your Added Value Why can�t you get more than your Added Value (= the surplus created by you joining the group)? Because if you get more than your Added Value, the group would get more by refusing to cooperate with you. It�s as if they think about whether or not to �gang up� on you, and exclude you.

16. Added Value - The Movie When Macaulay Culkin was picked for Home Alone, he took the role for little more than $100,000. Twentieth Century-Fox released the film in 1990. It grossed $286 million in the home market alone and went on to become the sixth highest grossing movie ever.

17. Added Value - The Sequel The story of the sequel, Home Alone 2: Lost in New York, was very different. This time, Macaulay got paid around $5 million, plus five percent of the domestic gross. The sequel rapidly grossed $174 million, and that added another $8.7 million to Macaulay�s paycheck, helping him become the youngest of Hollywood�s top-40 grossing artists.

18. Added Value

19. No more than your Added Value! Calculate Macaulay Culkin�s Added Value if: His potential replacement would earn $100,000 in another movie Macaulay would earn $2 million in another movie The studio expects to earn $80 million (before deducting salary of actor playing central role) if Macaulay plays in HA2, and only $10 million if another actor plays central role. Would the studio ever pay Macaulay more than his Added Value?

20. ? Limit their Added Value! A key aspect of strategy = try to limit the Added Value of other players = make them dispensable! If the other players all have limited Added Value, you might have guaranteed yourself a big slice of the pie = �competitive advantage� Back to the Joint Venture example: How much of the pie is guaranteed to player B?

21. Buying and Selling:Using Added Value Monopoly Multiple buyers and sellers

22. Monopoly If you are indispensable to negotiations, your Added Value is the whole surplus In 2-person negotiations, each person�s Added Value is equal to the Total Surplus Check that using the definitions They can�t both get their whole Added Value! In multi-person negotiations: If you are a monopoly (or monopsony), your added value equals the whole surplus In other words, individuals or subgroups that do not include you do not get any payoff.

23. Applying CORE Bargaining In-class exercise: There is a monopolist with restricted capacity: he can only produce 1 unit, at a marginal cost of $2k. There are two interested buyers: Firm Alpha, with a WTP of $8k, and Firm Beta, with a WTP of $6k. Step a: Figure out what the surplus-maximising agreement is. Step b: Calculate the Added Value of buyer A. Step c: �Buyer A can�t get more surplus than his AV� ? only certain prices are possible: if A pays too low a price, she gets too much surplus ? convert the statement into a range of possible prices

24. How to do step c: We have calculated in step (b) that firm Alpha�s added value is $2k Firm Alpha can�t walk away with more than $2k of surplus. Remember that a buyer�s surplus is measured graphically, from the WTP downward: If my WTP is $8k and I pay $5k, then I got $3k of surplus that means I paid too much!

25. How to do step c:

26. (using Property 2: Equity) CORE bargaining can only tell us what the range of possible prices is. But sometimes we need a more specific answer! Sometimes we assume an Equity Property: that the negotiators split the range of possible prices with each buyer. (But this is just an assumption�it will not necessarily happen!) IF we make that assumption, what is the outcome, in terms of prices?

27. Multiple Buyers and Sellers Now let�s think about a market where there are several buyers and several sellers: it sounds complicated, but the Added Value approach still works! Suppose there are three sellers, S1, S2 and S3, who can each produce one unit only (remember, most firms have some capacity constraints!) There are three buyers, A and B and C, with different WTP

28. Applying CORE Bargaining Step 1: Figure out what the surplus-maximising agreement is. Figure this out using marginal thinking: does it create surplus to produce one unit? If so, does it create more surplus to produce a second unit? If so, does it create more surplus to produce a third unit? � (here there are only 3 units; otherwise can keep going) There exists a very helpful tool for this: graph the WTP in descending order and the WTS in ascending order

29. WTP and WTS with many buyers and sellers

30. Applying CORE Bargaining Step 2: Calculate the Added Value of each player (do this in turn for each player). Step 3: �No player can get more surplus than his AV� ? only certain prices are possible: if A pays too low a price, he gets too much surplus; if S1 gets too high a price, she gets too much surplus ? convert the statements into ranges of possible prices ? do this for each player

31. Outcome with Multiple Buyers and Sellers Result: the excluded buyers and sellers put limits on the range of possible prices If either buyer pays more than $6, excluded seller S3 will jump in with an offer to sell for a little less ? price will be pushed down below $6 If any seller gets less than $5 from her buyer, excluded buyer C will jump in with an offer to pay a little more ? price will be pushed up above $5. ? buyers will be paying very similar prices (This is different from the result with a monopolist: if there is a monopolist, buyers could be paying very different prices, based on their WTP. But with competition between sellers, the presence of excluded sellers puts a ceiling on prices.)

32. Bargaining outcome with very many Buyers and Sellers As more and more buyers and sellers join the market, there is less and less gap between the WTP of different buyers and the WTS of different sellers. Lining up the buyers according to their WTP starts to look like a smooth line, not a �staircase� With many buyers & sellers, there is almost no variation in the possible prices that can be negotiated: If a seller tries to get a higher price, there are lots of sellers willing to sell for less If a buyer tries to get a lower price, there are lots of buyers willing to pay more = the �law of one price�: in a big market, most transactions take place at very similar prices. Ex: Foreign exchange markets

33. WTP and WTS with 5 buyers and 5 sellers

34. WTP and WTS with many buyers and sellers With many buyers & sellers, and a trading pit, there is almost no variation in the possible prices that can be negotiated = the �law of one price�