Bargaining and Coalition Formation Dr James Tremewan (james.tremewan@univie.ac.at) Focal Points
Focal Points Tacit Coordination • The scenarios you have just made choices in are examples of ”tacit coordination.” They are situations where some surplus is available to two parties if they can reach agreement without communication . • These examples (and most of today’s class) are taken from chapter 3 of ”The Strategy of Conflict” by Thomas Schelling (1960). • Schelling reports results of some ”unscientific experiments.” 2/32
Focal Points Tacit coordination: Schelling’s results • Name ”heads” or ”tails.” If you and your partner name the same, you both win a prize. • 36 people chose heads, and only six chose tails. • Circle one of the numbers listed in the line below (7,100,13,261,99,555). You win if everybody chooses the same number. • The first three numbers received 37 out of 41 votes. • Put a check mark in one of the sixteen squares. You win if everybody chooses the same square. • 24 out of 41 chose the upper left square. • Write some positive number. If you all write the same number, you win. • Two-fifths of people chose the number 1. 3/32
Focal Points Tacit coordination: Schelling’s results • Name an amount of money. If you all name the same amount, you can have as much as you named. • 12 out of 41 people chose $1,000,000. • You are to divide e 100 into two piles, labeled A and B. Your partner is to divide e 100 into two piles, labeled A and B. If you allot the same amounts to A and B, respectively, that your partner does, each of you gets e 100. If your amounts differ from his, neither of you gets anything. • 36 out of 41 split the total 50-50. • Where to meet on the map? • 7 out of 8 chose the bridge. 4/32
Focal Points Tacit coordination • Even without the ability to communicate, people can often coordinate much more than would be expected by chance. • The appropriate strategy is not to simply choose what you expect the other to choose because they will be choosing what they expect you to chose. • The trick is to choose what you expect the other to expect you to expect them to expect you to expect.... • It is all about coordinating expectations and identifying a signal that helps you do so, i.e. a particularly prominent option, or focal point . • But what does this have to do with bargaining? 5/32
Focal Points Tacit bargaining • The scenarios you have just made choices in are examples of ”tacit bargaining.” They are situations where some surplus is available be shared between two parties with divergent interests, but only if they can reach agreement without communication . • May seem contrived, but can be thought of as situations where both parties can commit to a position, but at the time they must commit, are unaware if the other party has committed to a possibly uncompatible position. • In many examples of tacit bargaining people are able to coordinate, despite divergent interests and a large number of possibilities for failure. • Schelling reports results of some ”unscientific experiments.” 6/32
Focal Points Extract from a letter by Goethe dated January 16, 1797, to the publisher Vieweg : ”I am inclined to offer Mr. Vieweg from Berlin an epic poem, Hermann and Dorothea, which will have approximately 2000 hexameters.... Concerning the royalty we will proceed as follows: I will hand over to Mr. Counsel Bottiger a sealed note which contains my demand, and I wait for what Mr. Vieweg will suggest to offer for my work. If his offer is lower than my demand, then I take my note back, unopened, and the negotiation is broken. If, however, his offer is higher, then I will not ask for more than what is written in the note to be opened by Mr. Bottiger.” 7/32
Focal Points Tacit bargaining: Schelling’s results • A and B are to choose “heads” or “tails” without communicating. If both choose “heads,” A gets e 3 and B gets e 2; if both choose “tails,” A gets e 2 and B gets e 3. If they choose differently, neither gets anything. • 16 out of 22 A’s and 15 out of 22 B’s chose heads, and on average did substantially better than choosing at random. 8/32
Focal Points Tacit bargaining: Schelling’s results • You and your partner both have a box beneath this question. One of the boxes is blank, and the other has an “X” written in it. The one who gets the “X” has the option of leaving it alone, or scribbling it out; the one who gets the blank box has the option of leaving it blank or writing an“X” in it. If, when you have made your choices without communication, there is an “X” in only one box, the person who has the “X” in their box gets e 3 and the one without an “X” gets e 2. If both sheets have “X”s or both sheets are blank, neither gets anything. • 18 out of 22 with the original X left it, and 14 out of 19 with a blank box left it blank, and on average did substantially better than choosing at random. 9/32
Focal Points Tacit bargaining: Schelling’s results • You and your partner are to be given e 100 if you can agree on how to divide it without communicating. Each of you is to write the amount of your claim on their own sheet of paper; if the two claims add to no more than e 100, each gets exactly what they claimed. If the two claims exceed e 100, neither of you get anything. How much do you claim? • 36 out of 40 chose exactly e 50. 10/32
Focal Points Tacit bargaining: Schelling’s results 14 of 22 x’s and 14 of 23 y’s drew their boundaries exactly along the river. The other 15 chose 14 different lines. 11/32
Focal Points Tacit bargaining: Schelling’s results • A and B have incomes of e 100 and e 150 per year, respectively. They are notified of each other’s income and told that they must begin paying taxes totaling e 25 per year. If they can reach agreement on shares of this total, they may share the annual tax bill in whatever manner they agree on. But they must reach agreement without communication; each is to write down the share they propose to pay, and if the shares total e 25 or more, each will pay exactly what they propose. If the proposed shares fail to add up to e 25, however, each will individually be required to pay the full e 25, and the tax collectors will keep the surplus. • 7 out of 10 A’s chose e 10 and 5 out of 6 B’s chose e 15, coordinating on shares proportional to income. 12/32
Focal Points Tacit bargaining • People use a variety of features to coordinate: • Heads and tails: coordinated on first option (?). • Xs in boxes: coordinated on status quo. • Splitting e 100: coordinated on 50-50 split. • Map: coordinated on natural geographical feature. • Taxes: coordinated on shares proportional to income. Note that if extra information was given, such as family size, expenditure, etc. choices moved to 50-50 split. • As with tacit coordination with common interests, the parties must coordinate expectations of what the other will do by identifying a focal point. 13/32
Focal Points Explicit bargaining • In explicit bargaining situations, logically arbitrary but focal outcomes are also common: • Round numbers in final prices. • Wage increases of integer %. • International agreement on contribution to UN Relief and Rehabilition Adminstration after WWII of 1% of GDP. • Korea divided along the 38th parallel (circle of latitude). • Why not agree on a price of e 17.34, a wage increase of 1.96%, a contribution of 1.03% of GDP, 37 ◦ 18 ′ 39 ′′ N? If latitude was defined by grads instead of degrees, would North Korea be a little bit bigger or smaller? 14/32
Focal Points Explicit bargaining • In explicit bargaining, parties must coordinate expectations : • ”The final outcome must be a point from which neither expects the other to retreat; yet the main ingredient of this expectation is what one thinks the other expects the first to expect, and so on.” • Because of divergent interests, these expectations cannot be credibly communicated , thus the analogy with tacit bargaining. • E.g. If the army retreats beyond the 38th parallel, then where will they stop? • E.g. The feasible wage increases may be between 1.6 and 2.3 %. If the union drops below 2% then how low will it go? • Focal points seem to provide natural points at which one party may dig their heels in, and the other may expect them to dig their heels in. • Key question: ”If not here, then where?” 15/32
Focal Points Focal points and bargaining: a summary • In a bargaining situation, many different divisions of the surplus are possible which would benifit both/all parties. • In order for agreement to be reached, the parties must coordinate their expectations about what each of them are willing to accept. • Because the interests of the parties are divergent, what they are willing to accept (and their expectations of what the others are willing to accept, etc.) cannot be credibly communicated. • Focal points help people coordinate their expectations and reach agreement. • Important note: Chapters 2 and 3 of ”The Strategy of Conflict” by Schelling are compulsory reading (will be available on moodle soon). I may ask questions related to them in the final exam! 16/32
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