Bargaining and Coalition Formation Dr James Tremewan - - PowerPoint PPT Presentation

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.”

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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.

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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 e100 into two piles, labeled A and B. Your

partner is to divide e100 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 e100. 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.

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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?

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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.”

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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.”

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Focal Points

Tacit bargaining: Schelling’s results

• A and B are to choose “heads” or “tails” without
• communicating. If both choose “heads,” A gets e3 and B gets

e2; if both choose “tails,” A gets e2 and B gets e3. 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.

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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,
• r scribbling it out; the one who gets the blank box has the
• ption 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 e3 and the one without an “X” gets e2. 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.

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Focal Points

Tacit bargaining: Schelling’s results

• You and your partner are to be given e100 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 e100, each gets exactly what they

• claimed. If the two claims exceed e100, neither of you get
• anything. How much do you claim?
• 36 out of 40 chose exactly e50.

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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.

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Focal Points

Tacit bargaining: Schelling’s results

• A and B have incomes of e100 and e150 per year, respectively.

They are notified of each other’s income and told that they must begin paying taxes totaling e25 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 e25 or more, each will pay exactly what they propose. If the proposed shares fail to add up to e25, however, each will individually be required to pay the full e25, and the tax collectors will keep the surplus.

• 7 out of 10 A’s chose e10 and 5 out of 6 B’s chose e15,

coordinating on shares proportional to income.

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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 e100: 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.

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Focal Points

Explicit bargaining

• In explicit bargaining situations, logically arbitrary but focal
• utcomes 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 e17.34, 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?

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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

• n.”
• 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?”

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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!

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Experiments on focal points in bargaining

Focal points in tacit bargaining problems: Experimental evidence

• Isoni et al (2013) is specifically designed to test Schelling’s

hypothesis about the nature and effectiveness of focal points in tacit bargaining problems.

• Idea: set up a bargaining environment where there are sometimes

payoff irrelevant cues and see if they help subjects to coordinate.

• Also, do focal points help if they imply asymmetric payments?

(i.e. if one player gets a larger share of the pie). Some earlier evidence from a different context suggests that even small deviations from symmetry can destroy the usefulness of focal points (Crawford et al; 2008).

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Experiments on focal points in bargaining

The games

• Subjects were either Red or Blue. They had to click on the discs

they wanted to claim without communicating with the other. If they each claimed different discs, they received points equal to the sum of the numbers on the discs they had claimed. If any disc was claimed by both, both received zero.

• The location of each persons ”base” is irrelevant to payoffs.

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Experiments on focal points in bargaining

The games: equality compatible/incompatible

• Games had two, four, or eight discs. In some games it was

possible to split the points equally, and in some it was not. The ”least unequal efficient” distribution of points varied from 5:5 to 10:1.

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Experiments on focal points in bargaining

The games: ”closeness” (type C)

• Half the discs are on one side, and half on the other. Each is

matched with a ”neutral” game which has the same discs, but in the middle column (type N or B, the latter if the discs were grouped in two blocks).

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Experiments on focal points in bargaining

The games: ”accession” (type A)

• There are discs in the middle column, but each of these is next

to a disc that is in one of the halves. Again, each is matched with a neutral game.

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Experiments on focal points in bargaining

Results

• Own side effect: subjects more often claimed discs on their side:
• Discs on the left side: claimed 69-81% of the time by L players,

13-21% by R players.

• Discs on the right side: claimed 7-16% of the time by L players,

64-81% by R players.

• Accession effect: if a central disc is attached to a block on the

LHS (RHS) it is more often claimed by the L (R) player.S

• Top-left/bottom-right effect: discs in the top half are more often

claimed by L players, whereas discs in the bottom half are more

• ften claimed by R players.
• Bottom bias: subjects are more likely to choose discs in the

bottom half than the top half.

• Remember: the location of discs is irrelevant to payoffs!

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Experiments on focal points in bargaining

Results: efficiency

• Do these effects (relational cues) assist coordination and increase

efficiency? (note that bottom bias should reduce efficiency)

• For the two-disc games there is a unique mixed-strategy Nash

equilibrium to use as a baseline (Nash efficiency).

• Blind efficiency uses the data from type N games and calculates

the expected value of efficiency if they chose the same number and values of discs, but randomized across locations (attempts to remove residual effects of spatial cues from N-game data).

• Standardized efficiency: expected value of efficiency after

random matching of data.

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Experiments on focal points in bargaining 24/32

Experiments on focal points in bargaining

Results: efficiency

• ”Closeness” is a powerful focal point in the equality-compatible

game, almost doubling efficiency compared to neutral games and theoretical prediction.

• The effect on efficiency diminishes as inequality in payoffs

decreases, but does not immediately disappear.

• Closeness allows the ”favoured player” (i.e. the player with the

higher value disc on their side) to earn significantly more in all 2-disc games.

• 4 and 8 disc games:
• Closeness increases efficiency significantly.
• Accession increases efficiency, but in most cases less than

closeness.

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Experiments on focal points in bargaining 26/32

Experiments on focal points in bargaining

Sticking to Prices?

• Holm and Svennson (2011) compare a standard Nash demand

game with one where the subjects bargain over an object with a well known standard price. This creates a second focal point in addition to the equal split.

• Nash demand game:
• 100 SEK plus an object of value v to be divided between a

”buyer” and ”seller”.

• Each submits a bid (b or s).
• If b ≥ s the buyer receives the 100 SEK and the object and

pays the seller p = (b + s)/2.

• If b < s, both receive nothing.
• ”Hypothetical treatment”: no object (v = 0).
• ”Milk treatment”: one litre of milk (usually priced around 8

SEK, but no price mentioned in experiment).

• Each participant makes decision in same role in both treatments

(order reversed in different sessions).

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Experiments on focal points in bargaining

Results

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Experiments on focal points in bargaining

Results

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Experiments on focal points in bargaining

Results

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Experiments on focal points in bargaining 31/32

Experiments on focal points in bargaining

• In the H treatment, the distribution is unimodal with a peak

around the equal split. In the M treatment there are two ”clumps”, one around the equal split, and one around the standard price of milk.

• Two focal points:
• Buyers are more likely than sellers to switch to the unequal

focal point (it benefits them).

• ”Self-serving bias”: when there are multiple ideas of fairness,

people tend to choose the one that benefits them.

• Probability of choosing according to milk price focal point:
• Decreasing in cognitive ability (smart people less affected by

arbitrary anchors and focus on underlying strategic situation).

• Increasing in milk consumption (increased salience of focal

point).

• Efficiency: adding a second focal point substantially reduced

efficiency (from 81% to 48%).

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