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

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Bargaining and Coalition Formation

Dr James Tremewan (james.tremewan@univie.ac.at) Early experiments on non-cooperative bargaining models

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Early experiments on non-cooperative bargaining models

An Experimental Analysis of Ultimatum Bargaining, G¨

uth et al (1982).

Looks at one round of bargaining and finds significant

deviations from predictions.

Testing Noncooperative Bargaining Theory: A Preliminary

Study, Binmore et al (1985).

Looks at two rounds of bargaining and fnds results more

supportive of predictions.

A Further Test of Noncooperative Bargaining Theory:

Comment, Neelin et al (1988).

Looks at two, three, and five rounds of bargaining, and...
An Experimental Study of Sequential bargaining, Ochs and Roth

(1989)

Investigates the experiments of the previous three papers more

methodically and gains new insights.

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SLIDE 3

G¨ uth et al (1982)

An Experimental Analysis of Ultimatum Bargaining, G¨ uth et al (1982)

Paper includes the first published experiment on the Ultimatum

Game (also another bargaining experiment).

Subjects were graduate students of economics (apparently

unlikely to be familiar with game theory).

Each played one UG as either proposer or receiver for somewhere

between four and 10 DM.

Same subjects repeat the experiment one week later with

(possibly) different amount and partner, but same role.

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SLIDE 4

G¨ uth et al (1982)

Results

Each experiment consisted of 21 games.
Average demands: 65% (naive); 69% (experienced).
50/50 splits: 7 (naive); 3 (experienced).
Rejections: 2 (naive); 6 (experienced).
Demands were far from SPE prediction (100%).
Rejections occured, counter to SPE prediction.
With experience, demands moved closer to SPE, but number of

rejections increased.

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SLIDE 5

Binmore et al (1985)

Testing Noncooperative Bargaining Theory: A Preliminary Study, Binmore et al (1985)

Two stage game:
Stage 1: Cake is worth 100 pence. Player 1 makes proposal

(X). Player 2 accepts (1 receives X, 2 receives 1 − X) or rejects (game continues).

Stage 2: Cake is worth 25 pence. Player 2 makes proposal (X ′).

Player 1 accepts (1 receives X ′, 2 receives 1 − X ′) or rejects (both receive zero).

SPE outcome: Player 1 demands 74-76 pence and Player 2

accepts.

After initial play (Game A), subjects exchange roles (Game B).

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SLIDE 6

Binmore et al (1985)

Results: Opening Demands

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SLIDE 7

Neelin et al (1988)

A Further Test of Noncooperative Bargaining Theory: Comment, Neelin et al (1988)

Subjects (intermediate micro-theory students) with played either

two, three, or five round alternating offer bargaining games.

Two rounds: Cake worth $5, then $1.25.
Three rounds: Cake worth $5, then $2.50, then $1.25.
Five rounds: Cake worth $5, then $1.70, then $0.58, then $0.20,

then $0.07.

Amounts chosen such that SPE predicts demand of $3.75 in first

round in each game.

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SLIDE 8

Neelin et al (1988)

Results: First round

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SLIDE 9

Neelin et al (1988)

Results

Two round game replicates Game B of previous study: modal

demand as per SPE.

Three round game: modal demand equal split... fairness?
Five round game: modal demand leaves $1.70 for Player 2...

=size of round two cake.

Common thread: In each case Player 1 leaves Player 2 the

maximum they could receive if the game continues to the next round.

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SLIDE 10

Interlude

Interlude: the story so far

Subjects do exploit their strategic advantage to some extent in

longer games, when they understand it (e.g. after experience, or micro-theory class).

In two round games, SPE was a good predictor.
In longer games, less so. Subjects seem to only look one round

ahead, but still reason to some extent a la game theory.

In the UG, initial demands are typically a long way from SPE

prediction, and substantial offers are rejected. Why the difference? Possibilities:

In equilibrium, Receiver is indifferent between accepting and
rejecting. For small offers they may reject at almost no cost.

Proposer must guess minimum to make rejection costly.

In SPE, initial offer in UG is blatently unfair... in longer games,

less so.

In longer games there is a new focal point (the size of cake in

second round); in UG only zero offer or 50-50 split.

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SLIDE 11

Interlude

Interlude: the story so far

Difficult to draw conclusions from comparing these studies:
Different subject pools (level of knowledge of game theory etc.).
Different experimental instructions:
Binmore et al: ”YOU WILL BE DOING US A FAVOUR IF YOU

SIMPLY SET OUT TO MAXIMIZE YOUR WINNINGS.”

Neelin et al: ”You will be discussing the theory this experiment

is designed to test in class.”

Different degrees of anonymity:
G¨

uth et al: subjects could see each other and used pencil and paper.

Binmore et al: subjects interacted via computer.
Multiple things changed at once, so cannot isolate cause of

effects, e.g. Neelin et al changes number of rounds and discount factors simultaneously.

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SLIDE 12

Ochs and Roth (1989)

Ameliorates some of the concerns in the previous slide.
Introduces a new factor:
In some treatments the two subjects have different discount

factors.

Achieved by altering exchange rates: subjects always bargain
ver 100 tokens, but exchange rate varies between subjects and

between rounds.

Subjects undergraduate economics students; played 10 rounds of

stranger-matching in one role only; mediated by computer (each role in seperate room); one round paid at random.

4 x 2 design:
Different discount rates:

(δ1, δ2) ∈ {(0.4, 0.4), (0.6, 0.4), (0.6, 0.6), (0.4, 0.6)}.

Two or three period games.

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SLIDE 13

Ochs and Roth (1989) 13/19

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Ochs and Roth (1989)

Results: SPE as prediction

Poor point prediction of first period offer: average within 2

standard deviations of SPE only in Cell 1.

Also fails to account for qualitative differences:
In 2-period game δ1 should not affect offer, but significant

difference between 1-2 and 3-4 (”more patient” P1 offers less).

Holding discount factors constant, initial offer should be lower

in 3-period than 2-period game: true in only two of four comparisons.

SPE predicts a qualitative difference in means in 25

comparisons: direction correct in 17 out of 25 (coin toss correct 12.5 times).

SPE predicts zero rejections, but 125/760 first period offers

rejected (10/76 in final round).

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SLIDE 15

Ochs and Roth (1989)

Observed (unpredicted) regularities

Consistent first-mover advantage in all cells.
Discount factor of player 1 had influence even in 2-period games.
Substantial fraction of offers rejected.
Observed mean agreements deviated from SPE in direction of

equal division.

A substantial fraction of rejected offers were followed by

counterproposals where the new proposer got less than they had just rejected - strong evidence that utility is determined by more than simply own earnings.

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SLIDE 16

Ochs and Roth (1989)

Explaining the regularities

Authors discuss ”mimimum acceptance thresholds” (in absolute

terms): can explain first three regularities, but not the last two.

Authors claim that disutility of ”unfair” offers, where unfairness

is deviation from 50-50 split as the most promising explanation

f their data (explains all five regularities).
Note that this does not mean that ”fair” offers imply that

proposer is fair, just uncertainty over others’ fairness concerns.

Evidence of heterogenous fairness concerns as private info:
16/76 P1s always offered 50% in first period.
28/76 P1s started high in first round and reduced offers in later

rounds if accepted.

14/76 P1s started low in first round offered more in later rounds

if rejected.

Some genuine nice guys, and others searching for the biggest

cut they can get.

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SLIDE 17

Discussion

General Discussion of Experimental Evidence

Experimental results appear to find significant deviations from

game theoretic predictions.

Offers are too fair.
Not enough efficiency (some offers are rejected).
Failure to perform backward induction more than one round.
But so far the theory has been about perfect information games;

have the experiments involved perfect information?

These experiments involved perfect information about payoffs...

but not about preferences!

It is preferences over payoffs that determine actions!
Way forward:
Build model of fairness concerns, and allow for imperfect

information about other’s preferences.

Models of bounded rationality (not for this course).
Game Theory is dead! Long live Game Theory!

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SLIDE 18

Mid-term Exam

Part 1: Maths
Find the Nash Bargaining solution given a particular set of

utilities or profits. (25%)

Solve a slight variation on the alternating bargaining model you

have seen in slides. (25%)

Part 2: Short essays. Four of the following six topics will be in

the exam. Write a short essay on two. (25% each)

Explain the differences between the axiomatic and

non-cooperative approaches to modeling bargaining. What are the advantages of each?

What are some testable predictions of the Nash Bargaining

Solution? To what extent are these predictions supported by experimental or empirical evidence?

How can infinitely repeated alternating bargaining games be

implemented in the laboratory? How well does the experimental evidence support the predictions? *(Not in slides)

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SLIDE 19

Mid-term Exam

Part 2: Short essays (continued)
Discuss the case for modeling household consumption decisions

as the result of bargaining rather than as a decision of a single

agent. Refer to empirical evidence in favour of the model, and

theoretical implications.

What is the evidence that culture plays a role in influencing

bargaining behaviour?

What is the evidence that biology plays a role in influencing

bargaining behaviour?

Essays should make coherent argument and not be a series of

bullet points. Information from slides is sufficient to pass, extra evidence from presented papers is better. Relevant reading

utside suggested papers will be rewarded (but please cite).
Part 3: Surprise Bonus Question! (maybe 5%).

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