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Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

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Page 1: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Group Reputations, Stereotypes, and Cooperationin a Repeated Labor Market

Paul J. Healy

U. Pitt. Feb. 2006

Carnegie Mellon University

Page 2: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Plan

• Introduce the basic game

• Review of past experiments– What is really going on?

• Develop a model of group reputations

• New experiments & fit to model

Page 3: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The “Gift Exchange” Game• n workers, m firms, n > m• Stage 1

– Each firm j posts a wage wj {5,10,15,…}

– Workers can each accept one wage offer– Each firm hires only one worker unemployment

• Stage 2– Each hired worker i selects an effort ei {1,…,10}

• Payoffs– Firm: j(w,e) increasing in e, decreasing in w

– Worker: ui(w,e) increasing in w, decreasing in e

– Prediction: e*=1 and w* = min{w : ui(w,e*) 0}

Page 4: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Fehr Kirchsteiger & Riedl ‘93

• Two rooms: buyers & sellers• Period: 3 min. or all firms are matched• Wage offers: open out-cry• Wage revisions: must beat outstanding offers• Worker acceptance: open out-cry (hectic!)• Effort choice:

– Private decisions at end of period

Page 5: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

FKR93 Payoff Functions

j(w,e) = (126 – w)(e/10)

“your” buyer’s conversion rate depends on you

ui(w,e) = w – 26 – c(e)

Unmatched agents receive zero payoff

e 1 2 3 4 5 6 7 8 9 10

c(e) 0 1 2 4 6 8 10 12 15 18

w 0, 5, 10, 15, 20,

e 1 w 30

Page 6: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

FKR93 Isoprofit Lines

Page 7: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

FKR93 Results

Page 8: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

FKR93 Results

• Wage/effort correlation => reciprocity

Page 9: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Charness 98• Treatment: Wage chosen or randomly assigned• Exogenous matching design• Results:

– Reciprocity (wage/effort correlation)– Less reciprocity with random wages

Charness 98

0.1

0.2

0.3

0.4

1 2 3 4 5 6 7 8 9 10Period

Average Wage

Average Effort

Page 10: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Fehr & Falk 99• Wages: Double auction• Treatments: Effort chosen or given

Page 11: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Hannan, Kagel & Moser ‘02• One-sided posted wage market• Motivation: USA vs. Europe• Result: MBAs different from undergrads

Page 12: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

FKR98

• Same design + exogenous effort treatment

• Results– Significant reciprocity in 13/16 workers– High wages are generally profitable

– Group reputation: does et affect wt+1? No

– Exogenous effort => wages drop toward equil.

Page 13: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Session 1

0

0.1

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1

0 6 12 18 24 30 36 42 48Bid #

Wage

Effort

Session 3

0

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0 7 14 21 28 35 42 49 56Bid #

Wage

Effort

Session 4

0.00

0.10

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1.00

0 8 16 24 32 40 48 56 64Bid #

Wage

Effort

Session 2

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0 6 12 18 24 30 36 42 48Bid #

Wage

Effort

Page 14: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Charness, Frechette & Kagel 01

• Less cooperation when payoff table is given• More significant time trends (“humpback”)

Page 15: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Rigdon ‘02• (Slightly) Increase marginal cost of effort• Computerized => less experimenter effect

j(w,e) = v(e) – w ui(w,e) = w – 2(e –1)

e from 1 to 6 w from 10 to 35

Page 16: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Brandts & Charness 03

• Excess supply of workers vs. firms• Minimum wage

j(w,e) = 10 – w + 5e

ui(w,e) = 10 – e + 5w

Page 17: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Riedl & Tyran 04• Tax-side equivalence

j(w,e) = 30 – w + 10e [– 20]

ui(w,e) = w – e [– 20]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 16 32

w (ToF/ToW)

e (ToF/ToW)

w (ToW/ToF)

e (ToW/ToF)

Page 18: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Lynch Miller Plott Porter #21

• Wage: Double auction• Effort: Binary (e = 0 or 1)• ID# and effort choices are publicly observed• Subjects experienced in >2 other treatments• Multiple units, Quasi-linear payoffs

j(w,e) = v(q,e) – w– High cost:

ui(w,e) = w – 20 – 100e– Low cost:

ui(w,e) = w – 20 – 25e

Page 19: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

LMPP #21 Results

Page 20: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Other LMPP Results

• Some end-game effects (low effort at high price)

• Price received by a seller depends on:– own history of effort (usually)– market history of effort (sometimes)

• Also get “lemons” with high costs when IDs & choices are private

Page 21: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Summary of Previous Data

• Reciprocity is very strong• Individual-level heterogeneity• Subject pool effects• Wage & effort need to be choice variables• Matching mechanism not important• Surplus of labor not important• Cooperation sensitive to payoffs

– Quasi-linearity not necessarily important

• Often time trends, end-game effects

Page 22: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Developing a Story

1. Time trend => repeated game effects

2. But finite repetition => unraveling

3. Kreps, Milgrom, Roberts & Wilson (1982)“Reputation building” in repeated P.D.

We do observe heterogeneity…

4. But anonymity => no reputation building

• Recall LMPP: “market reputation”• Need a modified KMRW story

Page 23: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model I: 2 players, 2 actions

• 1 worker, 1 firm, 1 period

w w,w e e , e

1 -1 2 0

1 2 -1 0

Page 24: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model I: 2 players, 2 actions

• Unconditionally reciprocal worker

(Generally, e is a particular increasing function of w)

1 -1 2 0

1 2 -1 0

ew e ew e

X X

Page 25: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model I: 2 players, 2 actions

• Firm uncertainty:

1 0 1 -1 2 0

1 0 1 2 -1 0

E w 2p 1E w 0

PrReciprocal p

Page 26: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

w, e w, e w, e w, e

p w, e 1 p w, e w, e

p w , e w , e w , e w , e

: p

Page 27: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model I: Full Reputation Equil.

• T-Period “Full Reputation Equilibrium”:

Common knowledge prior: p0 0, 1p t p0 if e was "reciprocal" tp t 0 otherwise

w t w tet e t TRational: eT eReciprocal: eTw e

eTw e

Page 28: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model I: Full Reputation Equil.• Period T :

• Period T-1 :Assume wT 1 w

e pT p0 uw, e uw, e e pT 0 uw, e uw, e

e e uw , e uw , e uw , e uw , e

:

1, and we assume 1Assume wT 1 w

Playing e reduces payoff now, sets pT 0.

Worker behavior is sequentially rational.Firm: assume p0 p . So pT p0 w

Page 29: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model I: Full Reputation Equil.

• Period T-1 Firm:

Proposition: With 2 players, a full reputation equilibrium exists iff

Note: there are many other sequential equilibria!

p0 p and

w w, e Period T with pT pT 1w w, e Period T with pT pT 1

Page 30: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model II: Multiple Agents

• m firms, n workers, m > n• “Random” matching

– Unmatched players earn zero

• Identities, partners, & actions are public info

• Same argument, except1. Each worker has their own reputation (pj)

2. Worker discount factor in T-1:

Proposition: FRE exists iff

m/n

p0 p and m/n

Page 31: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model III: Anonymous Matching

1. All actions are publicly observed• At least: all wages are publicly observed

2. Firms don’t know ID of other firms’ workers

3. Firms don’t know ID of their own worker• Minimizes reputation-building• Beliefs are symmetric, tractable• Matches experimental environments

Page 32: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

• Firms carry one belief about all workers: pt

• One worker defects in period t :

• Suppose

If one worker defects,

Proposition: A full reputation equilibrium exists iff

The Model III: Anonymous Matching

p t 1 p t n 1n

pT 1 p nn 1

pT p wT w

p0 p , nn 1p and m/n

Page 33: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model III: Anonymous Matching

• FKR93:

• Need something else…

w, e 30, 1 w, e 100, 10m/n 2/3 0. 257p 0. 299p 0. 299, 0. 336

Page 34: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model IV: Type Correlation

“Stereotyping” parameter

1. Rational: uncertainty about type distribution

2. Irrational: stereotyping

PrRecip i p0

Pr Recip i |Selfishj 1 p0

0, 1

Page 35: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Stereotyping in the Lab

• Economics Experiments:– McEvily, Weber et al.: Trustworthiness in trust games

is inferred from (irrelevant) group membership (MGP)

• Social Psychology Experiments:– Acknowledging heterogeneity no stereotyping– Stereotype formation when the group affects you– Stereotype formation in group competitions– Under cognitive load:

Stereotype formation Stereotypes change more dramatically w/ new

info

Page 36: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model IV: Type Correlation

• One worker defects in period t :

• Proposition: A full reputation equilibrium exists iff

• Gamma large => back to public matching:

p t 1 1 p t n 1n

p0 p , 11

nn 1p and m/n

p0 p and m/n

Page 37: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Summary of Previous Data (Again)

• Reciprocity is very strong• Individual-level heterogeneity• Subject pool effects• Wage & effort need to be choice variables• Matching mechanism not important• Surplus of labor not important• Cooperation sensitive to payoffs

– Quasi-linearity not necessarily important

• Often time trends, end-game effects

Page 38: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

The Model IV: Type Correlation

• Get and from experiment parameters– Depend on and

• Don’t know and

• Assume:

p

p0

p0 U0, 1 U0, 1

w, e w, e

Prexists p 1 ln p n

n 1nn 1

1 if m/n

0 if m/n

maxPrexists e n 1n

Page 39: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University
Page 40: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

New Experiments

1. Replicate FKR93 at Caltech Same instructions, protocol, payoffs

2. Same as (1.), but decisions are public

Wages & effort linked to ID#s

Effort chosen immediately

3. Same as (2.), but payoffs make F.R.E. unlikely

Page 41: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Predictions: 1• Treatment 1: p 0. 299 m/n

Existence if p0 0. 3, 0. 68 and 1/2

Page 42: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

Page 43: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

Page 44: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

• Effort and wage are positively correlatedCorrelation coefficients > 0.446, significant

• Cooperation “pops” completely in final periodSignificant

• Wage increasing in periods 1 through 11

• Suggests: subject pool differences

Page 45: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Predictions: 2• Treatment 2:

Hypothesis:

individual reputations strengthen reciprocity

p 0. 299 m/n

Page 46: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

Page 47: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

Page 48: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

• Wages and efforts are significantly higher

• End-game effects

• Heterogeneity in end-game play

Page 49: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Predictions: 3• Treatment 3: w, e 126ve w

uw, e w 26 3ce

e c(e) v(e)

1 0 .35

2 1 .42

3 2 .49

4 4 .57

5 6 .64

6 8 .71

7 10 .78

8 12 .86

9 15 .93

10 18 1.0

Page 50: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Predictions: 3

• Don’t need stereotyping to get reputation effect• But…

F.R.E. rarely exists & bound on beliefs is high

m/n 6/9 0. 771p 0. 855

Page 51: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

Page 52: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

Page 53: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

Page 54: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

Page 55: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Results

• Min. effort is modal choice

• Effort converges to stage game equilibrium

• Reservation wage is modal choice

Page 56: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Switching: FKR New

Page 57: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Switching: FKR New

Page 58: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Riedl & Tyran

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 16 32

w (ToF/ToW)

e (ToF/ToW)

w (ToW/ToF)

e (ToW/ToF)

Page 59: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Rigdon

Page 60: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Lynch Miller Plott Porter

Page 61: Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market Paul J. Healy U. Pitt. Feb. 2006 Carnegie Mellon University

Conclusions

• Past data suggestive of repeated game effects• Group reputation-building story is plausible

– Can turn reciprocity on and off!– Stereotyping can increase social welfare

• Applications & directions– Any repeated moral hazard setting with many agents

• Insurance, IMF loans, unemployment, lemons markets…

– Group reputation effects in other domains• Asset bubbles, public goods, coordination problems…