Group reputations stereotypes and cooperation in a repeated labor market
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Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market. Paul J. Healy. Carnegie Mellon University. U. Pitt. Feb. 2006. The Plan. Introduce the basic game Review of past experiments What is really going on? Develop a model of group reputations

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Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market

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Group reputations stereotypes and cooperation in a repeated labor market

Group Reputations, Stereotypes, and Cooperationin a Repeated Labor Market

Paul J. Healy

Carnegie Mellon University

U. Pitt. Feb. 2006


The plan

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


The gift exchange game

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}


Fehr kirchsteiger riedl 93

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


Fkr93 payoff functions

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


Fkr93 isoprofit lines

FKR93 Isoprofit Lines


Fkr93 results

FKR93 Results


Fkr93 results1

FKR93 Results

  • Wage/effort correlation => reciprocity


Charness 98

Charness 98

  • Treatment: Wage chosen or randomly assigned

  • Exogenous matching design

  • Results:

    • Reciprocity (wage/effort correlation)

    • Less reciprocity with random wages


Fehr falk 99

Fehr & Falk 99

  • Wages: Double auction

  • Treatments: Effort chosen or given


Hannan kagel moser 02

Hannan, Kagel & Moser ‘02

  • One-sided posted wage market

  • Motivation: USA vs. Europe

  • Result: MBAs different from undergrads


Fkr98

FKR98

  • Same design + exogenous effort treatment

  • Results

    • Significant reciprocity in 13/16 workers

    • High wages are generally profitable

    • Group reputation: does etaffect wt+1? No

    • Exogenous effort => wages drop toward equil.


Charness frechette kagel 01

Charness, Frechette & Kagel 01

  • Less cooperation when payoff table is given

  • More significant time trends (“humpback”)


Rigdon 02

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


Brandts charness 03

Brandts & Charness 03

  • Excess supply of workers vs. firms

  • Minimum wage

    j(w,e) = 10 – w + 5e

    ui(w,e) = 10 – e + 5w


Riedl tyran 04

Riedl & Tyran 04

  • Tax-side equivalence

    j(w,e) = 30 – w + 10e [– 20]

    ui(w,e) = w – e [– 20]


Lynch miller plott porter 21

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


Lmpp 21 results

LMPP #21 Results


Other lmpp results

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


Summary of previous data

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


Developing a story

Developing a Story

  • Time trend => repeated game effects

  • But finite repetition => unraveling

  • Kreps, Milgrom, Roberts & Wilson (1982)

    “Reputation building” in repeated P.D.

    We do observe heterogeneity…

  • But anonymity => no reputation building

  • Recall LMPP: “market reputation”

  • Need a modified KMRW story


The model i 2 players 2 actions

The Model I: 2 players, 2 actions

  • 1 worker, 1 firm, 1 period

1 -1 2 0

1 2 -1 0


The model i 2 players 2 actions1

The Model I: 2 players, 2 actions

  • Unconditionally reciprocal worker

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

X

X

1 -1 2 0

1 2 -1 0


The model i 2 players 2 actions2

The Model I: 2 players, 2 actions

  • Firm uncertainty:

1 0 1 -1 2 0

1 0 1 2 -1 0


The model i full reputation equil

The Model I: Full Reputation Equil.

  • T-Period “Full Reputation Equilibrium”:


The model i full reputation equil1

The Model I: Full Reputation Equil.

  • Period T :

  • Period T-1 :


The model i full reputation equil2

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!


The model ii multiple agents

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, except

    • Each worker has their own reputation (pj)

    • Worker discount factor in T-1:

      Proposition: FRE exists iff


The model iii anonymous matching

The Model III: Anonymous Matching

  • All actions are publicly observed

    • At least: all wages are publicly observed

  • Firms don’t know ID of other firms’ workers

  • Firms don’t know ID of their own worker

    • Minimizes reputation-building

    • Beliefs are symmetric, tractable

    • Matches experimental environments


Group reputations stereotypes and cooperation in a repeated labor market

The Model III: Anonymous Matching

  • 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 matching1

The Model III: Anonymous Matching

  • FKR93:

  • Need something else…


The model iv type correlation

The Model IV: Type Correlation

“Stereotyping” parameter

  • Rational: uncertainty about type distribution

  • Irrational: stereotyping


Stereotyping in the lab

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


The model iv type correlation1

The Model IV: Type Correlation

  • One worker defects in period t :

  • Proposition: A full reputation equilibrium exists iff

  • Gamma large => back to public matching:


Summary of previous data again

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


The model iv type correlation2

The Model IV: Type Correlation

  • Get and from experiment parameters

    • Depend on and

  • Don’t know and

  • Assume:


New experiments

New Experiments

  • Replicate FKR93 at Caltech

    Same instructions, protocol, payoffs

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

    Wages & effort linked to ID#s

    Effort chosen immediately

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


Predictions 1

Predictions: 1

  • Treatment 1:


Results

Results


Results1

Results


Results2

Results

  • Effort and wage are positively correlated

    Correlation coefficients > 0.446, significant

  • Cooperation “pops” completely in final period

    Significant

  • Wage increasing in periods 1 through 11

  • Suggests: subject pool differences


Predictions 2

Predictions: 2

  • Treatment 2:

    Hypothesis:

    individual reputations strengthen reciprocity


Results3

Results


Results4

Results


Results5

Results

  • Wages and efforts are significantly higher

  • End-game effects

  • Heterogeneity in end-game play


Predictions 3

Predictions: 3

  • Treatment 3:


Predictions 31

Predictions: 3

  • Don’t need stereotyping to get reputation effect

  • But…

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


Results6

Results


Results7

Results


Results8

Results


Results9

Results


Results10

Results

  • Min. effort is modal choice

  • Effort converges to stage game equilibrium

  • Reservation wage is modal choice


Switching fkr new

Switching: FKR  New


Group reputations stereotypes and cooperation in a repeated labor market

Switching: FKR  New


Riedl tyran

Riedl & Tyran


Rigdon

Rigdon


Lynch miller plott porter

Lynch Miller Plott Porter


Conclusions

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…


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