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

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

2. 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

3. 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}

4. 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

5. 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

6. FKR93 Isoprofit Lines

7. FKR93 Results

8. FKR93 Results • Wage/effort correlation => reciprocity

9. Charness 98 • Treatment: Wage chosen or randomly assigned • Exogenous matching design • Results: • Reciprocity (wage/effort correlation) • Less reciprocity with random wages

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

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

12. 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.

14. Charness, Frechette & Kagel 01 • Less cooperation when payoff table is given • More significant time trends (“humpback”)

15. 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

16. Brandts & Charness 03 • Excess supply of workers vs. firms • Minimum wage j(w,e) = 10 – w + 5e ui(w,e) = 10 – e + 5w

17. Riedl & Tyran 04 • Tax-side equivalence j(w,e) = 30 – w + 10e [– 20] ui(w,e) = w – e [– 20]

18. 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

19. LMPP #21 Results

20. 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

21. 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

22. 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

23. The Model I: 2 players, 2 actions • 1 worker, 1 firm, 1 period 1 -1 2 0 1 2 -1 0

24. 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

25. The Model I: 2 players, 2 actions • Firm uncertainty: 1 0 1 -1 2 0 1 0 1 2 -1 0

27. The Model I: Full Reputation Equil. • T-Period “Full Reputation Equilibrium”:

28. The Model I: Full Reputation Equil. • Period T : • Period T-1 :

29. 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!

30. 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

31. 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

32. 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

33. The Model III: Anonymous Matching • FKR93: • Need something else…

34. The Model IV: Type Correlation “Stereotyping” parameter • Rational: uncertainty about type distribution • Irrational: stereotyping

35. 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

36. The Model IV: Type Correlation • One worker defects in period t : • Proposition: A full reputation equilibrium exists iff • Gamma large => back to public matching:

37. 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

38. The Model IV: Type Correlation • Get and from experiment parameters • Depend on and • Don’t know and • Assume:

40. 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

41. Predictions: 1 • Treatment 1:

42. Results

43. Results

44. 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

45. Predictions: 2 • Treatment 2: Hypothesis: individual reputations strengthen reciprocity

46. Results

47. Results

48. Results • Wages and efforts are significantly higher • End-game effects • Heterogeneity in end-game play

49. Predictions: 3 • Treatment 3:

50. Predictions: 3 • Don’t need stereotyping to get reputation effect • But… F.R.E. rarely exists & bound on beliefs is high