Is Dishonesty Contagious by Robert Innes Arnab Mitra
Is Dishonesty Contagious? by Robert Innes & Arnab Mitra University of California, Merced 1
Motivation • Importance of individual honesty/trustworthiness in economic interactions – – Cooperation Contracts Legal Institutions Economic growth (Zak and Knack, 2001; Guiso, et al, 2004) • Differences across cultures and countries – Stylized fact: Corruption is bi-modal 2
Distribution of World GDP by Level of Corruption Figure 1 A 0. 50 0. 40 0. 30 0. 20 0. 10 0. 00 Less Corrupt Countries Medium Corrupt Countries Highly Corrupt Countries *Corruption is measured by Transparency International’s Corruption Perception Index. “Less Corrupt” countries are those with CPI values in the top third of the range; “Medium Corrupt” in the middle third; and “Highly Corrupt” in the bottom third. We exclude India and China from the population distribution (Figure 1 B), but include them in the GDP distribution (Figure 1 A) 3
Distribution of World Population by Level of Corruption Figure 1 B 0. 70 0. 60 0. 50 0. 40 0. 30 0. 20 0. 10 0. 00 Less Corrupt Countries Medium Corrupt Countries Highly Corrupt Countries 4
Motivation • Differences across cultures and countries – Stylized fact: Corruption is bi-modal • Possible contributing explanation: Honesty is contagious – Honesty breeds more honesty – Dishonesty breeds more dishonesty 5
Overview of Paper • (A) Study whether honesty is contagious in an experiment – Experiment mirrors deception game of Gneezy (2005) – Stimulate perceptions that peers tend to be more honest or dishonest – Study effect on individual decisions to be honest/dishonest – Findings: • Dishonesty is contagious (Arizona, California) • Honesty is contagious (India) • (B) Try to understand observed contagion – Existing theories of other-regarding preferences – Evolutionary motive for in-bred contagious preferences 6
Literature • To our knowledge, only study that (indirectly) addresses “contagion in honesty”: • Fisman and Miguel (2007) on parking tickets in NY: immunity-protected diplomats take their home country propensities for lawlessness with them • Interpretation: No contagion because diplomats ignore U. S. values • Dispute this interpretation: – 1) no ceteris paribus: diplomats may temper behavior relative to home countries – 2) may reflect different peer groups: diplomats sensitive to homecountry peers 7
Contribution to the Literature • Two key literatures – Experimental economics on impact of social information on behavior – Psychology literature on conformity (e. g. , Cialdini and Goldstein, 2004) • Broad distinction with present paper – Our design voids prevalent theoretical explanations for conformity / obeying social norms (social status, herd behavior, networks, sanctions) • We identify “intrinsic” contagion – Behavior is PRIVATE – Conduct (truthfulness) of others is IRRELEVANT TO PAYOFFS – Focus on deception game (vs. other games) 8
Literature (cont. ) • EE literature on social information that is payoff relevant – Ultimatum games • Knez and Camerer (1995), Bohnet and Zekhauser (2004): due to norm of equity, information about other proposer offers is payoff relevant • Duffy and Feltovitch (1999): social learning – Social learning in coordination games • Fischbacher, Gachter and Fehr (2001), Schotter and Sopher (2003), Chaudhuri, Graziano and Maitra (2006), Eckel and Wilson (2007) – On-line participation in Movie Lens • Chen, et al. , (2009) – Charitable contributions • Frey and Meier (2004), Shang and Croson (2006) 9
Literature (cont. ) • Experimental economics literature that also identifies intrinsic contagion in dictator games – – Bichieri and Xiao (2008) Krupka and Weber (2009) Duffy and Kornienko (2009) (sort of) Cason and Mui (1998) (not really) • Distinction: Deception vs. Dictator – Note: even framing effects matter • List (2007) • Bardsley (2008) 10
Literature (cont. ) • Other experimental work on Deception Games – Gneezy (2005) – Sanchez-Pages and Vorsatz (2007) – Ederer and Fehr (2007) – Sutter (2009) – Rode (2008) – Charness and Dufwenberg (2005) – Hurkens and Kartik (2009) 11
Who cares? Want to understand mechanisms for spread of honesty/dishonesty in order to understand how society/policy-makers can promote this trait and reap its benefits Questions: 1) Is there contagion? (Our paper. ) 2) Mechanisms? (A start…) 12
Remainder of Talk • Evidence – – Arizona Survey Fall 2007 Arizona Experiment Spring 2008 Calcutta Experiment Spring 2009 UC Merced Experiment Spring 2010 • Theory to explain results – Other-regarding preferences • Guilt Aversion (CD, BD): Some more results • Inequity Aversion (FS, BO) – An alternative: Hard-wired contagious preferences – Note: Hard-wired preferences akin to heuristic Psychology interpretations of some conformity • Behavioral mimicry • Cognitive “short cuts” • Reference points 13
The Survey • Survey of – 174 economics undergraduates – University of Arizona – Fall 2007 • Asked whether they would be – Truthful (to their material disadvantage) – Untruthful (to their material advantage) – In a specific situation 14
The Situation • “Suppose that you have been visiting a country called Bayeb. Before leaving the country permanently, you must sell your used car. A local person (unknown to you) agrees to buy the car for US $2, 000 and pay you in cash. However, you know that the radiator in your car is not functioning properly and the problem will only become noticeable after 2 months. The buyer does not know about the problem. If you tell him/her about the problem, then you have to reduce the price of the car by US $250 and sell it for US $1, 750. However, if you do not reveal the problem, then you can sell the car for US $2, 000 and the buyer will have to fix the car after 2 months, spending US $250. Would you tell the buyer about the radiator problem? ” • Anonymity – Buyer/Seller unknown to each other • No sanctions – Leaving the country permanently – Problem can’t be tied to seller 15
Treatments • 1) Control • 2) Truthful: Respondents told – “Surveys in Bayeb indicate that, in a situation like yours, 9 out of 10 people would tell the buyer about the radiator problem. ” • 3) Untruthful: Respondents told – “Surveys in Bayeb indicate that, in a situation like yours, 9 out of 10 people would not tell the buyer about the radiator problem. ” 16
Survey Results Z-Statistic (Control Treatment) Treatment Number of Subjects Percent Truthful Control 43 69. 8% Truthful 63 79. 4% – 1. 108 Untruthful 68 50. 0% 2. 134** Z-Statistic (Truthful. Untruthful) 3. 707*** **, *** denotes significant at 5% (**) and 1% (***) levels 17
The Experiment • Deception Game: Gneezy (2005) • Player Pairs: Sender and Receiver • Two Payoff Distributions: A, B – One advantageous to Sender – Other advantageous to Receiver • Sender knows payoffs, Receiver does not 18
The Experiment (contd. ) • Sender sends one of two messages to Receiver Message A: “Option A will earn you (the Receiver) more money than Option B. ” Message B: “Option B will earn you (the Receiver) more money than Option A. ” • Knowing only the Message, Receiver chooses Option A or B • Payments made based on Receiver’s chosen Option • Payment Options (we varied labels) A: Sender $6, Receiver $3 B: Sender $4, Receiver $6 19
The Treatments • 1) Control: No information about choices of other Senders • 2) Truthful/Untruthful – Based on results from Control, Senders were told: “Out of 20 Sender messages from a past session of this experiment, with identical payment options, X (= Y%) were UNTRUTHFUL and (20 – X) (= (100 – Y)%) were TRUTHFUL” • 4 treatments – – Y = 15% (heavily truthful) Y = 40% Y = 60% Y = 85% (heavily untruthful) 20
Hypothesis • Contagion Hypothesis: The likelihood of untruthful behavior by a Sender rises with the perceived likelihood that other Senders are untruthful • Does higher Y induce more untruthful behavior? 21
Sender Beliefs About Receiver Behavior • A) Based on Gneezy (78% of Receivers followed recommendations), Senders told: – “In past experiments like this one, roughly 8 out of 10 Receivers chose the Option recommended by their Senders. ” – Receivers NOT given this information • B) Following Gneezy (2005) – Asked Senders to predict Receiver choice – Paid them $1 for correct prediction – Why did this? To Verify: Sender concern for morality/fairness, not strategy Measure Sutter (2009) deception – 73. 4% of Senders predicted Receiver acceptance Same for “Truthful” and “Untruthful” Senders – 73% of Receivers accepted recommendations 22
Other Details • Experiment conducted in – Undergraduate economics classes – University of Arizona – Spring 2008 • 233 Sender / Receiver pairs • Anonymity with id numbers • Receivers in different classes than Senders • No student participated more than once 23
Experiment Results Treatment Number Z-Statistic (Reported Percent Predicting of (Control. Propensity of Truthful Receiver Acceptance Subjects Treatment) Untruthful Senders) Control 97 58. 8% 74. 2% Y = 15% 25 64. 0% – 0. 480 76. 0% Y = 40% 26 53. 8% 0. 455 80. 8% Y = 60% Y = 85% 33 52 54. 5% 19. 2% 0. 430 5. 349*** 63. 6% 73. 1% Overall 233 49. 3% 73. 4% *** denotes significant at 1% level 24
Table 2 Probit Regression of Arizona Sender Message Choices (Truthful vs. Untruthful) with Course Fixed Effects • Variable Coefficient z-stat Marg. Ef. z-stat • • • Constant Y=85% Treatment Y=60% Treatment Y=40% Treatment Y=15% Treatment 0. 7004** -1. 0385*** -0. 4358 -0. 5554 0. 0206 2. 06 -3. 92 -1. 17 -1. 44 0. 06 -0. 3703*** -0. 1480 -0. 1873 0. 0073 -4. 58 -1. 25 -1. 58 0. 06 25
Calcutta Lab Experiment We find that dishonesty promotes dishonesty when - most people are otherwise honest - Arizona undergraduates What about other direction: Does honesty promote honesty when - most people are otherwise dishonest? - in corrupt societies? 26
The Experiment • Spring of 2009 • Jadavpur University, Calcutta • Willing undergraduate participants fluent in English • 60 Sender / Receiver pairs • Two treatments – Control – Strongly truthful (based on Calcutta control subjects): • “Out of 15 Sender messages from a past session of this experiment here in Calcutta, 13 out of 15 (85%) were TRUTHFUL and 2 out of 15 (15%) were UNTRUTHFUL. ” 27
The Payoffs • Two options: – A: 160 Rupees to Sender, 160 Rs to Receiver – B: 200 Rupees to Sender, 100 Rs to Receiver • Criteria: – Same ratio of Receiver loss from deceit and Sender gain from deceit (3/2) as in AZ – Minimum payment requirements – Substantial stakes • Stakes – 40 Rs (Sender gain from deceit) is less than $1 – Average daily consumption expenditure in India: • 19 Rs in rural India • 35 Rs in urban India – Fehr, Hoff and Kshetramade, 2008: • “ 50 Rupees are roughly equal to a day’s skilled wage” 28
Calcutta Results • • • Treatment (Reported Propensity Untruthful Senders) Number of Percent Subjects Truthful • Control 29 44. 8% • Y=15% 31 67. 7% • Overall 60 56. 6% • * denotes significant at 10% level (two-sided). z-statistic (Control Treatment) Percent Predicting Receiver Acceptance 82. 7% -1. 836* 74. 2% 78. 3% 29
Criticisms / Interpretations • 1) Experimenter Demand Effects • 2) Treatments Affect Generosity, not Aversion to Lying • 3) Sutter (2009) (Sophisticated) Deception • (1)-(2): UC Merced experiment 30
UC Merced Experiment • Modify Arizona Experiment in 3 ways • 1) Treatment subjects draw their own sample of 5 Sender messages from a box containing all Sender messages from one of the Arizona experiments (akin to Krupka and Weber, 2009). (Criticism 1: Demand Effects. ) • 2) Subjects play parallel deception and dictator games so that can measure effects of treatments on generosity. (Criticism 2: Generosity. ) • 3) Measure Sender beliefs about other Senders’ propensity for truthfulness. 31
More on UCM Experiment • Deception Game • Identical to Arizona in structure – Same payoff options – Same information to all Senders on “ 80% propensity” of Receivers to accept – Same information to Receivers • Treatments: – Control – Message draws: 2 boxes • 1) Sender messages from Arizona Control • 2) Sender messages from Arizona Heavily Untruthful Treatment 32
More on UCM Experiment (cont) • Parallel Dictator Game • Instructions: • “You and your Receiver will participate in two different decisionmaking situations, which we identify by K and L below. Both of you will be paid for ONE of the two situations. The situation for which you will be paid will be determined by a flip of a coin after all decisions have been made by all participants. You should therefore make your decision in each situation as if it is the one for which you will be paid. • • You and your Receiver will be paid for situation K if the coin toss comes up Heads. • • You and your Receiver will be paid for situation L if the coin toss comes up Tails. ” • K=Deception Game • L=Dictator Game 33
More on UCM Experiment (cont) • • Dictator Game Same payoff options Sender simply chooses the payment option Computer assigns payments based on Senderchosen option with 80% probability, other option 20% (to mimic 80% Receiver acceptance, following Gneezy (2005)) • If Treatment (message draws) affects generosity, expect Senders to choose “generous” (4 -6) option more often when other Senders more truthful 34
More on UCM Experiment (cont) • Measuring Sender Beliefs • Final Question: • “What proportion of Senders in this class do you think will send Truthful messages? CIRCLE ONE OF THE FOLLOWING PERCENTAGES. If your prediction is correct (within five percentage points of the actual choice, plus or minus), you will receive an additional $1 payment. • 0 -5 5 -10 … “ 35
More on UCM Experiment (cont) • Experiment conducted in – Undergraduate economics classes (Senders), political science class (Receivers) – UCM Spring 2010 – As always: anonymity, no communication, no class overlaps – For symmetry in handling of subjects, all Sender subjects directed to a “Station” for information • 105 Sender / Receiver pairs 36
Deception (Full Sample): Raw Results • • • Control (No draws) Observations 26 Percent Truthful 57. 69% z Stat 1 (Cont. -Treat. ) z Stat 2 (012 -345) z Stat 3 (Cont. +012 – 345) Average Sender Belief 28. 65% z Stat for Belief (012 -Ct/345) 3. 064*** Truthful Untruthful (0 -1 -2 U (3 -4 -5 U draws out of 5) 27 62. 96% -0. 3925 - 52 28. 85% 2. 4980** 3. 0412*** - 3. 4279*** 50. 28% 32. 31% - 3. 027*** 37
Dictator (Full Sample): Raw Results • • Control (No draws) • Observations • • • 26 Percent “Selfish” 69. 23% z Stat 1 (Cont. -Treat. ) z Stat 2 (012 -345) z Stat 3 (Cont. +012 – 345) - Truthful Untruthful (0 -1 -2 U (3 -4 -5 U draws out of 5) 27 52 81. 48% -1. 0436 - 65. 38% 0. 3434 1. 6144 - 1. 1388 • Note: Less Selfish with more Untruthful draws (though not significant). Contrary to “generosity” explanation for deception results. 38
Difference in Difference 39
Deception (Subsample): Raw Results • • Control (No draws) • • • Observations 26 Percent Truthful 57. 69% z Stat 1 (Cont. -Treat. ) z Stat 2 (012 -345) z Stat 3 (Cont. +012 – 345) Average Sender Belief 28. 65% z Stat for Belief (012 -Ct/345) 2. 862*** Truthful Untruthful (0 -1 -2 U (3 -4 -5 U draws out of 5) 24 62. 50% -. 3473 - 13 23. 08% 2. 2804** 2. 5760*** - 2. 7179*** 49. 58% - 35. 19% 1. 817* 40
UCM Results (cont) • Probit Regressions for Merced Sender Decisions • • • • A) Truthful (y=1) vs. Untruthful (y=0) • *First-stage instrument: 3 -4 -5 U message dummy, F-stat (p-value)=9. 57 (. 0026). Model Constant Control (=1 if Control) 1. 5592* (. 3285) -. 3652 (. 4113) 2. 3309 (. 2461) -. 1368 (. 3490) 3. 1992 (. 2048) -. 0052 (. 3212) 4 -2. 1557*** (. 6788). 9326*** (. 3358) Treatment: Number of U Messages -. 2611*** (. 0967)/[-. 1031] Dummy for 3 -4 -5 U Messages -. 8888*** (. 3072)/[-. 3398] Dummy for 4 -5 U Messages -. 8930*** (. 2961)/[-. 3349] Sender Belief (about Percent. 0495** Truthful Senders) Instrumented* (. 0196)/[. 0195] 41
UCM Conclusions • Arizona conclusions (Dishonesty is contagious) robust to alternative design • Cannot explain effect of “untruthful treatment” by changes in generosity • Find significant effect (in predicted positive direction) of Sender beliefs about the proportion of truthful Senders ON Sender truthfulness 42
Explaining Contagion with Other-Regarding Preferences • Weighting Social Welfare (Charness and Rabin, 2002) – Impact of Sender’s decision on SW invariant to what other Senders do • Reciprocity (Charness and Rabin, 2002; Cox, 2004; many others) – Punish “bad” behavior – Reward “good” behavior – We control for beliefs about Receiver behavior • More promising: – A) Guilt Aversion (Charness and Dufwenberg, CD, 2006) – B) Weighting Relative payoffs (Bolton and Ockenfels, 2000) Inequality aversion (Fehr and Schmidt, 1999) 43
Guilt Aversion • CD: Subjects averse to disappointing their partners – If: Receiver obtains payoff less than he expects (based on Sender beliefs about Receiver beliefs), – Then: Sender suffers guilt aversion proportional to the difference • In our experiment, suppose – When Sender believes other Senders more truthful, then Sender believes that Receiver believes Senders are more truthful → (Sender-anticipated) Receiver disappointment from “untruthful” is greater → Sender guilt aversion from “untruthful” is greater → Sender less likely to be “untruthful” 44 → Observed contagion
Guilt Aversion (cont. ) • In our experiment – Receivers never told Options → no basis for disappointment – Our treatment (Sender information about Sender behavior) is only given to Senders, not Receivers and senders know this • We control for Sender beliefs about Receiver behavior – Our statement on Receiver behavior – Sender elicited beliefs about Receiver behavior • If Sender beliefs about Receiver beliefs were affected by our treatments, then so too would Sender beliefs about Receiver behavior • If Senders believe Receivers expect “untruthful” messages, would also expect Receiver rejections. No such effect (Table 1). • If Senders believe Receivers expect truthful messages, would also expect more Receiver acceptances. No such effect (Table 4). 45
Guilt Aversion (cont. ) • We elicited Sender beliefs about Receiver expectations of proportion of Senders that truthful. – 57 Arizona Senders, 28 control, 29 strongly untruthful treatment – All 60 Calcutta Senders – All UCM Senders • Two questions: • 1) Are Sender Beliefs (about Receiver beliefs) affected by the treatments? • 2) If so, do Treatment effects (on Sender truthfulness) persist when controlling for Sender beliefs (about Receiver beliefs)? If “yes, ” then Guilt Aversion isn’t the whole story… 46
1) Are Sender Beliefs (about Receiver beliefs) affected by the treatments? • Results: • Arizona – Control: 58. 6%, Treatment: 38%, z-stat: 3. 26 • India – Control: 65. 1%, Treatment: 69. 1%, z-stat: 0. 85 47
1) Are Sender Beliefs (about Receiver beliefs) affected by the treatments? Merced Results • • • Treatment Control O U Messages 1 U Messages 2 U Messages 3 U Messages 4 U Messages 5 U Messages N 26 4 12 11 11 25 16 Average Sender Belief About Receiver Beliefs 50. 58% 46. 25% 45. 00% 51. 13% 52. 50% 52. 90% 36. 25% z-stat (Control. Treatment). 16. 32 -. 03 -. 11 -. 17. 92 48
Question 2 • 2) Do Treatment effects (on Sender truthfulness) persist when controlling for Sender beliefs (about Receiver beliefs)? If “yes, ” then Guilt Aversion isn’t the whole story… 49
Question 2: Table 5 Probit Regression of Sender Message Choices on Treatments and Sender Beliefs about Receiver Beliefs • Coefficient z-stat Marginal Effect Constant Y=85% Treatment Sender Belief -0. 0215 -0. 9275** 0. 0034 -0. 04 -2. 43 0. 45 -0. 3396 0. 0012 Merced Subjects Constant Control Number of U Messages Sender Belief 0. 9898** -0. 3636 -0. 2742*** -0. 0084* 2. 405 -0. 881 -2. 818 -1. 757 -0. 1401 -0. 1082 -0. 0033 • Variable • Arizona Subjects • • 50
Guilt Aversion and Contagion • Conclusion: • Our evidence: Guilt aversion does not explain observed contagion in our experiments – AZ, India, Merced: Treatment effects robust to control for Sender beliefs about Receiver beliefs – AZ, India: No correlation (truthfulness, beliefs) in regressions – Merced: Some correlation in opposite (vs. predicted) direction • Caveat: – This does NOT say that guilt aversion does NOT drive deception choices – Rather, our results suggest CHANGES in guilt aversion preferences (or lying aversion) as a result of treatments (contagion) – Guilt aversion does not explain these CHANGES 51
Inequity Aversion • Fehr and Schmidt (1999): Subject obtains disutility when, relative to others, he/she – Is worse off – Is better off – But suffers more disutility when worse off • Formally: – – – - δa + w Σj=1, …, n Xj where X = (X 1, …, Xn) = monetary payoffs for j ε{1, …, n} X 1 ≥ X 2 ≥……. . …≥ Xn , w≥ 0, a≥ 0, δ=1 if Untruthful (0 otherwise) U increasing, weakly concave V , increasing, weakly convex V(0) = 0 and V(z) ≥ (z) for z > 0 52
Applying Inequality Aversion to Our Experiment • Assume reference group is entire subject pool (Senders/Receiver) • Result: For Arizona payoffs, net benefit of untruthful (vs. truthful) conduct rises with the perceived propensity for Sender honesty in the subject pool → Inequality aversion predicts OPPOSITE result (anti-contagion) • This Result is reversed –so that inequality aversion predicts our results – If Reference group is SENDERS ONLY (not Receivers) in the experiment – OR, Inequality aversion is CONCAVE – But these conditions are implausible 53
Explaining Our Results: A Theory of Moral Contagion • Suppose the following are hard-wired traits that evolve – Honesty – Dishonesty/Selfishness – Contagious Honesty • Why should they evolve? View honesty/morality as trait that can help overcome barriers to cooperation, modeled as costs of Prisoner’s Dilemma • Contagious preferences are a rule/routine that dictates: – Be honest/moral if most others honest – Be dishonest/selfish if most others dishonest 54
The Main Argument • Claim: Contagious preferences can enhance individual fitness and therefore survive evolution • Two elements to the argument – 1) Conformity is advantageous Pays to be honest/dishonest when others are This is not obvious: Frank (1987) concludes the opposite – 2) Contagion is advantageous When interactions between two groups One honest One selfish Advantageous to have adaptable / contagious preferences 55
The Model • Two types of people: H (honest), D (selfish/dishonest) • Two strategies in Prisoner’s Dilemma (PD) game: – H (honest/cooperate) – D (selfish/defect) • H-type person always chooses H – Suffers penalty/guilt from D strategy so that H is dominant strategy • D-type person suffers no guilt – Pursues selfish D strategy • Players have outside option (of not playing the PD game) – Payoff to outside option = x 0 56
Figure 1: Payoffs in the Prisoner’s Dilemma Game Player 1 Strategy H D H (x 3, x 3) (x 4, x 1) D (x 1, x 4) (x 2, x 2) Player 2 Strategy Note: x 4 > x 3 > x 2 > x 1 57
Differences With Frank (1987) • Two key differences: 1) Players are matched in pairs RANDOMLY, 2) Outside option payoff x 0 < x 2 = Payoff to (D, D) joint venture – But, of course, x 0 > x 1 = exploitation payoff – Otherwise, outside option never exercised • Let h = proportion of H-types in the population • Will show (contrary to Frank), in variety of settings: – 1) E(x│H, h) = expected payoff to H-type > E(x│D, h) = expected payoff to D-type when h > h* (0, 1) – 2) E(x│H, h) = expected payoff to H-type < E(x│D, h) = expected payoff to D-type when h < h* 58
Setting 1: Perfect Signals of Type • Partners know each others’ types • H-types play – with other H’s – not with D’s • D-types play with other D’s → E(x│H, h) = h x 3 + (1 – h) x 0 → E(x│D, h) = h x 0 + (1 – h) x 2 → E(x│H, h) > (<) E(x│D, h) for h > (<) h*, where h* = (x 2 – x 0)/{( x 3 – x 0) + ( x 2 – x 0)} ε (0, 1) 59
Figure 2: Expected Payoffs with Perfect Signals of Type x 3 E(x; H, h) x 2 x 0 E(x; D, h) h* 1 h 60
Intuition • When h is high (lots of H types), – H’s almost always play with H’s, get x 3 – D’s cannot play with H’s, get x 0<x 3 • When h is low (lots of D types) – H’s almost always face D’s, get x 0 – D’s almost always play with D’s, get x 2>x 0 61
Imperfect Signals of Type • q ε {H, D} not directly observable • Observable correlated signal S – tendency to blush or – stand up for others • H-type signal S density f. H(S), support [LH, UH] • D-type signal S density f. D(S), support [LD, UD] • LH > LD, UH ≥ UD, f. H(S)/f. D(S) increasing → S is perfectly informative when S ε [LD, LH) (signaling q = D) when S ε [UD, UH) (signaling q = H) → S is imperfectly informative otherwise 62
Imperfect Signals (contd. ) • As partner’s S rises, probability that partner is H-type (vs. D) rises • For H-types, there is critical S* such that – if partner’s S > S*, it pays to play PD – if partner’s S < S*, it pays to opt out – S* falls with h (because then, for any S, higher probability that partner is H) • For D-types, it always pays to play PD 63
Equilibrium Strategies • H-types: Play only if own S and partner’s S > S* • D-types always play • Expected payoffs (with S* = S*(h)): E(x│H, h) = FH(S*) x 0 + (1 – FH(S*)){h[ FH(S*) x 0 + (1 – FH(S*)) x 3] + (1 – h)[FD(S*) x 0 + (1 – FD(S*)) x 1]} E(x│D, h) = (1 – h) x 2 + h{ FH(S*) x 0 + (1 – FH(S*)) [FD(S*) x 0 + (1 – FD(S*)) x 4]} 64
The Numerical Example • f. H and f. D normalized standard normals • μH=4, μD=2 • Truncated at +/- two standard deviations • For simplicity: • x 4 -x 3=x 3 -x 2=x 2 -x 0=x 0 -x 1=1 65
Figure 3: Expected Payoffs with Imperfect Signals • Numerical example with h* = 0. 46 66
Resampling with Perfect Signals • Suppose players can resample for new partners at cost c > 0 • Assume (paper generalizes): – (A): – (B): (1/2)(x 3 – x 2) < c ≤ (1/2)(x 2 – x 0) sequential resampling: 1) all players matched and either play PD, withdraw (get x 0), or resample 2) resampling players matched, etc. 67
Resampling with Perfect Signals (contd. ) • Then can show that: – when H-type meets D-type, BOTH resample – when like types meet, they play PD – probability of H-type partner in resampling rounds = ½ → E(x│H, h) > (<) E(x│D, h) when: h > (<) h*= {2 c – (x 3 – x 2)} / 4 c ε (0, 1/2) 68
Genesis of Contagion • “Pure” preferences: m = H vs. m = D • “Contagious” preferences: m(h) = H(D) when h > (<)h* • So far: – Two ESS equilibria: h = 1, h = 0 • Suppose: – 1) Period 1: Two groups separately evolve to ESS 1: h = 1 ESS 2: h = 0 – 2) Period 2: Profitable inter-group PD opportunities with probability i, each group 1 member has intergroup opportunity can accept or reject (partner likewise) if reject, then matched within group 1 – 3) group 1 (2) size = n 1 (n 2) 69
Genesis of Contagion (contd. ) • Period 2 payoffs – – G = (x 1, x 2, x 3, x 4), x 1 = 0 Payoff = δ(n)G n = number of partnerships (group 1, 2, intergroup) δ’< 0, δ(0) large • Note: – 1) With pure (m = H) preference, intergroup payoff for group 1 member = δ(0) x 1 = 0 – 2) Expected payoff to contagious group 1 mutant = (1 – i) δ(n 1/2)x 3 + i δ(0)x 2 > δ(n 1/2)x 3 = payoff to “purely honest” group 1 member → Contagious mutation advantageous 70
Genesis of Contagion (contd. ) • Equilibrium: – minimum number of group 1 mutants = M* – group 2 mutants migrate to group 1 to equalize payoffs: δ(i. M*) x 2 = δ((n 1 – i. M*)/2)x 3 = δ((n 2 – i. M*) / 2)x 2 71
Conclusion We find evidence that dishonesty is contagious – Dishonesty promotes dishonesty when most people are otherwise honest (Arizona, California) – Honesty promotes honesty when most people are otherwise dishonest (Calcutta) • We argue that this cannot be explained by existing theories of other regarding preferences • We argue that hard-wired contagious moral preferences may evolve as a mechanism to promote advantageous joint ventures 72
Conclusion (contd. ) • Some testable predictions of theory: – Migrants are more likely to be contagious – Contagious individuals are more likely to work with others “outside of their group” – Trade promotes contagious preferences • Problems/questions from theory: – Do little to address (un)observability of type (mimicry) – General class of preferences (beyond conditional honesty, vengeance) – Do contagious (vs. parameter) mutations inhibit or promote movement from one equilibrium to another (Kandori, et al. , 1993)? 73
Conclusion (cont. ) • Why care? Positive: Understanding behavior. Normative: Importance of “culture of honesty” in a business - Absent contagion, “culture” within business unimportant - With contagion, “culture” matters Hope in promotion of honesty in corrupt societies • Questions raised: How promote norm of honesty in practice? -Rode (2009) -strength of different peer groups -authority figures? Role of trade, migration How robust is India result? -higher stakes? -only super-majority effects? 74
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