Theories of Social Preferences II

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Theories of Social Preferences II
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Theories of social preferences - Models

• Theories of inequality aversion Subjects dont
  like inequality relative to relevant comparison
  groups.
• Fehr Schmidt, QJE 1999
• Bolton Ockenfels, AER 2000.

• Theories of reciprocity Intentions (Kindness
  or Unkindness) are explicitly modeled.
• Rabin, AER 1993.
• Falk Fischbacher, GEB 2006.
• Dufwenberg Kirchsteiger, GEB 2004.

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Theories of inequality aversion

• What the models (BO, FS) have in common
• Outcome based view of fairness
• Assume that fairness intentions are irrelevant
• The models differ in the way that xj influences
  Ui
• FS
• BO

Share of total surplus (the utility function is
maximized in this argument if share1/n
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Warm-up

• Imagine a country with three classes (upper,
  middle, lower). The middle class is in
  government. Whom would a govt with FS (BO)
  preferences tax and to whom would they
  redistribute?
• Both models make identical qualitative
  predictions for many games. Can you think of (or
  remember) a game for which this would not be the
  case?

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Falk, Fehr and Fischbacher (Ectra, 2003)- Design

• Three person one-shot public goods game with
  punishment opportunity
• 1st Stage public goods game
• Contribute 20 points (cooperate) or nothing
  (defect)
• Payoff
• 20 - own contribution
• 0.6 sum of all contributions

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Falk, Fehr and Fischbacher (Ectra, 2003)- Design

• 2nd stage Reduce the other player's payoff at a
  cost
• Punishing cooperators 1 point reduction costs .3
  points.
• Punishing defectors 1 point reduction costs .4
  points.
• It is cheaper to punish cooperators.
• How does this design generate different
  predictions for BO and FS?

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Falk, Fehr and Fischbacher (Ectra, 2003) -
Predictions

• BO predict that if cooperators punish, they
  punish other cooperators.
• It is the cheapest way to reduce inequity because
  it reduces the average payoff of the other
  players most
• How does Ui depend on p-I Share pi/Spj
• Inequity measured towards the whole group and not
  individually
• FS predicts that if cooperators punish, they
  punish defectors.
• Because fairness is evaluated for each other
  player separately, those are punished who
  deserve punishment because they have a higher
  payoff (FS)

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Falk, Fehr and Fischbacher (Ectra, 2003) -
Experimental Results
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Theories of Inequality Aversion - Summary

• Models of inequality aversion are consistent with
  the experimental results in large class of games.
• They (in particular FS) have become very popular,
  also because of their tractability.
• However, they are likely to mispredict in certain
  situations as the following example will show...

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Which hypothesis was tested with the following
experiment?
Treatment 1
Treatment 2
10/27
17/27
1/3
11/17
2/3
6/17
Intentions matter!
McCabe et al, JEBO 2003
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Theories of reciprocity - Models

• Theories of reciprocity
• Rabin, AER 1993.
• Falk Fischbacher, GEB 2006.
• Dufwenberg Kirchsteiger, GEB 2004.

• Reciprocity willingness to reward kind behavior
  and to punish unkind behavior even at a cost to
  oneself
• Which behavior is kind and which unkind?
• Intentions (Kindness or Unkindness) are
  explicitly modeled

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A Game Tree and Psychological Game Theory

• Is player 1s move B kind or unkind?
• Kindness depends on what player 1 expects player
  2 will choose. Why?
• (second order) beliefs are important
• Concept of Psychological Game Theory
  Geanakoplos, Pearce, Stacchetti (1989)
• Example by Dufwenberg and Kirchsteiger

1
A
B
2
1 1
C
D
0 2
2 0
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Psychological Game Theory Geanakoplos, Pearce,
Stacchetti (GEB 1989)

• Remarks
• Beliefs are not part of the action space, i.e.,
  beliefs cannot be formed strategically.
• Psychological Nash equilibrium Nash equilibrium
  plus the requirement that all beliefs match
  actual behaviour.
• Reciprocity models are psychological games.

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Reciprocity models Rabin (AER 1993) Falk
Fischbacher (2006) Dufwenberg Kirchsteiger
(GEB 2004)

• Structure of reciprocity models
• Ui pi ri S Kindness j to i Response i to j
• (Response is often modelled with pj)
• If the other player is kind (kindness gt0), then
  player i chooses a positive response.
• If the other player is unkind (kindness lt0), then
  player i chooses a negative response.

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Reciprocity Models (Rabin,DK,FF)

• Models differ by what determines kindness
• Payoff that player i is supposed to receive
  compared to reference payoff
• Absolute reference (FF)
• Intentions and outcomes count. Kindness is based
  on interpersonal comparisons.
• Relative reference (R, DK)
• reciprocity is exclusively intentions driven
• people do not consider whether they have more or
  less than their opponents, rather compare
  actually chosen outcome with alternative actions
  opponents could have chosen
• Intentions are incorporated into the theory by
  considering the alternatives.

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Intentions

• DK predicts zero rejection rate when 82 is
  offered
• Subjects do not consider the 82 offer as unkind
  because 100 is even more unkind.
• FF predict positive rejection rates
• Fairness is determined by the outcome and the
  intention of the other subject.
• 9 of subejcts actually reject 82

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Conclusion

• Fairness can be captured by incorporating
  preferences for fairness into the utility
  function.
• Models reconcile results with equal outcomes as
  well as with unequal outcomes (e.g. UG vs.
  competitive markets).
• Fairness is evaluated individually.
• Intentions and outcome matter.
• Reciprocity models give a better description of
  human behavior but at a cost in tractability.

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Do the Reciprocal Trust Less?Dohmen et al.
(forthcoming), Economics Letters
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Motivation

• Test a within subject prediction of several
  theories of social preferences for the trust game

x 3
Sender
Receiver
Endowment 3 t - amount returned
Endowment t amount returned
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Motivation

• Test a within subject prediction of several
  theories of social preferences for the trust game
• These theories predict (ceteris paribus)
• Subjects who are inequality averse/reciprocal
  should
• return more, i.e., be more trustworthy as
  receivers and
• trust less, i.e., send a smaller amount t as
  senders
• than their selfish counterparts.
• Intuition?

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Motivation

• Selfish sender just suffers from the loss of her
  investment if receiver sends back too little
• Inequality averse/reciprocal sender experiences
  additional disutility because payoffs are
  unequal/his trust has been exploited (unkind
  action).
• Fehr et al. (2007) fairness preferences inhibit
  trusting behavior because trust typically
  involves a risk of being cheated.

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Warm-up

• What would an ideal data set to test this
  prediction look like?

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We use a trust game to measure trust and
reciprocal inclination.

• Two players with an endowment of 120 each
• Amount sent t used as a measure of trust
• Amount returned used to construct a measure of
  reciprocity.

x 3
Sender
Receiver
120 3 t - amount returned
120 t amount returned
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Our design measures trust and reciprocity for
each subject in the same strategic environment.

• We use the strategy method to elicit each
  subjects trust and reciprocal inclination
• Subjects make decisions for both roles
• For the role of the receiver subjects decide how
  much to send back for any possible amount
  received
• Random mechanism determines actual role at the
  end of experiment
• Trust game played only once in anonymously
  matched pairs

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We construct a reciprocity measure from the
choices made for the amount returned.

• Trust Amount Sent
• Reciprocity data on amount returned for every
  potential amount sent

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We measure reciprocity in the following way.

• Reciprocity data on amount returned for every
  potential amount sent
• Coefficient r from OLS without constant as
  measure for reciprocity

Completely selfish r 0
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We measure reciprocity in the following way.

• Reciprocity data on amount returned for every
  potential amount sent
• Coefficient r from OLS without constant as
  measure for reciprocity

Sending back the amount received r 1
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We measure reciprocity in the following way.

• Reciprocity data on amount returned for every
  potential amount sent
• Coefficient r from OLS without constant as
  measure for reciprocity
• Selfish r 0
• Intermediate 0lt r lt 1
• Reciprocal r gt 1

Splitting the pie equally r 2
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Distribution of reciprocity coefficients
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The reciprocal trust more.

• Subjects who split equally trust most (amount
  sent 83.5)

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The reciprocal trust more.
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There are (at least) two plausible
interpretations for our results.

• Norm adherence
• People may value the adherence to a certain norm
  in itself
• Norm dictating cooperative behavior in both roles
  could explain our main finding
• Systemmatic heterogeneity in beliefs
• Reciprocal and selfish types may have different
  beliefs regarding the behavior of others
• Example False consensus effect
• Could lead different types to select into
  different institutional settings

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Conclusions

• Strong positive relationship between a persons
  reciprocal inclination and her trusting behavior
• Further research needed on underlying driving
  force(s) of main finding