TRUST_ FEAR_ RECIPROCITY_ AND ALTRUISM Theory and by fanzhongqing

VIEWS: 2 PAGES: 60

									   TRUST, FEAR,
 RECIPROCITY, AND
     ALTRUISM:
Theory and Experiment
       James C. Cox
    University of Arizona
   and Indiana University
 Central Objective of the Research

Improve theory through a program of:

• Experimental testing; and

• Theoretical modeling motivated by data
      Implications of Parsimony

Design experiments to identify:

• When the “economic man” model does not
  predict well … and models of “other-
  regarding” preferences are needed

• When the other-regarding preferences
  need to include beliefs and intentions
           Parsimony (cont.)

Develop an integrated approach to
 modeling behavior that is:

• Unconditional on intentions; or

• Conditional on others’ revealed intentions
                  Contents
• Experimental designs that discriminate
  among unconditional altruism, positive
  reciprocity, trust, negative reciprocity, and
  fear

• Effects of social distance and decision
  context on reciprocal behavior
            Contents (cont.)
• Direct tests of alternative models

• New models of patterns of behavior that:

 (a) are conditional; or

 (b) are not conditional on others’ intentions
 and status
    An Example: The Investment Game

•   Subjects are paired
•   Each subject in each pair is given $10
•   Second movers are told to keep their $10
•   First movers can either:
    – Keep their $10; or
    – Give some or all of it to the second mover
• Any amount given is multiplied by 3 by the
  experimenter
       Investment Game (cont.)
• Second movers can either:
  – Keep all of any amount received; or
  – Return part or all of it to the first mover

• All of the above is common information
  given to all subjects

• The game is played only once
            Predictions of
     the “Economic Man” Model
• Since second movers care only about their
  own material gain, they will keep any
  tripled amount sent by first movers

• Since first movers care only about their
  own material gain, and know that second
  movers have the same kind of
  preferences, first movers send nothing
           Predictions (cont.)
• Zero returned and sent is the subgame
  perfect equilibrium of this game, given the
  economic man assumption about
  preferences

• The predicted outcome is inefficient: Each
  subject pair is predicted to get $20 in
  payoff … just the endowment … when it
  could have gotten as much as $40
Behavior in the Investment Game
                   Definitions
• Self-regarding (or “economic man”)
  preferences are characterized by positively
  monotonic utility for one’s own material payoffs
  and indifference about others’ material payoffs

• Other-regarding preferences are characterized
  by utility that is not constant with respect to
  variations in one’s own or others’ material
  payoffs

• Altruistic preferences are characterized by
  utility that is monotonically increasing in others’
  material payoffs and one’s own payoffs
              Definitions (cont.)
• (direct) Positive reciprocity is a motivation to
  adopt a generous action that benefits someone
  else, at one’s own material cost, because that
  person’s intentional behavior was perceived to be
  beneficial to oneself


• Trust is a belief that one agent has about
  another. A trusting action is one that creates the
  possibility of mutual benefit and the risk of loss of
  one’s own utility if the other person defects
              Definitions (cont.)
• (direct) Negative reciprocity is a motivation to
  adopt an action that harms someone else, at
  one’s own material cost, because that person’s
  intentional behavior was perceived to be harmful
  to oneself

• Fear is a belief that one agent has about
  another. An action that is fearful of another is
  one that forgoes an otherwise preferred action
  because of a belief that the other agent will inflict
  costly punishment as a response to choice of the
  otherwise-preferred action
Investment Game Triadic Design
Treatment A is the investment game

Treatment B is a dictator game that gives
dictators the same choices that first movers
have in the investment game

Treatment C is a dictator game that gives
dictators the same choices that second movers
have in the investment game
   Comparison of the Amounts Sent
       in Treatments A and B
                                  Figure 2 : Am ounts Sent in Treatm ents A and B


                     14

                     12


                     10
Number of Subjects




                     8

                     6

                     4

                     2

                     0
                          0   1    2        3       4          5         6       7   8   9   10
                                                        Am ounts Sent

                                                 Treatment A       Treatment B
Comparison of the Amounts “Returned”
       in Treatments A and C
                         Figure 3 : Am ounts Returned in Treatm ents A and C


                    25


                    20


                    15
Am ounts Returned
                    10


                    5


                    0




                       m
                      0a
                      0b

                      0d
                      0e

                      2a
                      3a
                      4a
                      4b
                      5a
                      5b

                      5d
                      5e

                      5g
                      6a
                    10 a




                        k
                     10i
                    10 j

                    10 l
                      0c




                      5c




                    10a
                    10b

                    10d
                     10e

                    10g
                       h
                    10 f
                    10c
                      0f




                      5f




                     10


                     10
                      7




                                                 Am ount Sent/Subject Pair

                                                   Treatment C   Treatment A
     Conclusions about Behavior
• Behavior in the investment game is known to
  exhibit trust because first movers send
  significantly more in the investment game than in
  the first-mover dictator control treatment

• Behavior in the investment game is known to
  exhibit positive reciprocity because second
  movers return significantly more in the
  investment game than in the second-mover
  dictator control treatment
        Implications for Theory
• Data-consistent models of first-mover
  behavior in the investment game must
  incorporate beliefs about others’ behavior

• Data-consistent models of second-mover
  behavior in the investment game must
  incorporate others’ intentions
     Conclusions from Many Other
     Experiments with Game Triads
• Positive reciprocity is significant in the
  moonlighting game but negative reciprocity is
  not significant
• Trust is significant in the moonlighting game
  but fear is not significant
• Positive reciprocity is significant in the trust
  game with a single blind protocol but not with
  a double blind protocol
• Positive reciprocity in the trust game is
  invariant with a doubling of money payoffs
  Conclusions from Triads (cont.)
• Negative reciprocity and fear are not
  significant in the punishment mini-
  ultimatum game (MUG)

• Play in the punishment MUG is invariant
  with framing the task as market exchange

• Negative reciprocity is significant in the
  punishment MUG if it is embedded within
  a context of similar games
  Conclusions from Triads (cont.)


• Females are less positively reciprocal in
  the investment game than are males

• Groups are less generous in the
  investment game than are individuals
Models of Other-regarding Preferences
• Inequality aversion models (Fehr &
  Schmidt, QJE, 1999; Bolton & Ockenfels,
  AER, 2000): utility is increasing with one’s
  own money payoff but decreasing with the
  difference between one’s own and others’
  money payoffs

• Quasi-maximin model (Charness &
  Rabin, QJE, 2003): utility is increasing with
  an agent’s own money payoff, with the
  lowest of all agents’ payoffs, and with the
  total of all agents’ payoffs
 Alternative Model Motivated by Data


Egocentric altruism model (Cox & Sadiraj):
 other-regarding preferences characterized
 by monotonicity, convexity, and
 egocentricity
         Exp.1: A Direct Test of
          Inequality Aversion
 This test is provided by the first-mover dictator
 control treatment for the investment game triad:

• The dictator is given $10
• The anonymously-paired subject is given $10
• The dictator can keep all of his $10 or give any
  integral part of it to the paired person
• Any amount given is tripled by the experimenter
Prediction of the Fehr-Schmidt Model

     40
     35
     30                               45o line

     25
   y 20
     15
                                        Predicted
                                        choice
     10
      5
      0
          0   5   10   15   20   25     30       35   40
                            m
Prediction of the Bolton-Ockenfels
               Model
               40

               35
                                                       i
                                                       n
                                                    45ol e




               30                                            45o line


               25

               20
       y




           y                                                     Predicted
               15                                                choice

               10

                5

                0
                    0   5   10   15       20   25              30       35   40

                                  m   m
                        Behavior in Experiment 1

                         0.4


                        0.35


                         0.3
proportion of choices




                        0.25


                         0.2


                        0.15


                         0.1


                        0.05


                          0
                               0   1   2   3     4          5           6   7   8   9   10

                                               number of dollars sent
  Behavior in Experiment 1 (cont.)
• 19 of 30 or 63% of the dictators gave
  positive amounts to the other person.

• The average amount given was $3.63

• The average payoff of dictators was $6.37
  and the average payoff of non-dictators
  was $20.89
     The Quasi-Maximin Model


   u (m, y 2 , y 2  , y n )
 (1   )m   [ min{m, y2 , y3 ,  , yn }
 (1   )(m  y2  y3      yn )]
Direct Tests of Quasi-Maximin

         Experiment 2

        m    y1 y2   y3
        10    0  6    6
        10    0 15   15
        10    0 2    33
Direct Tests of Quasi-Maximin (cont.)

            Experiment 3

          m    y1   y2   y3
          10   0    15   15
          10   3    12   15
          10   4     5   21
Subjects’ Choices in Experiments 2 and 3
                             33


                             30


                             27                 Exp 2

                             24                 Exp 3

                             21
     number of choices ...




                             18


                             15


                             12


                             9


                             6


                             3


                             0
                                  1    2    3
                                      row
Behavior in Experiments 2 and 3 (cont.)

• The choices of 85% of the subjects in
  experiment 2 are inconsistent with quasi-
  maximin preferences

• The choices of 94% of the subjects in
  experiment 3 are inconsistent with quasi-
  maximin preferences
        More Information about
        Subjects’ Preferences
• Experiment 4 differs from experiment 1
  only by introduction of the opportunity to
  take money as well as give it

• Amounts given are multiplied by 3

• Amounts taken are not transformed

• Amounts taken cannot exceed 5 (first-
  mover control for the moonlighting triad)
Choices in Experiments 1 and 4
                        0.6




                        0.5                                                                 Exp. 1
                                                                                            Exp. 4
                        0.4
proportion of choices




                        0.3




                        0.2




                        0.1




                         0
                              -5   -4   -3   -2   -1   0   1      2      3      4   5   6   7    8   9   10


                                                           number of dollars sent
Behavior Changes Character when
   the Feasible Set Changes
• In experiment 1, 67% of dictators gave money to
  others who would, as a result, have significantly
  higher payoffs than the dictators

• In experiment 4, 70% of dictators took money
  from the others who would, as a result, have
  significantly lower payoffs than the dictators

• How can such behavior be explained?
With a Model of Egocentric
  Altruistic Preferences
      40


      35


      30


      25
  y




      20

                                            45o line
      15
               Choice 1
      10
                                                            Choice 2

       5


       0
           0              5   10       15              20              25

                                   m
    The Two-Agent
Egocentric Altruism Model
                               1
                        
 u(m, y)  [(1   )m  y ]    


 where
    , m  y
    , m  y
        Properties of the Model
• Monotonicity
• Convexity
• Egocentricity

  Two Agent Special Case of Egocentricity:

   u(b, a)  u(a, b)   for all   ba0
        Consistency with Data
The egocentric altruism model is consistent
 with data for:

• 100% of subjects in experiments 1 and 4

• 85% of subjects in experiment 2

• 88% of subjects in experiment 3
         The Model is Robust
The model can also rationalize behavior in
 experiments with:

• Proposer competition

• Responder competition

• Voluntary contributions to public goods
        Incorporating Intentions
          in a Tractable Way
                       1
         u (m, y )        (m  y )
                       
                                                   1
Note that MRS =    (u / m) /(u / y)   ( y / m)
                                           1



    = WTP = 1/MRS at an allocation on the 45°
line where m = y

Convexity implies higher WTP if          m y
and lower WTP if m  y
     Reciprocity and Status
We assume


   (r , s)
where:
 • r is a “reciprocity variable”
 • s is a “status variable”
             Definition of r
   r  m( x)  mo
• where m(x) is the max. payoff for the
  second mover, given the first mover’s
  choice x

• and m0 is m(x) when x is neutral
           Definition of s
   s  s1  s2
where s1 and s 2 are the status of the first
and second movers in the context of the
game currently played
  Assumptions Used in Estimation
• A.1 Individuals choose so as to maximize
  a utility function of the given form

• A.2 The emotional state function  (r, s) is
  identical across individuals and there is a
  zero-mean idiosyncratic term such that:

   i   (r , s)   i
 Model Assumption that is Tested
• A.3  (r, s) is weakly increasing in r and s
Data Used in Estimating the Model

• Dictator games, with and without a status treatment

• Stackelberg duopoly games

• Mini-ultimatum games with variable reference
  payoff conditions

• Ultimatum games with random and earned
  entitlements to be first mover

• Moonlighting games
Summary Conclusions from Estimation

• The model captures baseline altruism in
  dictator games

• The model explains how status affects
  altruism in dictator games

• The model explains reciprocal responses
  in Stackelberg duopoly games
     Summary Conclusions (cont.)

• The model explains how changing perceptions
  of “property rights” affect reciprocity in mini-
  ultimatum games

• The model explains the interaction of status and
  reciprocity in ultimatum games

• The model explains reciprocal behavior in
  moonlighting games
Work in Progress: A Nonparametric
   Model of Revealed Altruism
Elements of the Model
• Partial Ordering of Preferences: “more
  altruistic than” (MAT)
• Partial Ordering of Budget Sets: “more
  generous than” (MGT)
• Reciprocity Axiom: more generous
  choices by the first mover induce more
  altruistic preferences in the second mover
    Applications of the Model
• Stackelberg duopoly game data

• Stackelberg mini-game data
     .




  SUMMARY
CONCLUSIONS
 Behavior in Fairness Games Exhibits

• Unconditional altruism: “others’ payoffs
  matter”

• Trust and fear: “beliefs matter”

• Reciprocity: “intentions matter”
  Whether Trust, Fear, Reciprocity or
  Altruism is Exhibited Depends on
• Single-blind vs. double-blind protocol:
  “who is observing matters”
• Context in which a specific game is
  embedded: “fairness is a relative concept”
• Type of agent:
  – Group or individual
  – Male or female
     Modeling Fairness Games
Behavior is not generally characterized by:

• Inequality aversion
• Maxi-min
• Efficiency
            Modeling (cont.)
Behavior is characterized by other-regarding
 preferences that are:

• Egocentric
• Convex
• Positively monotonic in others’ payoffs,
  except when they are conditional on
  intentions
            Modeling (cont.)
• Intentions (“reciprocity”) and status can be
  incorporated in a tractable model of other-
  regarding preferences

• Individual-subject differences can be
  parsimoniously incorporated in a model of
  other-regarding preferences
                               References

•   James C. Cox, “Trust, Reciprocity, and Other-Regarding Preferences:
    Groups vs. Individuals and Males vs. Females,” in R. Zwick and A.
    Rapoport, (eds.), Advances in Experimental Business Research, Kluwer
    Academic Publishers, 2002.
•   James C. Cox, “How to Identify Trust and Reciprocity,” Games and
    Economic Behavior, 46, no. 2, 2004, pp. 260-281
•   James C. Cox and Cary A. Deck, “On the Nature of Reciprocal Motives,”
    Economic Inquiry, forthcoming.
•   James C. Cox, Daniel Friedman, and Steven Gjerstad, “A Tractable Model
    of Reciprocity and Fairness,” University of Arizona Discussion Paper, 2005.
•   James C. Cox and Vjollca Sadiraj, “Direct Tests of Models of Social
    Preferences and Introduction of a New Model,” University of Arizona
    Discussion Paper, 2005.
•   James C. Cox, Klarita Sadiraj, and Vjollca Sadiraj, “Implications of Trust,
    Fear, and Reciprocity for Modeling Economic Behavior,” University of
    Arizona Discussion Paper, 2004.

								
To top