Non-selfish preferences
1
2
The Standard Model
1. Nature
Self-interest and self-regarding preferences
2. Anomalies
 Tipping waiters
 Giving to charity
 Voting
 Completing tax returns honestly
 Voluntary unpaid work
 etc.
Limited Self Interest
• In basic neo-classical model decision makers
perfectly maximize their own payoff.
• How do we incorporate interpersonal values:
prestige, fairness, justice?
– people care about how they are perceived by others
– people are willing to sacrifice some of their own
money so others can have more
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Limited Self Interest: Altruism
• Altruism – regard for others’ well being
Person 2’s
consumption
U2
U1
Utility max. point for
altruistic person
Utility max. point for
selfish person
Person 1’s
consumption
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Limited Self Interest: Fairness
Standard Ultimatum Game
.
1
Low
.
Accept
9, 1
Even
2
Reject
0, 0
Accept
5, 5
.
2
Reject
0, 0
What is the predicted outcome for this game?
Player 1 chooses Low and Player 2 Accepts.
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Limited Self Interest: Fairness
Symmetric Fairness
.
1
Low
.
Even
2
Accept
Reject
1, -7
0, 0
Accept
5, 5
.
2
Reject
0, 0
Now Player 1 offers an even amount, which is accepted.
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Limited Self Interest: Fairness
Envy
.
1
Low
.
Even
2
Accept
Reject
9, -7
0, 0
Accept
5, 5
.
2
Reject
0, 0
Again Player 1 offers an even amount, which is accepted.
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Limited Self Interest: Fairness
• How do you decide what motivates player 1 to
offer an even amount?
– Player 1 offers an even amount out of fairness.
– Player 1 offers an even amount because he fears
Player 2 will reject uneven offers due to envy.
• Dictator Game – Like the Ultimatum Game but no
second stage. Player 1 simply gets to decide how
to split the money.
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Limited Self Interest: Fairness
• Are there other motives for even splits that you can think
of?
– Reciprocity – reward good behavior and punish bad. (Rabin)
– People care that they are perceived as being fair.
• Market vs. Personal Dealings
– Your interpersonal values will differ depending on who you
deal with: friends or strangers.
– They also may depend on whether a transaction is commercial
or personal.
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Nature of Social Preferences
 Social preferences and fairness – 'as if they value the payoff
of relevant reference agents positively or negatively.’ (Fehr
& Fischbacher, 2005)




Beliefs and intentions of others
Fairness: distribution of costs and benefits
Dual entitlement: reference transactions; outcomes
Strong reciprocity
Fairness Games and the Standard Model
 Ultimatum game - 60% to 80% of offers between 0.4 and 0.5,




rarely below 0.2.
Dictator games – Cherry et al. (2002): Baseline situation 17%
zero offers; 80% with 'earned' wealth
Trust games – 30-40% purely selfish; also more complex (trust
↔ reciprocity)
Prisoner’s dilemma games – 50% cooperate even in one-shot
games
Public goods games – effect of punishment
Factors Affecting SPs
 Setting - repetition and learning, stakes, anonymity,
communication, entitlement, competition, available
information, number of players, intentions, ...
 Descriptive – framing effects
 Demographic - gender, age, academic major, culture, and
social distance
 Social norms: Fehr & Gächter (2000)
1) behavioral regularities
2) socially shared belief regarding how one ought to
behave
3) enforcement by informal social sanctions
(but: what triggers a particular norm?)
Ultimatum Game, again
• Player 1 has a fixed amount of money
(say $10) and must offer some fraction
to Player 2 (from $0 and $10). If
Player 2 accepts, they split the money
as proposed. If Player 2 rejects, no one
gets any money.
• Empirically, responders will reject offers
below $2, but such low offers would be
rare. Offers will fall in the $3–$5 range
and will typically be accepted.
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Ultimatum Game, cont.
• Strictly speaking, a game is defined
in terms of utilities, not dollars. So
let us suppose u(x)=x.
• If so, the only subgame-perfect
equilibrium is the one in which Player
2 accepts all offers and Player 1
offers nothing.
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Dictator Game
• Similar to the ultimatum game
except Player 2 does not have the
opportunity to reject.
• Empirically, dictators offer about 1030% of their money.
• Assuming u(x)=x, once again, the
only subgame-perfect equilibrium is
where the “dictator” offers nothing.
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Social Preferences
• Social preferences reflect other
people’s attainment y as well as the
agent’s own x.
• If P derives positive utility from Q’s
attainment, P is said to have
altruistic preferences.
• If P derives negative utility from Q’s
attainment, P is said to have
envious preferences.
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Social Preferences, cont.
• A person with Rawlsian preferences (or
preferences for fairness) tries to maximize
the minimum utility associated with the
allocation.
• A person who wishes to minimize the
difference between the best and the worst
off is said to have inequality averse
preferences. (Fehr and Schnidt, Bolton, et.
Al.)
• Individuals who want to maximize the total
amount of utility have utilitarian
preferences.
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Example
• Find all Nash equilibria in pure strategies
when played by:
a)
b)
c)
d)
egoists with u(x,y)=√x;
utilitarians with u(x,y)=√x+√y;
enviers with u(x,y)=√x-√y;
Rawlsians with u(x,y)=min(√x,√y).
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Intentions and Reciprocity
• Whether a responder will accept depends
not just on the proposed allocation (e.g., an
80-20 split), but on the options available to
the proposer.
• This suggests that responders base their
decisions in part on perceived intentions of
the proposer.
– Respondents exhibit positive reciprocity
when they reward others with good intentions.
– Respondents exhibit negative reciprocity
when they punish players with bad intentions.
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Empirical Evidence
Neuroscientific studies – useful for estimating emotions when
people unaware/unwilling to admit (reverse inference from
relevant brain areas)
Show:
 Pleasure of cooperation and punishment
 Anger/outrage at unfair offers
 Empathy/lack of empathy based on previous fair/unfair
play
Kahneman, Knetsch and Thaler
Firms deserve fair profit
should not take advantage of customers or workers
Sluggish market adjustments indicate firms are constrained in
behavior by more than legal issues or budgets. Surveys show
fairness in pricing and wages is important.
Fairness is thought of as an enforceable implicit contract
Transactors avoid offending firms
Games show willingness to punish
Kahneman, Knetsch and Thaler (cont)
Fairness:
Is more important in established
relationships that new relationships.
Price increases in response to cost increases
is ok; price increases in response to demand
increases are not.
Fairness is relative to reference price. OK to
up price to protect profit
Similar findings with respect to wages.
Implications for Markets
When excess demand is unaccompanied by increases in costs
the market will fail to clear.
When a single supplier provides a family of goods for which
there is differential demand and different costs, there will be
shortages in the most valued items.
- This implies for most goods there will be shortages at peak
demand times (like for vacation hotels).
Price changes are more responsive to cost changes than to
demand changes, and mre responsive to cost increases than to
cost decreases.
Price decreases take the form of temporary discounts.
Wages are sticky downward.
-Firms will frame part of compensation as bonueses or
profit sharing to minimize reductions in compensation
during slack periods.
Contrary evidence of social
preferences
• Forsyth, Horowitz, Savin and Sefton find most
players give away nontrivial portions of the
money available to them.
• They use an ultimatum game and dictator
game
– Rational agents, offerer keeps (almost all)
– Fair agents have a more equal split
• However, the tests of the fairness hypothesis
fail.
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• Found in all experiments most players give away
non trivial portions of the pie, which violates
neoclassical theory of selfish preferences.
• Fairness hypothesis states that the distribution of
proposals in ultimatum game and dictator game
should be the same.
– Players are more generous in the ultimatum game.
– So Reject fairness hypothesis at p=0.01
• One explanation is that different types of players;
some receivers are gamesman, some are
spiteful, so offerers who are gamesman find it
optimal to offer a nontrivial share
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Modelling Social Preferences
 Objectives
 explanation and prediction
 psychological basis
 Issues in modelling
Reference standard; intentions; purpose of punishment;
reference agent
 Psychological game theory
Based on beliefs and intentions. Takes into account
emotions.
Social Preferences
• Occur whenever Ui=Ui(xi.xj) i≠j where xi
and xj are allocations.
• Altruism is when Ui depends directly on xj.
• Distributive Preferences (Fairness) is Ui
depends on the comparison of xi to xj.
Inequality-Aversion
Fehr-Schmidt model (WJE, 1999) – 'guilt/envy'
Ui(x) = xi – αi /(n-1)Σ max(xj–xi,0) – βi /(n-1) Σ max(xi–xj,0)
i≠j where α and β are ‘envy’ and ‘guilt’ coefficients from
comparing own allocation to others. Expect αi > βi so disutility
is greater if others are better off.
1. Based on pure self-interest
2. A minority of selfish individuals can dominate a market
3. Ignores reciprocity
Ui(xj||xi)
45o
xi
Red line is the utility line
xj
Inequality-Aversion (2)
Bolton-Ockenfels model (AER, 2000)
'ERC-model' (equity, reciprocity, competition)
Players prefer a relative payoff that is equal to the average payoff.
Ui (x) = U(xi, xi/ Σxj)
Differences between BO and FS model:
1. BO model: relative shares.
2. BO model does not compare each player’s payoffs with the maximum
and minimum of the other payoffs, like the FS model does.
3. BO model: symmetrical attitude towards inequality, guilt and envy equal
in force (αi = βi); FS model: envy stronger than guilt.
FS model generally performing better
Inequality-Aversion (3)
Charness and Rabin (QJE, 2002)
Rawlsian distributive justice (quasi maximin)
Social Welfare Function
W(xi, xk)= *min{xi, xk} +(1-)(xi + xk)
Utility
Ui(xi, xk)= (1-)xi, + W(xi ,xk)
(0,1)
(0,1)
Cares less about person j if person j is better off
Inequity-Aversion
Konow (AER, 2003)
“Entitlement” or “right” allocation
j is the right allocation for person j
Utility
Ui(xi, xj,j)= U(xi) – fi(xj - j)
fi is inequity aversion function
j
-fj
Example, fi(xj - j) = (xj - j)2
 depends on
1. Accountability
2. Efficiency
3. Need
For example,
If person i is twice as productive as person j,
the allocation depends on the cause of the
higher productivity.
If the greater productivity is due to endogenous
issues like greater effort, the allocation should
be double.
If the allocation is due to exogenous issues, the
allocation should be more equal.
Application, Rosenman, “The public finance of
healthy behavior”, Public Choice, 2011
Reciprocity Models
Rabin (1993) – tit-for-tat
1. Be kind in response to actual or perceived or expected kindness
2. Be unkind in response to actual or perceived or expected
unkindness
Ui = xi + gj(1+fi)
Where gi is the believe of how he will be treated and fi is
how he will treat j.
Utility increases if treatment given is the same as
treatment received/expected. Hence reciprocity model.
Rabin Model (simple)
• Utility for player i depends on player i’s material payoff i, her
rival’s payoff j, and her view about how she is “playing the
game” relative to her rival
• ci is agent i‘s action (choice)
• αi is the belief about rival’s intention.
• αi =1, rival is helpful
• αi =0, rival is neutral
• αi =-1, rival is harmful
• i0 is the rate at which rival’s material payoff affects player i
• Utility for agent i
U i   i (ci , c j )   i i j (c j , ci )
• Standard game theory is when αii=0
Simple Rabin Model (application)
• Pure Nash strategies are (B,B) and (F,F)
• Fairness equilibrium bring in psychological factors
• With (B,F) player 1 thinks player 2 is being mean (if he would play B they
would both be better off)
U1   1 ( B, F )  11 2 ( B, F )  0  (1) 1 0  0
• If player 1 plays F instead her utility is
U1   1 ( F , F )  11 2 ( F , F )  1  ( 1) 1 2  1  2 1  0 if 1  1
2
• If 1 player 1 sticks with F even though the direct payoff is lower,
because it also harms player 2 who is perceived as being mean
• If player 2 has a symmetric view of player 1 (B,F) ends up being fairness
equilibria
Simple Rabin Model (application)
• Now suppose α1=α2=1
U1   1 (c1 , c2 )  11 2 (c2 , c1 ) and U 2   2 (c2 , c1 )  11 1 (c1 , c2 )
• What will determine the equilibrium?
• The relative sizes of 1 and 2
Simple Rabin Model (Chicken game)
• (Swerve, Straight) is a Nash Equilibrium
• Player 1: α1=-1 since straight by player 2 harms player 1
• If Player 1 plays “swerve” while expecting player 2 to play
“straight”
U1   1 (c1 , c2 )  11 2 (c2 , c1 )  2 1
• But if player 1 instead plays “straight”
U1   1 (c1 , c2 )  11 2 (c2 , c1 )  2  2 1
• If 2  21  21  1  1 2 player 1 will choose straight even if she
thinks player 1 will also choose straight
• Mutually assured destruction is a “fairness equilibrium”
Rabin Model (Fairness Equilibrium)
• Notation
• a1 and a2 are the strategies chosen by the 2 players
• b1 and b2 are players 1 and 2 respective beliefs about players 2 and
1 strategies (what they think the other person is following)
• c1 and c2 are players 1 and 2 respective beliefs about what they
think the other player believes is their strategy
• A strategy ai is a fairness equilibrium is for i=1,2 if
ai argmax ai Ai Ui(ai , aj ,bj,ci) and ai =bj=ci
• Fairness equilibrium means
•
•
Choose a strategy that give the highest utility
Beliefs about strategies are correct
Rabin’s “Fairness Functions” I
Rabin’s “Fairness Functions”
1.
Player i’s kindness to player j
2. Player i’s belief about player j’s kindness
which in equilibrium means
because expectations are correct
Rabin’s “Fairness Functions” II
Player i’s kindness to player j
Player i’s belief about player j’s kindness
which in equilibrium means
because expectations are correct.
Utility for play i is
Characteristics of Rabin Model
1. People will sacrifice their own material well-being to
help those being kind.
2. People will sacrifice their own material well-being to
punish those being unkind
3. Both these effects are bigger as the cost of the material
sacrifice is smaller
General Specification for Empirical
Testing
Efficiency requires Ui = xi + (xi + xk) where  is the MU of
aggregate x.
So specify
Ui = xi + (xi + xk) - αimax(xk – xi,0)
- imax(xi – xk,0)
So α measures envy and  measures guilt