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Non-selfish preferences

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The Standard Model

1. NatureSelf-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 1’s consumption

Person 2’s consumption

Utility max. point for selfish person

U1

U2

Utility max. point for altruistic person

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Limited Self Interest: Fairness

.. .

Low

Accept Accept

Even

Reject Reject

9, 1 0, 0 5, 5 0, 0

1

2 2

What is the predicted outcome for this game?Player 1 chooses Low and Player 2 Accepts.

Standard Ultimatum Game

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Limited Self Interest: Fairness

.. .

Low

Accept Accept

Even

Reject Reject

1, -7 0, 0 5, 5 0, 0

1

2 2

Symmetric Fairness

Now Player 1 offers an even amount, which is accepted.

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Limited Self Interest: Fairness

.. .

Low

Accept Accept

Even

Reject Reject

9, -7 0, 0 5, 5 0, 0

1

2 2

Envy

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.

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 regularities2) socially shared belief regarding how one ought to

behave3) enforcement by informal social sanctions(but: what triggers a particular norm?)

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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 10-30% 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) egoists with u(x,y)=√x;b) utilitarians with u(x,y)=√x+√y;c) enviers with u(x,y)=√x-√y;d) 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.

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 ThalerFirms 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 contractTransactors avoid offending firmsGames 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.

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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

Modelling Social Preferences Objectives

explanation and prediction psychological basis

Issues in modellingReference 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-interest2. A minority of selfish individuals can dominate a market3. Ignores reciprocity

45o

xj

xi

Ui(xj||xi)

Red line is the utility line

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) (0,1)

Utility Ui(xi, xk)= (1-)xi, + W(xi ,xk) (0,1)

Cares less about person j if person j is better off

Inequity-Aversion

Konow (AER, 2003)

“Entitlement” or “right” allocationj is the right allocation for person jUtility Ui(xi, xj,j)= U(xi) – fi(xj - j)

fi is inequity aversion function

j

-fj

Example, fi(xj - j) = (xj - j)2

F depends on1. Accountability2. Efficiency3. 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-tat1. Be kind in response to actual or perceived or expected kindness2. 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

• i0 is the rate at which rival’s material payoff affects player i • Utility for agent i

• Standard game theory is when αii=0

( , ) ( , )i i i j i i j j iU c c c c

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)

• If player 1 plays F instead her utility is

• 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

1 1 1 1 2 1( , ) ( , ) 0 ( 1) 0 0U B F B F

1 1 1 1 2 1 1 11( , ) ( , ) 1 ( 1) 2 1 2 0 if 2U F F F F

Simple Rabin Model (application)

• Now suppose α1=α2=1

• What will determine the equilibrium?

• The relative sizes of 1 and 2

1 1 1 2 1 2 2 1 2 2 2 1 1 1 1 2( , ) 1 ( , ) and ( , ) 1 ( , )U c c c c U c c c c

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”

• But if player 1 instead plays “straight”

• If player 1 will choose straight even if she thinks player 1 will also choose straight

• Mutually assured destruction is a “fairness equilibrium”

1 1 1 2 1 2 2 1 1( , ) 1 ( , ) 2U c c c c

1 1 1 2 1 2 2 1 1( , ) 1 ( , ) 2 2U c c c c

1 1 112 2 2 2

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” IIPlayer 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 Model1. 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