1. Non-selfish preferences

3. The Standard Model Nature Self-interest and self-regarding preferences
Anomalies
Tipping waiters
Giving to charity
Voting
Completing tax returns honestly
Voluntary unpaid work
etc.

4. 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

5. Limited Self Interest: Altruism
Altruism – regard for others’ well being U2
Person 2’s consumption U1
Utility max. point for altruistic person
Utility max. point for selfish person
Person 1’s consumption

6. Limited Self Interest: Fairness
Standard Ultimatum Game . 1 . .
Low
Even 2 2
Accept
Reject
Accept
Reject
9, 1
0, 0
5, 5
0, 0
What is the predicted outcome for this game?
Player 1 chooses Low and Player 2 Accepts.

7. Limited Self Interest: Fairness
Symmetric Fairness . 1 . .
Low
Even 2 2
Accept
Reject
Accept
Reject
1, -7
0, 0
5, 5
0, 0
Now Player 1 offers an even amount, which is accepted.

8. Limited Self Interest: Fairness
Envy . 1 . .
Low
Even 2 2
Accept
Reject
Accept
Reject
9, -7
0, 0
5, 5
0, 0
Again Player 1 offers an even amount, which is accepted.

9. 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.

10. 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.

11. 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

12. 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

13. 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)
behavioral regularities
socially shared belief regarding how one ought to behave
enforcement by informal social sanctions
(but: what triggers a particular norm?)

14. 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.

15. 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.

16. Dictator Game
Similar to the ultimatum game except Player 2 does not have the opportunity to reject.
Empirically, dictators offer about % of their money.
Assuming u(x)=x, once again, the only subgame-perfect equilibrium is where the “dictator” offers nothing.

17. 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.

18. 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.

19. Example Find all Nash equilibria in pure strategies when played by:
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).

20. Intentions and Reciprocity
Whether a responder will accept depends not just on the proposed allocation (e.g., an 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.

21. 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

22. 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

23. 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.

24. 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.

25. 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.

26. 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

27. 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.

28. 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.

29. Ui(x) = xi – αi /(n-1)Σ max(xj–xi,0) – βi /(n-1) Σ max(xi–xj,0)
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.
Based on pure self-interest
A minority of selfish individuals can dominate a market
Ignores reciprocity

30. Ui(xj||xi)
45o xi
Red line is the utility line xj

31. 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: 
BO model: relative shares.
BO model does not compare each player’s payoffs with the maximum and minimum of the other payoffs, like the FS model does.
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

32. 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

33. 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

34. Example, fi(xj - j) = (xj - j)2
-fj
Example, fi(xj - j) = (xj - j)2
depends on
Accountability
Efficiency
Need

35. 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

36. Reciprocity Models Ui = xi + gj(1+fi)
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.

37. 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
Standard game theory is when αii=0

38. 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

39. Simple Rabin Model (application)
Now suppose α1=α2=1
What will determine the equilibrium?
The relative sizes of 1 and 2

40. 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”

41. 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

42. Rabin’s “Fairness Functions” I

43. Rabin’s “Fairness Functions”
Player i’s kindness to player j
Player i’s belief about player j’s kindness
which in equilibrium means
because expectations are correct

44. 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

45. Characteristics of Rabin Model
People will sacrifice their own material well-being to help those being kind.
People will sacrifice their own material well-being to punish those being unkind
Both these effects are bigger as the cost of the material sacrifice is smaller

46. 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