non-selfish preferences 1. 2 the standard model 1.nature self-interest and self-regarding...
TRANSCRIPT
![Page 1: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/1.jpg)
1
Non-selfish preferences
![Page 2: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/2.jpg)
2
![Page 3: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/3.jpg)
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.
![Page 4: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/4.jpg)
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
4
![Page 5: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/5.jpg)
5
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
![Page 6: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/6.jpg)
6
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
![Page 7: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/7.jpg)
7
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.
![Page 8: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/8.jpg)
8
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.
![Page 9: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/9.jpg)
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.
![Page 10: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/10.jpg)
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.
![Page 11: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/11.jpg)
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
![Page 12: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/12.jpg)
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
![Page 13: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/13.jpg)
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?)
![Page 14: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/14.jpg)
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.
![Page 15: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/15.jpg)
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.
![Page 16: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/16.jpg)
16
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.
![Page 17: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/17.jpg)
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.
![Page 18: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/18.jpg)
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.
![Page 19: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/19.jpg)
19
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).
![Page 20: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/20.jpg)
20
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.
![Page 21: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/21.jpg)
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
![Page 22: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/22.jpg)
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
![Page 23: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/23.jpg)
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.
![Page 24: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/24.jpg)
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.
![Page 25: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/25.jpg)
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.
![Page 26: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/26.jpg)
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
![Page 27: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/27.jpg)
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.
![Page 28: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/28.jpg)
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.
![Page 29: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/29.jpg)
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
![Page 30: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/30.jpg)
45o
xj
xi
Ui(xj||xi)
Red line is the utility line
![Page 31: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/31.jpg)
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
![Page 32: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/32.jpg)
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
![Page 33: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/33.jpg)
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
![Page 34: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/34.jpg)
j
-fj
Example, fi(xj - j) = (xj - j)2
F depends on1. Accountability2. Efficiency3. Need
![Page 35: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/35.jpg)
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
![Page 36: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/36.jpg)
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.
![Page 37: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/37.jpg)
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
![Page 38: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/38.jpg)
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
![Page 39: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/39.jpg)
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
![Page 40: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/40.jpg)
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
![Page 41: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/41.jpg)
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
![Page 42: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/42.jpg)
Rabin’s “Fairness Functions” I
![Page 43: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/43.jpg)
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
![Page 44: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/44.jpg)
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
![Page 45: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/45.jpg)
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
![Page 46: Non-selfish preferences 1. 2 The Standard Model 1.Nature Self-interest and self-regarding preferences 2.Anomalies Tipping waiters Giving to charity](https://reader035.vdocument.in/reader035/viewer/2022062313/56649d0b5503460f949de5a0/html5/thumbnails/46.jpg)
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