Social preferences

Topic 3 –

Social preferences

Martin Kocher

University of Munich

Experimentelle Wirtschaftsforschung

Motivation

- “De gustibus non est disputandum.” (Stigler and Becker, 1977)

- “De gustibus non est disputandum, exceptum non- selfishum.” (Matt Rabin, much later)

A theory of moral sentiments

An re-introduction to the ‘villain’

- Unbounded rationality (e.g., common knowledge)

- Pure self-interest?

- Complete self-control - Fixed preferences and

variable restrictions

… homo oeconomicus

Preview of topic 3

Seminal models of social preferences

+ Fehr and Schmidt (1999) – inequity aversion + Bolton and Ockenfels (2000) – ERC

+ Charness and Rabin (2002) – Rawlsian motives and efficiency (quasi-maximin preferences)

Discussion

+ Engelmann and Strobel (2004) and responses + Konow (2003) – justice theory

- Outcome-based models, for which and not

- Intention-based models: reciprocity, kindness etc.

- Strong focus on experimental results (theory based on evidence, “feedback loop”)

- Multitude of citations to the leading models.

In the following we will focus on outcome-based models.

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U_{i i i j}

The basic idea

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- One of the first papers that tries to rigorously model the deviations from selfishness that have been observed in the laboratory.

- The basic idea: People may have a disutility from inequity; hence, inequity (inequality) aversion.

- The model is purely based on outcomes and can be applied to n players within a reference group. It

abstracts from intentions but does not say that they do not play a role.

- One important feature is that everybody compares with everybody else individually within his or her reference group.

Inequity aversion – Fehr and Schmidt

(1999)

- If x = (x₁, …, x_n) denotes the vector of monetary payoffs of the n subjects of a group, Fehr and Schmidt (1999) define subject i’s utility U_i as follows:

- It is assumed that β_i ≤ α_i and 0 ≤ β_i < 1 (self-centered inequity aversion) and that inequity aversion is linear.

- And in the two-player case:

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Inequity aversion – Fehr and Schmidt (1999)

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Inequity aversion – Fehr and Schmidt

(1999)

- Denote the offer by s that can be accepted or rejected.

The proposer receives a normalized 1-s if accepted and 0 if rejected. The responder receives s if accepted and 0 if rejected.

- Suppose that the proposer’s preferences are represented by (α₁^{, β}₁), while the responder’s preferences are characterized by (α₂^{, β}₂^).

- It is a dominant strategy for the responder to accept any offer s ≥ 0.5, to reject s if

and to accept s > s’(α₂^).

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Inequity aversion – Application ultimatum game

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- If the proposer knows the preferences of the responder (sic!), he will offer

- Group assignment: Try to proof (or solve intuitively)!

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Inequity aversion – Application

ultimatum game

- Roth et al. (1991) on four continents.

- The subgame perfect equilibrium under standard preferences of offering s=1 is preserved also under Fehr-Schmidt preferences.

- Intuition: There will be inequality anyway, but by winning the competition, player i can increase his or her own

monetary payoff, and he or she can turn the inequality to his or her advantage.

- Bilateral bargaining games versus market games in general.

Inequity aversion – Applic. ultimatum

game with responder competition

- “We conclude that competition renders fairness considerations irrelevant if and only if none of the competing players can punish the monopolist by

destroying some of the surplus and enforcing a more equitable outcome. This suggests that fairness plays a smaller role in most markets for goods than in labor markets.”

- “This follows from the fact that, in addition to the rejection of low wage offers, workers have some

discretion over their work effort. By varying their effort, they can exert a direct impact on the relative material payoff of the employer. Consumers, in contrast, have no similar option available.” (see Fehr and Schmidt, 1999, p. 835)

Inequity aversion – Competition and

fairness

- To be relegated to the ‘Cooperation’-Section.

- The utility function of Fehr and Schmidt (1999) can be and has been, of course, applied to a wide variety of games and distribution exercises.

Inequity aversion – Application public

goods games (with punishment)

- Estimate parameters from the ultimatum game and use it to predict behavior in other games.

Inequity aversion – Predictions across

games

Inequity aversion – Predictions across

games

- Linearity (dictator game).

- What if β_i < 0?

- What is the reference group (how are reference groups constituted)?

- Predictions across games: within subject versus averages over the population (newer evidence).

- Intentions?

Problems with the model

- ERC = Equity, Reciprocity and Competition - Explicitly wants to explain lab behavior.

- i = 1, 2, 3, … n players.

- y_i: monetary payoff of player i.

- Each player maximizes the expected value of the motivation function v_i = v_i (y_i, σ_i).

- Where

is i‘s relative share of the payoff and , i.e. the total monetary payout.

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ERC – Bolton and Ockenfels (2000)

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= y_i c

- Some not so innocuous assumptions about the motivation function (like continuity).

- Example for a motivation function:

- Details can be found in the paper.

ERC – Bolton and Ockenfels (2000)

- Comparison to average versus comparison to each other player in the reference group individually.

- Equal splits are unlikely in Bolton and Ockenfels though approximated.

- Different equilibria for the public goods game without punishment.

- Most of the predictions of the two models are, however, identical.

Fehr and Schmidt versus Bolton and

Ockenfels (2000)

- Combination of outcome-based and intention-based model.

- The first attempt in this spirit after Levine (1998).

- The outcome-based part builds on Rawlsian preferences.

- More specifically, a decision-maker cares for his/her own payoff, the average payoff (efficiency!) and the payoff of the least-off individual (Rawls): quasi-maximin

preferences.

- 29 different games, with 467 participants making 1697 decisions

Charness and Rabin (2002)

- Letting π_A and π_B be Player A's and B's money payoffs, CR consider the following simple formulation of Player B's preferences:

- where

- r = 1 if π_B > π_A , and r = 0 otherwise;

- s = 1 if π_B < π_A , and s = 0 otherwise;

- q = - 1 if A has misbehaved, and q = 0 otherwise.

B A

B A

B r s q r s q

U

Charness and Rabin (2002)

π θ

σ ρ

π θ

σ ρ

π

π

( ≡ + + + − − −

- This formulation says that B's utility is a weighted sum of her own material payoff and A's payoff, where the weight B places on A's payoff may depend on whether A is

getting a higher or lower payoff than B and on whether A has behaved unfairly. The parameters ρ, σ, and θ

capture various aspects of social preferences.

- The parameter θ provides a mechanism for modeling reciprocity.

- The parameters σ and ρ allow for a range of different distributional preferences that rely solely on the

outcomes and not on any notion of reciprocity.

Charness and Rabin (2002)

- One form of distributional preferences (consistent with the psychology of status) is simple competitive

preferences. These can be represented by assuming that σ ≤ ρ ≤ 0, meaning that Player B always prefers to do as well as possible in comparison to A, while also caring directly about her payoff.

- Difference aversion corresponds to σ < 0 < ρ < 1 . That is, B likes money, and prefers that payoffs are equal,

including wishing to lower A's payoff when A does better than B.

Charness and Rabin (2002)

- Andreoni and Miller (2002): efficiency preferences.

- Since social-welfare preferences assume that people

always prefer Pareto improvements, they cannot explain Pareto-damaging behavior such as rejections in the

ultimatum game. Of course, reciprocity is a natural alternative explanation for Pareto-damaging behavior.

- Several models say, roughly put, that B's values for ρ and σ vary with B's perception of player A's intentions.

- Examples.

Charness and Rabin (2002)

- In all their experimental games, either one or two

participants made decisions and decisions affected the allocation to either two or three players. In two-player games, money was allocated to players A and B based either solely on a decision by B, or on decisions of both A and B. In three-player games, money was allocated to players A, B, and C, based either solely on a decision by C, or on decisions by both A and C.

- In games where more than one player had choices, these were played sequentially.

Charness and Rabin (2002)

- Social welfare criterion:

- Utility function of player i without reciprocity concerns:

- Can be re-written as the function introduced above.

- Then they go on defining a social welfare equilibrium.

- Introducing reciprocity is left out.

Charness and Rabin (2002) – more

general (a “conceptual” model)

- Test Fehr and Schmidt, Bolton and Ockenfels (as well as Charness and Rabin) with (non-interactive) distribution exercises.

- They can assess the relative importance of efficiency concerns (maximize the group payoff), maximin

preferences (maximize the minimal payoff in the group) and inequity aversion.

- Reciprocity is ruled out because there is no interaction between the distributors and the receivers.

Engelmann and Strobel (2004)

- The decision sheet contained three different allocations of money between three persons, of which the subjects had to choose one. They were informed that ES would randomly form groups of three later on and would also assign the three roles randomly, hence subjects faced role uncertainty. Only the choice of the participant

selected as person 2 mattered.

- Two control treatments assigned fixed roles in advance, but kept the random ex post formation of groups (without effect).

- To avoid influence by computation errors they also noted the average payoffs of persons 1 and 3 and the total

payoff for each allocation in the decision sheet.

Engelmann and Strobel (2004) - Design

Some concepts:

- Egalitarianism, Rawlsian justice, Marxian justice (needs), Need principle.

- Utilitarianism, Pareto Principles (1. Pareto, 2.

Compensation Principle), Absence of Envy, Efficiency Principle.

- Nozick (principle of justice in acquisition and principle of justice in transfer), Theories of desert (Buchanan;

determinants of wealth and income: luck, choice, effort, birth – last is in conflict with justice), Equity theory

(Aristotle), Equity Principle.

- Context (KKT, 1986), also Camerer(2003); read yourself.

Konow (2003)