Bargaining II – Trust game

Bargaining II – Trust game

Martin Kocher

University of Munich

Course in Behavioral and Experimental

Economics

Motivation and preview of Topic 3

Trust is a necessary ingredient in a world with incomplete contracts, where it is possible that one party (voluntarily) makes itself vulnerable to the actions of another party.

Trust game

+ Berg et al. (1995) – The “original”

+ Sutter and Kocher (2007) – Trust and age + Bohnet et al. (2007) – Betrayal aversion + Fershtman and Gneezy (2001) – Trust and

discrimination

Trust

• Trust and reciprocity are important ‘ingredients‘ for the efficient functioning of markets and society in general.

• Trust is central in every sales transaction or professional relationship.

• More generally speaking, trust is important in any

decision where one’s outcome is not fully contractible and is partly under the control of another person (see Coleman, 1990).

Trust

• Knack and Keefer (1997) and LaPorta et al. (1997) have even established a connection between trust in a

country’s population and the level of economic growth of the respective country.

• Trust is measured with by the average answer to the following question from the world value survey:

“Generally speaking would you say that most people can be trusted or that you cannot be too careful in dealing

with people?”

Berg et al. (1995) have introduced the trust game (or investment game) to study trust and reciprocity.

Two-person game with double-blind procedure.

• Initial endowment of trustor and trustee of E > 0.

• Trustor can transfer x ≤ E to trustee. (TRUST)

• Trustee receives 3x (triple transfer).

• Trustee returns y ≤ 3x. (RECIPROCITY)

• Final payoffs:

– Trustor: E – x + y – Trustee: E + 3x - y

The trust game

Berg et al. (1995) – Results (no-history treatment)

30 out of 32 trustors send

positive amounts.

∅ transfer = 5.16.

∅ payback = 4.66.

Trust does not pay on average!

(Note positive payback for full trust.)

They also study behavior in a treatment where subjects are given the distribution of transfers and average returns in the no-history treatment.

Results are basically the same.

∅ transfer = 5.36.

∅ payback = 6.46.

Hence, providing social history to subjects does not discourage trust (as expected by the authors).

Berg et al. (1995)

• Many trust games have confirmed the basic patterns first reported in Berg et al. (1995). See the survey in Camerer (2003).

• In the following we discuss two recently investigated aspects of trust:

– Do trust and reciprocity develop with age, and - if so - how?

On the generality of trust

In order to study the development of trust and reciprocity with age they run an experimental trust game with subjects from 6 different age groups:

– 8-year olds (primary school)

– 12-year olds (secondary school) – 16-year olds (secondary school)

– Students (avg. age 22; std.dev. 2.8)

– Working professionals (avg. age 32; std.dev. 6.3) – Retired persons (avg. age 68; std.dev. 8.6)

Sutter and Kocher (2007) – Trust and age

• The standard trust game was used, except that the

trustees did not receive an initial endowment (note that the trustee‘s endowment could not be used for returns in the original paper of Berg et al., 1995).

• Assuming payoff-maximization and applying backward-

induction one arrives at the prediction that x = 0 and y = 0, i.e. no trust and no (opportunity for) reciprocity.

Sutter and Kocher (2007) – Design

• The trustor‘s endowment E was worth between 2 and 8

Euro in the different age groups (see Appendix of paper for checks on stake size effects).

• The game was framed as a two-person interaction between

„John/Joanna“ and „Michelle/Michael“.

• Subjects were always told that they would interact with a person from the same age group, which, however, was to be selected randomly from a different class or session.

Sutter and Kocher (2007) – Design

• The experiment was run as a paper and pencil

experiment, where decisions were recorded on a decision form (by marking transfers, respectively returns).

Sutter and Kocher (2007) – Design

• Piaget‘s and Kohlberg‘s research on the development of moral judgment have led to studies on the development of prosocial behavior (which is not purely self-interested and intends to benefit others at own costs).

• Moral reasoning as well as prosocial behavior advance with age (Eisenberg and Fabes, 1998).

Insights from developmental psychology

• Trust in strangers develops gradually from childhood to early adulthood (Krebs and van Hesteren, 1994;

Langford, 1997).

• Reciprocity (as a material tit-for-tat strategy) is typically established already at age 5-6 years (Youniss, 1980, 1986).

Developmental psychology

on trust and reciprocity

Hypothesis 1: Trust increases with age. The transfer x is expected to increase with age, at least until early

adulthood.

Hypothesis 2: Reciprocity is established at an early age. The return y should depend significantly positive on the

transfer x, irrespective of age.

Hypotheses from developmental

psychology

The following table contains the most important variables.

The two figures on the next slides illustrate the main results.

Sutter and Kocher (2007) – Results

Transfers (trust) increases almost linearly until early adulthood.

Sutter and Kocher (2007) – Results

Relative returns (reciprocity) seem to increase in steps.

Sutter and Kocher (2007) – Results

• Reciprocity is measured as the dependence of the return y on the transfer x.

• Use of a two-way censored tobit-regression with zero as left-side limit and 3x as right-side limit.

• All observations with x = 0 are excluded (N=18 in all age groups).

Measuring reciprocity

The marginal effects of the transfer on the return increases with

Results on reciprocity

In the age groups of children and adolescents it seldom pays to

Does trust pay off?

In the adult age group it typically pays to trust.

Does trust pay off?

• Trust in strangers increases significantly from childhood to early adulthood, and stays rather constant afterwards.

• Reciprocity is a prevailing pattern of behavior already at age 8, but becomes less self-serving with age.

Sutter and Kocher (2007) – Summary

• Trust always involves the risk of getting disappointed by a trustee not honoring trust. Bohnet et al. (2007) denote that as social risk.

• Of course, any game against nature (like a lottery choice) also involves risk.

• Holding the risk constant, does it make a difference for subjects whether the source of the risk is another person rather than nature?

• If so, this would indicate betrayal aversion (which might come on top of risk aversion).

Trust and risk – On the importance of

betrayal aversion

• If individuals have an aversion against being betrayed,

they will be less willing to take risks in a trust situation than in an equivalent situation where chance determines the

outcome.

• Bohnet et al. (2007) measure betrayal aversion in six countries:

– Brazil, China, Switzerland, Turkey, United Arab

Emirates, and United States. (In total 874 participants.)

Betrayal aversion

• They use a between-subjects design where subjects play one of the following three games

– Trust game

– Risky dictator game – Decision problem

• The possible payoffs are the same in all games – see next slide.

Bohnet, Greig, Herrmann and

Zeckhauser (2007)

Bohnet et al. (2007) – The games

Betrayal aversion

Social

preferences

Risk

aversion

In the trust game principals are asked for their “minimum acceptable probability” (MAP) for securing the high payoff to accept the risky decision rather than the secure payoff.

Agents had to indicate by strategy method whether to be

trustworthy (action 1) or not (action 2), and principals knew about this.

The fraction of trustworthy agents is denoted p*.

If a principal’s MAP > p* then no trust (secure payoff).

If a principal’s MAP < p* then trust (agent decides).

Bohnet et al. (2007) – The trust game

In the risky dictator game and the decision problem

principals again state their MAP. They are told that p* has been determined prior to the experiment. (The p* in the trust game of each country is taken.) After deciding on MAP, the p* is announced.

• If a principal’s MAP > p* then secure payoff.

• If a principal’s MAP < p* then lottery with p* probability.

The difference between risky dictator game and decision problem is that no second party is involved in the latter.

Bohnet et al. (2007) – The other games

MAP_TG – MAP_RDG  betrayal aversion: Difference in

willingness to take risk p* when p* either originates from another subject or from nature  positive difference

indicates betrayal aversion.

MAP_DP – MAP_RDG  social preferences: Difference in

willingness to accept risk when either no other subject is

involved or another subject can benefit  positive difference indicates that subjects take risks more often if another party can benefit from it.

MAP_DP – p’ (with p’ probability for fair lottery)  risk aversion.

Bohnet et al. (2007) – The measurement

Bohnet et al. (2007) – Results

Overall averages:

MAP_TG = 0.56 MAP_RDG = 0.41 MAP_DP = 0.48 p’ = 0.29

• Subjects are betrayal averse. Hence, the same risk is less tolerated if its source is another person’s behavior instead of nature.

• Social preferences exist, but are less robust.

• Risk aversion prevails in all subgroups.

Bohnet et al. (2007) – Summary

• Israeli Jews are mainly of two origins, either Ashkenazim (Western) or Eastern Jews (Sephardim).

• Obviously, there is a large gap in education and earnings between both groups (more so with respect to men than to women, though).

• Fershtman and Gneezy (2001) examine in a trust-game experiment whether the segmentation is related to

discrimination.

• Discrimination may reflect a taste for it, or be the consequence of ethnic stereotypes.

Fershtman and Gneezy (2001) – Trust

and discrimination

• Is there discrimination based on ethnic affiliation?

• Does discrimination reflect group bias (i.e., preferential in- group treatment)?

• Is discrimination driven by a taste for discrimination or by ethnic stereotyping?

• Are ethnic stereotypes accurate?

Fershtman and Gneezy (2001) –

Research questions

• Eastern Jews get less money in the trust game (from both groups!), though they send back the same amount as

Western ones. Hence, stereotypes are mistaken.

• This discrimination is restricted to men only. Women do not discriminate and are not discriminated.

• The source of discrimination is ethnic stereotyping (“the less trustful Eastern Jews”), not a taste for discrimination, as is shown in a control-Dictator game (where the transfers do not depend on ethnic origin).

Fershtman and Gneezy (2001) –

Summary of main findings

• Player A gets 20 NIS and can send any amount up to 20 NIS to a player B. The names of the counterpart is written on the instructions. (Names are the best indicator of ethnic origin!)

Fershtman and Gneezy (2001) – Design

of trust game

(c) M. Kocher and M. Sutter 37

Male Ashkenazic receive on average 15.15 NIS, vs. 8.06 NIS

Fershtman and Gneezy (2001) – Results

The difference is even more pronounced when considering

Fershtman and Gneezy (2001) – Results

Transfers to male Ashkenazic  no ethnic differences.

Fershtman and Gneezy (2001) – Results

Transfers to male Eastern  no ethnic differences. Mistrust is

Fershtman and Gneezy (2001) – Results

There is no significant difference in returns of players B,

depending on their ethnic origin. Stereotypes are mistaken!

Fershtman and Gneezy (2001) – Returns

No significant difference in transfers in the dictator game to recipients of different ethnic origin. Hence, the differences in

Taking the dictator game as control for

“taste of discrimination”