Brandts and Solà:
Reference Points and Negative Reciprocity in Simple Sequential Games
Economics 328
Spring 2005
How Can We Explain Other-regarding Behavior?
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In some games people seem to care greatly about fairness and equity. In others,
they seem to ignore such concerns.
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In ultimatum games, proposers typically offer a substantial portion of the pie to
responders. Responders often turn down small offers.
In dictator games, proposers still offer positive amounts of money even though there
exists no strategic reason to do so.
In gift-exchange games, increasing wages lead to an increase in the effort put forth by
workers.
In public goods games without punishment, there are initially many positive
contributions but this declines over time. With costly punishments, contributions rise
over time due to contributors punishing defectors.
In market experiments, the buyer rapidly ends up getting the entire surplus.
In best-shot games, play rapidly converges to a highly asymmetric equilibrium.
We would like to have a theory that can explain these disparate results.
How Can We Explain Other-regarding Behavior?
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There are also a number of real
world examples we would like to
be able to explain, as follows:
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Consumer’s feelings about the
fairness of firm’s short-run pricing
policies prevent firms from taking
full advantage of short-term
monopolies.
Firms’ wage setting is constrained by
workers’ feeling about what is fair.
In particular, firms will not cut wages
during recessions due to fear about
workers’ reactions to an “unfair”
wage cut.
Theories of Other-Regarding Behavior
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Two prominent recent papers, Bolton and Ockenfels (2000) and Fehr and Schmidt
(1999) have recently advanced theories that aim to provide a unified explanation
of these phenomena.
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In both theories, an individual’s utility function depends both on his/her own payoff
and on the payoffs of others. The theories differ primarily in the functional forms
assumed.
Both theories can explain many (but not all) of the observed anomalies.
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For example, in the ultimatum game suppose that I put positive weight on my monetary
payoff and negative weight on the difference between my payoff and the other player’s
payoff (F&S). For sufficiently low offers, I reject rather than accepting because the gain of
getting some money is less than the loss of getting much less than the other player.
The best-shot game is the notable exception that neither theory can explain.
Both theories are consequentialist – utility depends on the final outcome, not the
choices that led to the final outcome.
Do Intentions Matter?
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The great weakness of theories like Bolton and Ockenfels or Fehr and Schmidt is
that payoffs depend solely on consequences. There exists ample evidence that
intentions matter as well as outcomes. Consider the following examples:
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I am walking by you with a cup of hot coffee. I trip over a crack and spill the coffee
all over you, burning you and ruining your expensive new shirt.
I am walking by you with a cup of hot coffee. I turn to you, snarl, “I’ve never liked
you, you jerk,” and throw the coffee in your face, burning you and ruining your
expensive new shirt.
I am walking by you with a cup of hot coffee. Somebody runs up from behind and
hits me over the head with a 2 x 4. I collapse unconscious and spill the coffee all
over you, burning you and ruining your expensive new shirt.
Do you feel the same about me in each case? Suppose you could punish me for
a small fee (e.g. you fill out a form, I have to pay to replace your new shirt).
Would you be equally as interested in punishing me in each of the three cases?
Brandts and Solà
Research Question
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The theories advanced by Bolton-Ockenfels and
Fehr-Schmidt to explain fair behavior are
consequentialist in nature. All that matter is what
happened, not why it happened. Brandts and
Solà aim to show that these theories miss
important aspects of fair behavior, in particular
the importance of both intentions and
distributions of outcomes.
Brandts and Solà stress the importance of
reciprocity. “Positive reciprocity involves
rewarding perceived good intentions, while
negative reciprocity leads to punishing perceived
bad intentions.”
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Chooser dependence
Menu dependence
Experimental Design
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Ultimatum minigame: This is a stripped
down version of the ultimatum game in
which the proposer only has two options.
One of these options is held fixed in all
games at (320,80). The other is varied
systematically. The idea is to see whether
there is menu dependence in responder’s
reactions to the benchmark.
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All games have the same total payoff as the
benchmark, eliminating efficiency concerns.
Games 2, 3, and 4 have less asymmetry than
the benchmark. Game 3 has an equal split.
Games 1 and 5 have more asymmetry than
the benchmark.
Games 1 and 2 give the advantage to Player
1 while Games 4 and 5 give the higher
payoff to Player 2.
Experimental Procedures
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Ten sessions were run, two with each of the ultimatum minigames. The same
game was played for the entire experiment. There were 16 subjects per session.
Each subject was assigned to a role (proposer or responder) for the entire
experiment.
Each experiment consisted of eight games.
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Subjects were never matched against the same opponent twice.
Subjects learned the outcome of each game at the end of the round.
Payment was cumulative over the eight rounds.
Results
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The rejection rates for the benchmark split vary significantly depending on what the forgone
option was.
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Rejection rates are lowest when the foregone option was worse than the benchmark.
Rejection rates are the highest when the foregone option gave the responder a higher payoff than
the proposer and the payoffs were less asymmetric than the benchmark.
Comparing the two games where the responder gets a higher payoff than the proposer, the rejection
rate is far lower when the payoffs were more asymmetric than the benchmark. Apparently people
are expected to be fair but not saintly.
Conclusions
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The results of Brandts and Solà (2001), along with results by Falk, Fehr, and
Fischbacher (2000) and Kagel and Wolfe (1999), suggest the need for new
theories that combine preferences over distributions with preferences over
intentions.
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Two such theories have been advanced by Falk and Fischbacher (2000) and Charness
and Rabin (2002)
There already exist experimental violations of these new theories (Cooper and
Stockman, 2002).
Over the next few years, experimenters and theorists will be challenged to develop
a unified theory of other-regarding behavior. It may be that we settle for a theory
that explains many of the facts while accepting that it gets some things wrong.