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Sequential BargainingPart 2

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What are potential questions

• Do stakes matter?• Does more repetition matter?• What about different cultures?• Who is “fair”, i.e. why do proposers make

fair offers?• Is it intentions or outcomes that matter?

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Who is fair?

The ultimatum game does not allow us to determine why we observe offers above 0:

• Does the proposer want to be fair?• Can the responder use his power to

destroy the pie to enforce fairness?• Forsythe, Horowitz, Savin, and Sefton,

1994 (GEB): “Fairness in Simple Bargaining Experiments”

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Dictator and Ultimatum GameTo separate motivations of proposers and

responders: Game that is as similar to the ultimatum game as possible, but where the responder cannot express his preferences in any way.

Hence eliminating motivations of responders.Ultimatum Game: Proposer proposes a division of

M (10), responder accepts and division is implemented, or rejects, and M is destroyed, both agents get 0.

The Dictator Game: Proposer proposes a division of M (10), responder has to accept.

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Dictator and Ultimatum Game

It seems that both motivations of proposers, and responders are contributing to fair outcomes, but reposndersdeifnitely have a significant role.

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Ultimatum and dictator game: with and without payments:

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How far does “fairness” extend?Kagel, John and Katherine Wolfe, "Tests of Fairness Models Based on

Equity Considerations in a Three-Person Ultimatum Game," Experimental Economics, vol 4, 2001, pp 203-220.

They have 3 player ultimatum games: Player X allocates $15 between Y and Z. After that, one of the players Y and Z is chosen randomly to decide whether to accept the allocation of X or reject it. In case of rejection, the other (non-chosen) player receives a consolation prize: $0, $1, $3 and $12, and also -$10.

What happens when we have a third player, who gets $12 pie when the responder rejects: No effect.

Suppose a third person receives $-10 when the responder rejects: No effect.

(There are many more variants, many to try out the various fairness models…)

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• What happens when the proposer can only make “unfair” offers?

• Falk, Fehr and Fischbacher (1999) look whether “intentions” matter.

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What happens in different cultures?

• Roth, A.E., Prasnikar, V., Okuno-Fujiwara, M., and Zamir, S. "Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study," AER, vol. 81, December 1991, 1068-1095.

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OBJECTIVES1. Compare related bargaining and market environments

(both with extreme equilibrium predictions).2. Compare behavior in potentially very different subject

pools, in the bargaining and market environments.3. Use potential subject pool differences to test and refine

hypotheses about 'out of equilibrium' behavior already observed in these bargaining environments.

4. To learn from experience about some of the experimental design problems in multi-national experiments, especially if a goal is to explore culturaldifferences. (Control for languages, currencies, experimenters.)

To use such differences as may be found as the basis for preliminary conjectures about cultural differences.

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The Games

Ultimatum Game

The market Game:• There are 9 proposers for 1 responder.

Each proposer offers a price p. If the responder accepts one of the prices, then the relevant proposer receives 10-p and the responder receives p.

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Controlling for Between-Country Variables

Problem 1. Experimenter effects: Between-country differences might arise because of uncontrolled procedural differences, or because of uncontrolled personal differences among the experimenters.

Design solution: Each experimenter came to Pittsburgh, where they ran (at least) a bargaining session and a market session. The Pittsburgh data was therefore gathered by all of the experimenters before they returned to their home countries to gather the data there.

• In this way they were able to coordinate the detailed operational procedures among the different experimenters.

• And the Pittsburgh data can be used to detect any pure experimenter effect in the between-country comparisons

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Problem 2. Language effects: Because instructions are presented in English, Hebrew, Japanese, and Slovenian, systematic differences between countries might be observed because of the way the instructions are translated. (Consider for example the English words "bargaining," "negotiating," and "haggling," which are all approximate synonyms, but whose different connotations might possibly elicit differences in behavior.)

Design solutions: We addressed the problem of language effects both through the way in which the translations were made, and, more formally, in the way the instructions for the bargaining and market environments were related.

• a) Translations: Efforts were made to phrase the English instructions in terms that could be faithfully translated into each of the languages. Aside from avoiding terms with heavy or ambiguous connotations either in English or in translation, this also led to phrasing in less abstract terms than are sometimes used in single-culture experiments. (For example, subjects in bargaining experiments are sometimes instructed that they will be in the position of "player 1" or "player 2," but this turns out to be difficult to translate into Slovenian without sounding frivolous.)

• b) Control for translation differences: The instructions for the bargaining and market environments were written in parallel, using the same vocabulary. (For example, in both environments, those subjects who made proposals were referred to as "buyers," while those who made acceptances or rejections were termed "sellers.") So if a translation difference is responsible for an observed behavior difference between countries, it should show up in both the market and bargaining data.

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If the market data (like the bargaining data) also showed differences between the two countries, or if the market and bargaining data were the same in one of the countries, then we couldn't be sure that the between-country difference in the bargaining data wasn't due to some property of the translation.

But if the pattern of results is that similarities are present only in one treatment but not the other, then we can at least put an upper bound on the effect of the translation--it isn't large enough to cause the markets to yield different results in the different countries, or to cause the bargaining to yield the same results as the market in one of the countries. This would thus support the hypothesis that the translation isn't the cause of the observed difference in the bargaining.

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Problem 3. Currency effects: Because the subjects were paid in dinars, dollars, shekels, and yen, systematic differences between countries might be observed because of the different incentives that the potential payments give to subjects, or because of the different numerical scale on which payments are made. (That is, subjects in experiments often tend to choose round numbers and these may depend on the units involved, so that subjects proposing prices in dollars might choose different numbers than those dealing in thousands of yen, or hundreds of thousands of dinars.)

Design solutions: • a) To assess the extent to which between-country differences might

be due to differences in purchasing power, the Pittsburgh data establishes a baseline by including sessions in which the potential payoff ranged from $10 to $30. In each country the size of the payoffs was then chosen to give a purchasing power on the high side of $10. So if observed differences between countries fall outside the range of differences due to payoffs observed in Pittsburgh, they are likely to be due to other factors.

• b) To control for differences in units, proposed prices in all countries were made in terms of 1000 tokens, with increments being made inunits of 5 tokens.

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Other Aspects of the Design and Procedures

• A "one classroom" set of procedures was adopted, for portability between locations.

• In the bargaining sessions, 20 subjects were randomly divided into buyers and sellers. Each buyer bargained once with each seller, and learned only the outcome of his own negotiations.

• In the market sessions, there were 2 sellers and 18 buyers, divided into two markets, A and B. No subject knew which (other) buyers were in each market in each round. (This was to prevent the 10 rounds from becoming a repeated game among the same group of buyers.) The transaction price for each market was announced for each market

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• So the ultimatum game results are quite different from the market results—the same people (more precisely, people drawn from the same subject pool) who are willing to reject positive offers, are also willing to bid their profits down to zero.

• Let’s take a closer look at the bargaining data, to try to understand what’s going on. (One of the advantages of experimental data is you can look at it in as disaggregated form as you want.)

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Experimental design issues:• one way to increase the power of the experiment

to detect differences due to stakes is to increase the spread (we’re talking about within experiment comparisons, of course)

• another way is to allow players to gain experience: the experiments above all looked at games in which subjects did not get experience through repeated play. But differences may emerge more clearly with experience; i.e. experience may magnify differences that are initially hard to observe.

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Slonim, R. and A.E. Roth “Learning in High StakesUltimatum Games: An Experiment in the Slovak

Republic,” Econometrica, 66,3, May 1998, 569-596.Experimental Design• 10 periods of play against different others• 3 payoff scales: 60, 300, and 1500 Sk (all stakes were

presented as 1000 points to be divided, with different exchange rates).

10 periods of play will accomplish two things:• Does experience enlarge the effects of different stakes?• Are there interactions between stakes and learning?• Look at both proposer and responder behavior.

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Low Stakes

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Medium Stakes

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However, different participants may learn different things.

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“Two differences in the ultimatum game behavior were detected as stakes increased. First, responders (pooled over all rounds) rejected offers less often. Second, there was an interaction effect between stakes and experience: in the higher stakes conditions the offers decreased with experience. The experiment and learning simulations suggest that small initial differences in proposer behavior cannot account for the differential learning behavior, but that the lower likelihood of being rejected in the higher stakes can account for higher stakes proposers learning to make lower offers.…

In general, new kinds of theory allow us to explore different kinds of questions, and suggest different kinds of experiments. We therefore view this paper not only as an experiment designed to explore the effects of large changes in stakes, but also as an attempt to take seriously the demands that theories of learning place on (and the opportunities they provide for) experimental design and analysis.”