University of Pennsylvania ScholarlyCommons Operations, Information and Decisions Papers Wharton Faculty Research 8-1996 Information in Ultimatum Games: An Experimental Study Rachel Croson University of Pennsylvania Follow this and additional works at: https://repository.edu/oid_papers Part of the Behavioral Economics Commons, and the Other Economics Commons Recommended Citation Croson, R. Information in Ultimatum Games: An Experimental Study. Journal of Economic Behavior & Organization, 30 (2), 197-212.1016/S0167-2681(96)00857-8 This paper is posted at ScholarlyCommons.edu/oid_papers/37 For more information, please contact repository@pobox. Information in Ultimatum Games: An Experimental Study Abstract This study reports on an experiment using variations of the ultimatum game.
The experiment controls the amount and type of information known to the responder in the game. In two treatments, she knows both the absolute (money) and relative (fairness) payoffs from an offer. In the other two, she knows either only the absolute or only the relative payoffs. The predictions of four models for these treatments are tested: subgame-perfection, Bolton's comparative equilibrium, Ochs and Roth's absolute threshold, and Ochs and Roth's percentage threshold hypothesis.
Keywords experiment, ultimatum game, fairness, uncertainty, framing, contingent weighting Disciplines Behavioral Economics | Other Economics This journal article is available at ScholarlyCommons: https://repository.edu/oid_papers/37 "Information in Ultimatum Games: An Experimental Study" 95-03-01 Rachel Croson Information in Ultimatum Games: An Experimental Study* Rachel T. Croson Dep:utment of Operations and Information Management Whanon School of Business Uni versity of Pennsylvania November, 1993 ( reVIsed February. 1995) Abstract This study repons on a senes of variations of the ultimatum game. The experiment controls the amount and type of information known to the responder in the game.
In two treatments. she knows both the absolute (money) and relative (fairness) payoffs ftom an offer. In the other two, she knows either only the absolute or only the relative payoffs. The predictions of seven models for these treatments are tested: subgame-perfect.
Ochs and Roth's absolute threshold. Ochs and Roth's percentage threshold and a descriptive hypothesis. JEL Classification Codes: C9 Laboratory Experiments C72 Noncoperative Games Keywords: Experiment. Framing, Contingent Weighting •Rachel T.
1318 Steinberg Hall-Dietrich Hall. Department of OPIM. \1/hanon School of Business. University of Pennsylva~ia.
Philadelphia, PA 19104-6366 CrosonR @opim.edu Information in Ultimatum Games: An Experimental Study I. Introduction Ultimatum bargaining is a building block for more complicated, and more descriptive. types of bargaining. 1 Given its importance in models of strategic behavior.
it has been studied extensively through experimental methods. This research has found that proposers make larger offers than game-theoretic analysis would predict. Responders also reject small but positive offers·, again contrary to the predictions of game theory _1 The most popular explanation for these outcomes is that subjects care about fairness: in addition to valuing their absolute payoffs (money earned from the game ). subjects care about their payoffs relative to those of their bargaining partner (fairness of the division).; There have been a number of suggestions as to how preferences about fairness are exhibited in bargaining games.
This study was designed to differentiate between and to test these models of fairness preferences! The results of this study are consistent with the notion that subjects care about both money and fairness. However the framing of the game being played affects its outcome-offers made in percentage terms rather than in dollar amounts induce higher demands. and thus "fairer" outcomes. An explanation for this effect from the contingent weighting literature is offered which suggests placing more ·•weight" or value on the fairness part of one's preferences when offers are made in percentage terms and relative payoffs are particularly salient.
The experiment consists of four treatments in which subjects divide a $10 pie in an ultimatum game. The treatments are depicted in Table 1 below and are designated by a rwo- character code. The first character represents the form in which offers are made (dollar amounts [S] or percentages[%]) and the second represents the state of the responder's knowledge (Informed about the size of the pie [I] or Uninformed (U]). Insert Table 1 here First is the classical uitimaturn game (Sl) in which the size of the pie to be divided is conunon knowledge and offers are made in dollars.
In the $U treatment, only the proposer knows the size of the pie; the responder is give n no information about its size. although she knows the dollar offer she faces. In the %U treatment. the responder is offered only a percentage of the pie-not the corresponding dollar amount- and again, she does not know the total pie's size.
The final treatment (%1) completes the 2x2 design; with both players informed about the size of the pie, the offer is made in percentage terms. The information conditions between treatments one and four are identical; only the form of the offer (the frame of the problem) differs. The subgame-perfect e1uilibrium (offer e, accept) is the same in all four experimental treatments. two empirical differences emerge across the treatments.
First, in the treatments in which offers are made in dollars. uninformed responders face and accept substantially lower offers than their informed counterparts: the average offer in treatment SU is significantly lower than the average offer in SI. treatments $1 and %1 in which the siruations are identical except for the description of the offer. evoke different responder behavior: average demands made by responders in treatment %1 are significantly higher than those made in any other treatment.
including treatment Sl. This result is consistent with individuals placing greater value on fairness when relative payoffs are particularly salient. Section II describes the experimental procedure and design. Section III outlines the theoretical predictions of the experiments and section IV describes the results.
Section V presents some analysis and section VI contains an informal discussion of one possible explanation for the observations. Section VII describes other related experiments and their outcomes and section VIII concludes. Experimental Procedure and Design; Subjects were recruited from a variety of large undergraduate lecture classes at Harvard University Summer Session. Each treatment of the experiment was run in two sessions by the same experimenter.
The sessions for each treatment were scheduled within one day of each other. Evidence that economics students play ultimatum games differently from all other students is mixed (Carter and Irons (1991), Kagel, Kim and Moser ( 1992)); to sidestep such a debate. no economics classes were used for recruiting. Subjects were told that they could stay after class.
complete a questionnaire and panicipate in a decision problem (both of which together would take 30 to 45 minutes) to earn a guaranteed $5, possibly more.6 Subjects who remai ned were seated along the outside aisles of the classroom and asked to complete a decision-making questionnaire (unrelated to the ultimatum game) for which they would be paid $5 at the end of the session. Ultimatum game instructions were then distributed according to their chosen seating. Subjects at opposite ends of the same aisle were not paired with one another, nor were subjects seated closely together. A composite version of the instructions was read aloud.
with any questions answered publicly. 7 A shon quiz about the decisions to be made. and the payoffs which resulted from those decisions, was given and subjects' answers checked- and mistakes corrected-privately. All treatments involved subjects spl itting a $10 pie.
al though not all subjects knew the size of the pie in all treatments.8 At this point proposers. whose instructions included an offer/acceptance sheet, made their offers in writing. These sheets were collected and distributed to the appropriate responders. Responders replied to their respective offers: these responses were shown to (but not left wi th) the appropri ate proposer.
All subjects then completed a shon questionnaire about their perceptions of the game, brought their material s to the experimenters. were paid individually $5 plus their earnings, and left. All subjects panicipated in one and only one ultimatum decision, eliminating opporrunities either for reputati on effects or for learning by subjects. _ · -·-··· - --· ·--- This experiment manipulates both the amount and type of infonnation the responder has.
Offers are made either in dollar or percentage amounts. The responder can know the size of the pie to be divided or not. In treatments SI and %I the responder has complete infonnation; she knows both the absolute amount of money and the percentage of the pie she is being offered. These two treatments leave the responder with logically equivalent decisions.
In treatment SU she knows only the absolute amount of money she is being offered and not the relative payoffs (fairness) of the proposal. In treatment %U she knows only the percentage of the pie she is being offered and not the absolute (money) payoffs. This paper will focus on the predictions of a number of theories for comparisons between treatments of this experiment. Two considerations I wish to address here are preferences for fair outcomes on the pan of the proposers and unknown priors about the pie size on the pan of the responders.
There is some evidence that a proponion of the population of proposers has a preference for fairness. and is willing to give up money in order to produce equal monetary outcomes (see Forsythe ec al.'s ( 1994) and Hoffman ec a/. If this is so. a random assignment of subjects to treatments should equalize the proponion of these "fair" types in the role of proposer in each of the four treatments.
By focusing on comparisons between the various treatments. offers from these types of subjects should wash out. If anything, this washing out should serve to make the data from the various treatments more alike, which is what the subgame-perfect hypothesis predicts. having proposers with preferences for fairness will tend to support the subgame-perfect hypothesis• A similar random -assignment argument holds for the distribution of prior beliefs about the size of the pie (when it is unknown) held by responders.
If the sample is rruly random, these priors should be distributed identically in the two uninfonned treatments, influencing outcomes in both treatments similarly. So by comparing differences between these two treatments. the differences in subjects' priors are not being measured. Theoretical Predictions I examine five theories and their predictions about outcomes in this experiment.
Each of these theories is composed of two pans. The first specifies the arguments of the responder's utility function. The second stipulates that proposers know these arguments. and act accordingly- that is.
that they play best responses to the responder's demands." The subgame-perfect equilibrium (with pure self-interest) predicts no differences among these four treatments; responders should accept any positive amount or percentage.'2 Thus offers and responses should be identical in all four treatments Sl, $U, %U and %I. Bolton's (1991 ) comparative equilibrium relaxes the assumption that the responder will accept all positive offers. Bohon describes a utility function containing arguments of both absolute payoffs (money) and relative payoffs (an index of fairness). Players behave as expected-utility maximizers; in an ultimatum game, the responder would accept an offer of ~rc/2 only if the utility from accepting the offer z were greater than or equal to the utility of rejecting the offer.'l Since proposers know this.
they offer enough to make responders indifferent between accepting and rejecting the offer. which critical amount, depending on the preferences in question, may very well be significantly more than£. This theory predicts that offers and demands in treatments in which the pie size is known, $I and %I, will be identical. as the form of the offer has no effect on its acceptance' ' Ochs and Roth's ( 1989) minimum-absolute threshold hypothesis suggests that the minimum a given responder will accept is a constant dollar amount but need not be panicularly small.
It thus predicts that the acceptance patterns from treatments where the responder can calculate her absolute (money) payoff should be the same-all the responder cares about is getting her absolute minimum threshold; the size of the pie doesn't enter the analysis at all. Thus offers in three treatments $1. $U and %I should be identical.