Elicitation effects in a multi-stage bargaining experiment

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Experimental EconomicsA Journal of the Economic ScienceAssociation ISSN 1386-4157Volume 17Number 2 Exp Econ (2014) 17:335-345DOI 10.1007/s10683-013-9370-z

Elicitation effects in a multi-stagebargaining experiment

Swee-Hoon Chuah, Robert Hoffmann &Jeremy Larner

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Exp Econ (2014) 17:335–345DOI 10.1007/s10683-013-9370-z

O R I G I NA L PA P E R

Elicitation effects in a multi-stage bargainingexperiment

Swee-Hoon Chuah · Robert Hoffmann ·Jeremy Larner

Received: 20 August 2012 / Accepted: 11 July 2013 / Published online: 7 August 2013© Economic Science Association 2013

Abstract We examine elicitation effects in a multi-stage bargaining experiment withescalating stakes conducted under direct-response and strategy-method elicitation.We find a significantly greater incidence of decisions leading to bargaining failureunder direct responses. In addition, the predictive power of alternative risk attitudemeasures differs between the elicitation methods. Potential sources of the effects andresulting implications are discussed.

Keywords Elicitation effects · Bargaining · Emotion · Escalation

JEL Classification B49 · C72 · C90 · C91

1 Introduction

Bargaining situations, where parties make decisions in order to divide a surplus,have a central place in economics. Theoretical research has generated a myriad ofmodels including multi-stage versions of the chicken game (Bornstein et al. 2004),diminishing-pie approaches (Rubinstein 1982), the dollar auction (Shubik 1971) andthe war of attrition (Maynard Smith 1974). Studies using these models as experimen-tal platforms are important in identifying how different parameters of the situationand subject characteristics influence the likelihood of bargaining success or failure inpractice (see Roth 1995; Camerer 2003, Chap. 4).

An issue with experimental work generally concerns two alternative ways of elicit-ing subject decisions (e.g. Roth 1995; Brandts and Charness 2000). In direct-response

S.-H. Chuah · R. Hoffmann (B) · J. LarnerNottingham University Business School, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB,UKe-mail: [email protected]

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mailto:[email protected]

336 S.-H. Chuah et al.

or ‘hot’ elicitation, subjects make decisions in real time, i.e. responding when re-quired to any actual decisions of co-subjects similar to decision making in real con-texts. In strategy-method or ‘cold’ elicitation, subjects specify an overall strategy exante, i.e. record specific responses at every possible decision node which are subse-quently used as needed to determine actual outcomes. The advantage of the strategymethod is that it generates more data but it is unclear whether there may be elic-itation effects, i.e. differences in subject responses compared with direct-responseelicitation. They could take two forms (e.g. Brandts and Charness 2011, p. 392): first,measured subject behaviour under otherwise the same experimental conditions coulddiffer depending on elicitation method. Second, an inference about a particular treat-ment effect or predictive variable (such as demographics) in an experiment may besensitive to elicitation method. We call these two types first and second-order elicita-tion effects respectively. They constitute an important issue relating to the validity ofexperimental data, which warrants further examination (Brandts and Charness 2011,p. 387).

The present study is motivated by the thought that bargaining experiments, es-pecially those involving multiple stages, may be particularly prone to elicitation ef-fects. Because instrumental rationality yields the same decisions however elicited,elicitation effects may be rooted in specific aspects of human cognition outside ra-tional choice. Multi-stage bargaining may be associated with departures from ratio-nal decision making for several reasons. First, a number of experimental economistshave argued that compared with strategy-method choice, direct-response decisionsare more strongly associated with affect or emotional responses (Roth 1995, p. 323;Brandts and Charness 2000). Distributive decision making processes such as nego-tiations and bargaining are particularly associated with risk (de Heus et al. 2010),emotion (Barry et al. 2004) and cognitive biases (Thompson et al. 2004). These ef-fects are particularly pronounced in escalating bargaining processes (see Pruitt andKim 2003, pp. 88–89), i.e. where players incrementally and irreversibly raise the riskto get others to accede. Second, in contrast to direct responses, the strategy methodinvolves deliberation of all possible decision nodes rather than those actually reached.The higher resulting cognitive demands may entail greater potential for subject error(quantal responses, e.g. McKelvey and Palfrey 1998).1 As a result the question ariseswhether experimentalists are on safe ground availing themselves of the advantages ofcold elicitation or whether the method is blind to the effects of important psycholog-ical factors which should be examined as an integral part of bargaining processes.

Our paper is intended as a step towards a better understanding of elicitation ef-fects in bargaining experiments. We report an experiment with a multi-stage esca-lating bargaining game conducted under hot and cold conditions to test whether anytype of elicitation effect exists. Section 2 outlines the task, experimental design andimplementation. Section 3 contains the results. Section 4 discusses our findings.

1Thanks to an anonymous referee for pointing out this possibility.


Elicitation effects in a multi-stage bargaining experiment 337

Fig. 1 The escalation bargaining game in extensive form with the payoffs used in the experiment. Playersare denoted by Roman numerals

2 The experiment

We used a four-stage bargaining task (see Fig. 1) which entails the potential for bothdecision making over stages and escalating stakes. Two players make simultaneousdecisions between actions A and B in dividing 100 payoff points over four stages.Mutual A-decisions in any given stage results in a 50–50 split. If one player adoptsA unilaterally, the game ends in increasingly unequal division (over the four stages)in favour of the player choosing B. Mutual B-decisions carry the game into the nextstage. If neither plays A in any stage, the game ends in zero payoffs for both. Thegame has five pure strategies based on the stage (1–4) at which a player chooses A(i.e. A1, A2, A3, A4) if at all (Always B).2 There are two pure strategy equilibriawhere one player chooses A1 and the other Always B. In addition, the game has amixed-strategy equilibrium.

The task was administered between subjects under either direct response or strat-egy method elicitation as follows. In the hot escalation game, subjects were pairedwith a co-participant (and told so) before making mutual decisions which wererecorded simultaneously during a set period of one minute per decision displayedon the screen. Decisions were recorded for up to four stages or until an A-decisionwas made by either player which would end the game. Subjects in the cold escalationcondition entered decisions as A or B for every possible stage of the game (1 to 4) andwere told that if an A-decision was recorded for a stage, all decisions recorded forlater stages would be void. Each subject was then matched with a randomly-chosenco-participant and their recorded decisions used to determine the outcome.

After completion of the game task, subjects were asked to fill in a questionnairecontaining demographic questions. We also measured subjects’ risk attitudes usingthe binary choice lottery procedure by Holt and Laury (2002, hereafter HL) with theoriginal payoffs multiplied by twenty. In the task, subjects face ten binary choices be-tween safe and increasingly risky gambles. The task was designed as a measurementof individuals’ risk preferences, parameterised as the number of safe gambles chosenout of the ten. In addition we elicited subjects’ “willingness to take risks, in general”on an eleven-point scale following Dohmen et al. (2011, hereafter DO).

2Additional pure strategies exist if we also consider those which specify actions for nodes which cannever be reached by virtue of previous decisions. We do not consider these in the following as they arebehaviourally equivalent (i.e. generate identical payoffs) to the ones we are considering.



While our procedure for eliciting risk preferences after the task follows previousbargaining experiments such as Chuah et al. (2007) and Brandstätter and Königstein(2001), it raises the possibility of subjects’ experienced game outcomes influencingquestionnaire responses, especially in the hot condition. We performed a series oftests to examine whether subjects’ responses to either risk instrument differ depend-ing on game experience. First, no significant differences exist in measured risk prefer-ences between the hot and the cold condition. Second, we compared risk preferencesof subjects within the hot and the cold conditions respectively in every stage of thegame.3 We found no evidence of bias: none of the resulting tests yielded significantdifferences.

All sessions took place under standard experimental conditions in a computer lab-oratory of a private, English-spoken university in the People’s Republic of China withundergraduate student volunteers recruited via email and poster invitations. In eachsession, subjects were first briefed in Chinese about experimental discipline, subjectanonymity as well as cash incentives and their delivery. The games were then con-ducted on a computerised interface via z-Tree (Fischbacher 2007), with completeEnglish on-screen instructions. We used the specific payoffs shown in Fig. 1. Hard-copies of instructions in both English and Chinese were also provided. The programincluded a comprehension quiz as well as an unincentivised test run of the gameagainst a computer that played randomly. During experimental play, co-participantswere randomly matched at the session level and remained anonymous to each otherthroughout. A Chinese language pen-and-paper questionnaire with risk attitude anddemographic questions followed the task. Each session lasted about an hour, afterwhich subjects received a participation fee of 10 Chinese Renminbi (RMB) as wellas the pay-out in cash for one of the tasks chosen at random, on average about 38RMB.4

3 Results

Summary data for game behaviour in both the hot and the cold condition are shown inTable 1 and Fig. 2. The cold condition yielded the distribution of the 100 subjects overthe five pure strategies as displayed in the left panel of the table. Figure 2 displays thisalong with the distributions associated with mixed Nash equilibrium. The table andgraph suggest that hot players are more likely to choose ‘extreme’ strategies A1 andAlways B associated with the pure strategy equilibrium of the game. Cold subjectsare more evenly distributed and are closer to the 20 % mark representing random

3Measured risk attitudes may differ between subjects either due to underlying preferences which the in-struments are meant to measure or due to bias from the individually experienced game outcome. To dis-entangle the two we need to control for stage as risk appetite may influence progression in the game. Wecompared stated risk preferences of subjects who were observed to take the same decision in a given stagebut experienced a different action by their co-player. This test was repeated for every stage, for both riskmeasures and both elicitation methods.4Each payoff point received was paid out at 1 RMB. At the time of the experiment, 1 RMB traded at 0.146US $. In the area of China where the experiment was performed, students typically earn around 8 RMB anhour for casual work.



Table 1 Summary subject behaviour by elicitation condition. The p-values are for Fisher exact tests fordifferences compared with the cold condition on a stage-by-stage basis. Significance at the 90 and 95 %-levels given by * and **

Strategy Cold Hot (imputed) Hot (observed)

n n p Stage n A B p

A1 25 39 0.298 1 122 39 83 0.298

A2 14 17 0.842 2 58 12 46 0.827

A3 19 9 0.020 ** 3 38 5 33 0.054 *

A4 19 12 0.015 ** 4 28 6 22 0.047 **

Always B 23 45

Fig. 2 Percentage distributionsof subjects over the five purestrategies for the cold condition,according to mixed-strategyequilibrium (MSE) and the hotcondition by imputation

play. For the hot condition the right panel of Table 1 shows the number of subjectswho were observed opting for A and B respectively in each stage. In every stageon average about three quarters of subjects chose B such that a quarter are observedplaying B in every stage.

This latter number however understates the true number of Always B playing sub-jects in the hot condition. While all hot subjects who choose A in any stage exit thegame there, those subjects who choose B but are matched with someone playing Aalso exit in that stage. We call these latter subjects ‘unobserved’. For example, while83 subjects chose B in stage one under hot elicitation, 25 of them do not proceedto stage two. We cannot observe their behaviour at subsequent decision nodes to af-ford a straightforward comparison with behaviour from cold elicitation. It is theseunobserved data the strategy method is designed to elicit. We therefore imputed purestrategies for unobserved hot subjects. The following approach was adopted. In stage3, five subjects chose B but exited due to being matched with a co-player who choseA in that stage. These five subjects followed either the A4 or Always B strategy. Inorder to attribute one of the two strategies to each of them, we used the observedproportion of A4 to Always B in stage 4, which was 6/22. Applying this to the five



subjects, we impute that 3.93 are Always B and 1.07 are A4-subjects. We repeatthis process recursively to attribute strategies to all unobserved subjects from stage 4back to stage 1. The resulting imputed distribution of hot players over pure strategiesis given in the middle panel of Table 1 as well as in the black bars in Fig. 2. We nowexamine statistical differences in behaviour between the conditions.

3.1 First-order effects

First-order elicitation effects exist when measured subject behaviour differs signifi-cantly depending on elicitation method under otherwise the same experimental con-ditions. Overall, more than three times as many hot (13.1 %) as cold (4.0 %) gamesin our experiment resulted in bargaining failure: subjects in the hot condition are sig-nificantly more likely to experience it (p = 0.019).5 Bargaining failure depends onthe proportion of players choosing Always B, which is significantly greater in the hotcondition (using imputed data, p = 0.028). Correspondingly, there is a (marginally)significant difference in subjects’ experimental payoffs between the two conditions(2-tail t-test p = 0.072). The distribution of subjects over the game’s five pure strate-gies is significantly different between cold and observed hot (p = 0.002) as well asimputed hot (p = 0.009).

These differences in overall behaviour are supported by tests comparing behaviourbetween individual stages of the hot and the cold game. We examined whether, ineach of the four stages, the proportion of subjects opting for A and B respectivelydiffers between hot and cold elicitation. In stage one of the hot game, 39 of 122subjects (32.0 %) chose A, compared with 25 of 100 cold subjects who chose the A1-strategy. No difference exists between these two proportions (p = 0.298). In stagetwo of the hot game, 12 of 58 (20.7 %) of subjects chose A. We may compare thisproportion with the proportion of A2-subjects of all subjects whose strategies specifyB in stage one (non-A1) which is 14/75 (18.7 %). These proportions are not staticallydifferent (p = 0.827). Similarly, in stage three of the hot game, 5 of 38 hot subjectschose A (13.2 %). The proportion of A3-subjects of all non-A1 and A2 subjects inthe cold condition is 19/61, i.e. 31.1 % which is marginally greater (p = 0.054).Finally, in stage four, 6 of 28 (21.4 %) subjects chose A. In the cold condition, theproportion of A4 over A4 plus Always B-players is 19/42 (45.2 %), significantlygreater (p = 0.047). This is despite the falling number of observations (and lesserpower of our test) as we move from stage to stage subject to the exit of participantsplaying A. This latter result is important in that bargaining failure can only occurthrough both players choosing action B in the last stage of the game (i.e [0,0]), theonly Pareto inefficient outcome.

The existence of unobserved subjects in the hot condition means that the data un-derlying these tests are biased against subjects choosing B in a given stage. We there-fore repeated the stage-by-stage tests for difference compared with the cold conditionusing the imputed data for hot subjects which, in terms of significance, produce thesame results.

5We report Fisher exact 2-tail p-values in this section unless stated otherwise. The results are robust with

respect to using χ2-tests.



3.2 Second-order effects

We also tested for second-order elicitation effects, i.e. when an inference about therelationship between subject behaviour and an explanatory variable is sensitive toelicitation method. Explanatory variables may be experimental treatments or indi-vidual subject characteristics such as demographics, values or personality traits. Inthe current context of escalation bargaining we focus on risk attitudes. They arerelevant since subsequent stages of the escalation game are associated with risingrisk in an increasing variance in potential payoffs (cf. Engelmann and Steiner 2007;de Heus et al. 2010). Similar to Dohmen et al. (2011) but in contrast to Lönnqvistet al. (2011), the HL and DO measures we obtained were significantly correlated(Pearson r = 0.24, p < 0.001).

To examine how risk preferences predict game behaviour we performed a seriesof regressions6 on subjects’ chosen strategies (coded as 1 to 5) as the dependentvariable. We examined behaviour in the hot and cold conditions separately. Whenestimating chosen strategies in the cold condition using both HL and DO as predic-tors the former (p = 0.032) but not the latter (p = 0.508) is significant. Conversely,hot strategies are predicted by DO (p = 0.001) but not by HL (p = 0.884) responseswhen both are entered as independent variables. These results suggest that how wellthe respective risk measures predict behaviour depends on how it was elicited. This isfurther supported by regressions on behaviour pooled over hot and cold (Table 2). Inthe first model the two risk measures are individually insignificant. We then followedthe general-to-specific method (e.g. Campos et al. 2005) and iteratively removed in-significant explanators which produced the final model II. The interaction terms ofDO with hot as well as HL with cold are both significant. We estimated a numberof further models for additional support (not reported). The risk measures DO andHL were insignificant as individual independent variables in all these estimations. Inaddition, interaction terms of HL with hot as well as DO with cold respectively wereinsignificant throughout. Together these results further suggest that hot behaviour ispredicted by DO responses, while cold decisions are predicted by HL. We interpretthis as evidence for a second-order elicitation effect.

4 Discussion

In our experiment, multi-stage bargaining behaviour differs significantly dependingon elicitation method. First, B-decisions in the final stage are more likely to be ob-served through the hot than the cold method. Second, elicitation method significantlyaffects the extent to which different measures of risk attitude predict behaviour. Weconclude by discussing these two types of effect we found.

Why do subjects play B more often in the last stage of the hot than the cold game?One interpretation is more belligerent bargaining due to emotional effects in esca-lating bargaining processes (e.g. Pruitt and Kim 2003). Affect may harm bargaining

6We used the ordered Probit estimation method for all regressions reported in this section. All the resultsare robust with respect to using Tobit.



Table 2 Ordered Probit regression results for pure strategies used

Parameter Model I Model II

Coef. SE p Coef. SE p

HL 0.003 0.058 0.964

DO −0.048 0.068 0.479

Hot −1.271 0.575 0.027 −1.019 0.4423 0.021

Cold×HL 0.132 0.085 0.120 0.130 0.0615 0.035

Hot×DO 0.253 0.091 0.006 0.205 0.0579 0.000

N 177 177

p > χ2 0.001 0.000

Log likelihood −263.915 −264.167

Pseudo R2 0.039 0.038

outcomes through negative emotions (Barry et al. 2004) such as anger (Allred et al.1997) or spite (Glasl 1982). While our findings are consistent with this kind of effect,Brandts and Charness’s (2011) survey found no support for subject emotion or thenumber of stages in the task as sources of elicitation effects.7 Future work designedto measure affect in subjects physiologically could shed more light on this issue.

An alternative explanation of the result lies in quantal responses. It may be thatthe lesser incidence of B-decisions in the cold method is associated with subject er-ror. Figure 2 shows that compared to direct response, the frequencies of the five purestrategies for strategy method elicitation are generally closer to the 20 % mark associ-ated with random play. The reason may be that the greater cognitive demands associ-ated with deliberating conditional strategies ex ante generate greater error comparedwith the hot condition.8

Our second finding is that the predictive power of two risk measures differs be-tween methods used to elicit game behaviour. A potential explanation lies in dual-process models of human cognition generally and risk analysis in particular (e.g.Slovic et al. 2004; van Gelder et al. 2009). The experiential system assesses ‘riskas feeling’ rapidly, automatically using affect and concrete experience and is gearedtowards immediate response. The analytic system evaluates ‘risk as analysis’ con-sciously, deliberately and abstractly through logic and symbolic reasoning for de-layed responses. The systems may operate individually or together depending on thetask (Sloman 1996, p. 6).9 Both the HL measure and the cold escalation bargaining

7In their meta-analysis of elicitation effects, experiments are classified as (a) either involving or not in-volving emotion or multiple stages and (b) showing either evidence, mixed or no evidence for elicitationeffects. Two-tail χ2-tests are then performed to examine whether the two groups in terms of (a) havedifferent distributions over (b).8Comparing hot and cold behaviour in terms of quantal responses is hampered by the fact that the formerinvolves error at the level of each stage, and the latter at the level of the five reduced strategies (McKelveyand Palfrey 1998, p. 10).9“When a response is produced solely by the [experiential] system, a person is conscious only of the resultof the computation, not the process [. . .] The result is accessible, but the process is not. In contrast, aperson is aware of both the result and the process in a rule-based computation” (Sloman 1996, p. 6).



game involve relatively complicated hypothetical decisions likely to draw on analyt-ical reasoning. Conversely, both DO and the hot game entail thinking about specific,concrete and immediate situations with associated affect suited for experiential cog-nition. In other studies, DO was found to be easier to understand for subjects andbetter at predicting their self-reported behaviour in different specific risky situations(Dohmen et al. 2011) and experimental game decisions compared to HL (Lönnqvistet al. 2011).10 The implication of this explanation for our second finding is that thetwo elicitation methods may draw differentially on the respective dual processes in-volved in subject reasoning. The choice of elicitation method would then matter fordomains skewed either towards one or the other form of reasoning. However, in ourcurrent study this explanation is ex post: more work would be required to examinedual processing specifically and systematically as a potential source for elicitationeffects.

Our results should also be seen in the context of our Chinese subject pool.While there are no a priori reasons that our results are specific to Chinese sub-jects, differences in their behaviour to subjects from other cultures have been foundin contexts including cooperation (Cooper et al. 1999; Fan 2000; Hemesath 1994;Herrmann et al. 2008), trust (Buchan et al. 2002, 2006; Bohnet et al. 2008) as wellas market behaviour (Kachelmeier and Shehata 1992). Two studies examine bar-gaining of Chinese subjects using the ultimatum game (Hoffmann and Tee 2006;Chuah et al. 2009). Chuah et al. (2009) detected differences in offer levels betweenMalaysian Chinese and UK subjects which are explained with respect to culture.However, no other evidence for Chinese subjects in multi-stage bargaining gamesexists to provide a context for our findings here.

While overall our results are suggestive of elicitation effects in the game we study,further work is required to examine its source and generality in terms of other kindsof bargaining task or multi-stage game.

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Elicitation effects in a multi-stage bargaining experiment