1 Introduction

One aim of this study is to learn more about external validity of laboratory experiments with student participants. Since students are similar in age and education such laboratory experiments leave open the question how far results from the lab can be generalised.

To increase the variance of socio-demographic characteristics in the subject pool Roth et al. (Reference Roth, Prasnikar, Okuno-Fujiwara and Zamir1991) study the ultimatum game with students from different nationalities and find clear differences in behaviour between these groups. Murnighan and Saxon (Reference Murnighan and Saxon1998) look at the behaviour of children and observe that generosity in the ultimatum game decreases with age. In a similar study with children Harbaugh et al. (Reference Harbaugh, Krause and Liday2003) find that, once one controls for size, generosity increases with age. In a newspaper experiment with the ultimatum game (Güth et al. Reference Güth, Schmidt and Sutter2003) the medium of participation, Internet or postal mail, has an effect on generosity. Güth et al. (Reference Güth, Schmidt and Sutter2007) look at a three-person ultimatum game and show that fairness and rejection rates increase with age. Köhler et al. (Reference Köhler, Kuklys, Struck and Fischer2007) play an ultimatum game with a heterogeneous sample of German adults illustrating that generosity increases with age and income. Integrating their experiment into an existing survey, the Dutch CentER panel, Bellemare et al. (Reference Bellemare, Kröger and van Soest2008) let their participants play either the ultimatum or the dictator game and confirm that generosity increases with age.

Using the trust game, Fehr and List (Reference Fehr and List2004) compare the behaviour of students with that of CEOs who turn out to be more trusting, more trustworthy, and who punish less. Fehr et al. (Reference Fehr, Fischbacher, von Rosenbladt, Schupp and Wagner2003) report data from a trust game with a randomly selected sample of German households. Bellemare and Kröger (Reference Bellemare and Kröger2007) compare behaviour in the trust game played by students and households of the CentER panel to find a hump-shaped relation between age and trust, and a U-shaped relation between age and trustworthiness. Bornhorst et al. (Reference Bornhorst, Ichino, Kirchkamp, Schlag and Winter2010) play a trust game with Ph.D. students of different nationalities and find significant differences in trust and trustworthiness between different regions of origin. Sutter and Kocher (Reference Sutter and Kocher2007) study a trust game with participants from different age groups and observe a hump-shaped relation between age and trust and increasing trustworthiness with age.Footnote ¹

To explain why non-students outside the lab and students within the lab behave differently, Pull (Reference Pull1999) and Selten (Reference Selten2000) argue that student participants in a lab environment react more clearly to subtle strategic details than non-students outside the lab. It is, hence, essential to compare behaviour of student participants with a more heterogeneous population in other games, especially those related to the previously explored ones by differing only in subtle details. This is what we want to do in this paper.Footnote ² We will use a very simple and abstract game and concentrate on analysing the effect of stakes and the effects of the subject pool on the offers and on the willingness to accept.

Our workhorse is the Yes-No game which is a game where proposers suggest how to share a given positive monetary amount and responders decide without knowing the proposal. From ultimatum games (see Camerer Reference Camerer2003, for a survey of ultimatum experiments), Yes-No games differ since responders in ultimatum games know what they accept or reject.Footnote ³ Unlike to dictator experiments (e.g. Forsythe et al. Reference Forsythe, Horowitz, Savin and Sefton1994), the responder in Yes-No games still has full veto power in the sense that without his consent the pie of 100€ or 1000€ is lost.

We find the Yes-No game an interesting game for several reasons:

• • Many offers or opportunities in real life contain a certain as well as an uncertain component. E.g. a work contract might specify an explicit salary but might be silent about working hours, pensions, obligations of the worker and much more. Other examples include so-called experience goods whose quality is not known to customers or partnership proposals without knowing how reliable the partner(s) will be, as e.g. in joint ventures or spouse relationships. The ultimatum game studies as one extreme the (artificial) situation of an offer with no uncertainty at all. Everything that can be said about the offer is known to the responder. The Yes-No game looks at the other extreme: A situation where the offer is entirely unknown to the responder.

• • The Yes-No game also sheds new light on motives of behaviour in situations like the ultimatum game. Do proposers make generous offers in the ultimatum game because they fear rejection of a lower offer? Since the offer is unknown to the responder low offers are not more likely to be rejected than high offers. Proposers who make high offers must have other reasons.

  Even more interestingly, responders who reject unfair offers in the ultimatum game should when they expect to receive unfair offers in the Yes-No game reject these offers, too.

  We already know from ultimatum games with private information (Güth et al. Reference Güth, Huck and Ockenfels1996), where only the proposer knows whether the pie is large or small, that most proposers who could divide the large pie offered only a fair share of the small pie which was never rejected by the responder.

  Such response behaviour can be explained either by “in dubio pro reo” (the pie could be small) or by “in dubio pro meo” (better little than nothing). In the Yes-No game accepting an unknown offer can be similarly justified (Gehrig et al. Reference Gehrig, Güth, Levati, Levínský, Ockenfels, Uske and Weiland2007). But since in the Yes-No game the proposer can be more exploitative by offering only the smallest positive amount the responder may expect less what could weaken the “in dubio pro meo” argument. Will we therefore observe more rejections (No) by responders who expect a low offer? Will these rejections be more frequent if the pie is small (100€) and punishment is cheap?

• • Another reason for using the Yes-No game is, of course, that it only differs from the ultimatum game by one subtle detail, namely that one does not know the proposal when exercising one’s veto power. Is this a detail overlooked more frequently by non-students than by student participants? Furthermore, is it possible that not only students but also executives are paying more attention to subtleties like these. Do we have reasons to single out important and economically relevant subgroups of non-students?

In this paper we want to describe properties of a heterogeneous population playing the Yes-No game. Will participants with a socio-demographic background different from students as responders also rely to the same degree on “in dubio pro reo” or “in dubio pro meo”? And will they as proposers yield to the exploitation incentive or will they feel more committed to fairness concerns, at least when the pie is small (and exploitation less profitable)?

In Sect. 2, we introduce the design of the experiment and discuss some hypotheses which, in Sect. 3, are tested with the help of the rather large data set (involving altogether 1175 participants). Section 4 concludes.

2 Experiment

In this paper we will compare five different media to participate in the experiment:

• • 112 participants of a traditional lab experiment run by Gehrig et al. (Reference Gehrig, Güth, Levati, Levínský, Ockenfels, Uske and Weiland2007) with low stakes,Footnote ⁴

• • 64 participants of a lab experiment with high stakes where only some participants are paid,

• • 303 participants of a newspaper experiment with high stakes where only some participants are paid and who chose to respond by postal mail,

• • 568 participants of the same newspaper experiment with high stakes who chose to make their decision via the Internet,

• • 128 business executives who play essentially the same situation with high stakes and who respond with pencil and paper.Footnote ⁵

Table 1 shows characteristics of participants for the different media of participation.Footnote ⁶ Figure 1 shows boxplots of the distribution of age for the media of participation where we know the age.

Fig. 1 Boxplot of age for different media of participation with high stakes

Table 1 Characteristics of participants

Experiment	Num. of participants	Known sex [%]	Females [%]	Known age [%]	Mean age [years]	Median age [years]	Known profession [%]	Blue collar [%]
Internet	568	91.0	48.9	82.2	39.0	40.0	61.4	13.5
Mail	303	99.3	57.5	96.0	49.8	50.0	65.0	27.4
Lab high stakes	64	100.0	56.2	100.0	23.0	21.0	100.0	0.0
Executives	128	0.0		0.0			100.0	0.0
Lab small stakes	112	0.0		0.0			0.0
All	1175	75.1	52.4	70.0	41.6	42.0	62.8	13.7

For the media of participation with high stakes we used the strategy vector method, i.e. all participants submitted strategies and expectations for a pie of 100€ and for a pie of 1000€ and for both positions in the game (X and Y).Footnote ⁷ After all participants had submitted their decisions a small number of participants were selected to be rewarded by actually playing the game. First, these participants were randomly grouped into pairs of two players. One of these two players was the proposer in the Yes-No game (X-player), the other the responder (Y-player). Another random draw decided which pairs had to divide 100€ and which had to divide 1000€. For each pair the X-player chose a division. To simplify the use of the strategy vector method as well as the evaluation of the questionnaires we only allowed 10 possible divisions between 5€ and 95€ when 100€ could be divided. Similarly, 10 divisions between 50€ and 950€ were allowed when 1000€ could be divided. When the Y-player chose “yes” the amount was divided according to the proposal of the X-player. In case of “no” both players received zero. Details of the implementation are explained in the online-appendix B.

A materially opportunistic responder should accept the unknown but necessarily positive offer. Anticipating such opportunism, an equally opportunistic proposer should offer the lowest possible amount. We, however, do expect only few participants to behave in line with such common opportunism.

Whether “stakes” matter is often explored by using the same stakes in rich and poor countries, i.e., stake variation relies on large discrepancies of living conditions (see, e.g. Cameron Reference Cameron1999). We avoid confounding “stake” and culture in our within-subjects design: the same participants decide for a small (100€) and a much larger (1000€) pie. In view of the stake independence observed for offers in the closely related ultimatum game (Hoffman et al. Reference Hoffman, McCabe and Smith1996) we expect the relative shares, offered by proposers for both pie sizes, to be similar. Hoffman et al. (Reference Hoffman, McCabe and Smith1996) also observe that rejection rates in ultimatum games are lower when stakes are higher. A reason might be that “teaching fairness to proposers” might be too expensive when stakes are high. We hence expect lower rejection rates for high stakes.

We also suspect that student participants in the laboratory might be more clearly aware of the crucial aspect of the Yes-No game and that their behaviour is closer to the equilibrium solution of the game. As in Eckel and Grossman (Reference Eckel and Grossman1998, Reference Eckel and Grossman2001) we expect women to be more generous than men. In line with Harbaugh et al. (Reference Harbaugh, Krause and Liday2003), Güth et al. (Reference Güth, Schmidt and Sutter2007), Köhler et al. (Reference Köhler, Kuklys, Struck and Fischer2007) and Bellemare et al. (Reference Bellemare, Kröger and van Soest2008) we expect that older participants offer more as proposers and reject less as responders. In line with Güth et al. (Reference Güth, Schmidt and Sutter2003) we expect “more fairness in the mail than in the Internet”.