Instrumento y procedimiento

The standard ultimatum game certainly is the game most intensely studied in economic experiments, besides possibly the prisoner’s dilemma game. Results are regular and robust. Average offers are 30-40% of the pie, modal and median offers are 40-50%, more than half of the offers below 20% are rejected, offers below 10% and offers above 50% are rare, and the overall rejection rate is around 20%, see pages 50-55 in Camerer (2003).

Asymmetry, however, has rarely been investigated in the ultimatum game paradigm. An early study is the paper by Knez and Camerer (1995). They introduce positive and asymmetric outside options for both players. In two different treatments, responders have outside options of 20% and 40% of a $10 pie, whereas proposers always have an outside option of 30%. Knez and Camerer use the strategy method where responders state their minimal acceptable offer (MAO). On average, proposers send 38% (42.5%) of the pie in the low (high) outside option condition whereas responders demand 42.7% (49.6%) on average. The paper reports surprisingly high rejection rates of around 45-48% compared to a much lower percentage in other studies. Knez and Camerer attribute thisfinding to the ambiguity in fairness perceptions. Players might “... self-servingly disagree about what constitutes a fair offer” (p. 66).

Buchan, Croson, and Johnson (2004) study an asymmetric ultimatum game experiment run in the USA and Japan. The outside option of the proposer is either 20% of a 1000 token pie (worth $10 in the US andU2000 in Japan) in the high power condition or zero in the low power condition. The responder’s outside option is always zero. After 10 rounds of ultima-

tum bargaining with different anonymous partners, subjects completed a post-experimental questionnaire asking for their belief on the fair offer/demand. Proposers in both cultures offer significantly less in the high power condition. In the US, offers, averaged over the 10 rounds, decrease from around 45% to 40% in the high power condition. In Japan, the offers decrease from 51% to 46%. American responders demand less in the high power condition (average MAO of 33%) than in the control condition (average MAO of 38%). Contrary, Japanese responders demand significantly more in the high power condition (average MAO of 44%) than in the control condition (average MAO of 39%). Except for Japanese proposers, actual offers/demands are significantly correlated with subjects’ beliefs on “fair” offers/demands. Buchan, Croson, and Johnson do not report rejection rates, we thus compute these for each of their treatments.20 For behaviour in the first round, we find that the rejection rates are relatively high in both conditions, around 40% in the no power condition and 40-55% in the high power condition. For the US, the rejection rate in the high power condition is signif- icantly larger than in the no power condition, whereas there is no significant difference in Japan.21

The study by Schmitt (2004) investigates an ultimatum game with varying asymmetric chip valuations, asymmetric outside options and informational settings. Agents bargain over a 100 token pie where the conversion rate is either $0.10 or $0.30 per token, the outside option is either $2 or nothing and agents are either entirely informed about the conversion rate and outside option of their opponent or they only know that her/his conversion rate and outside option differ from their own. Schmitt finds that offers are higher when responders rather than proposers are endowed with the positive outside option. In thefirst round, the average offer is 53 (26.4) chips in the treatment with the high (low) conversion rate for the proposer and the high outside option for the responder, whereas the average offer is 26.4 (17.4) chips in the treatment with high (low) conversion rate for the proposer and positive outside option for the proposer. Similarly to Knez and Camerer (1995), rejection rates are very high. In the first round, they are 50% in the treatments where proposer have the positive outside option and around 30-40% in the treatments with positive outside options for the responders.22

Falk, Fehr, and Fischbacher (2001) present an experiment on a reduced ultimatum game with an outside option for the respondent. There, the proposer can choose between a split which gives herself 8 and the responder 12 and a split where she gets 5 and the responder gets 15. Whenever the responder rejects the offer, the proposer goes home with nothing and the responder gets an outside option of 10. The authors observe that 24% of the responders 2 0_{We use the original data set, sent to us by Buchan, Croson, and Johnson. To calculate the rejection}

rates, we match each proposer offer with each responder demand in each round. Wefind that rejection rates decrease over the 10 rounds.

2 1

Note that Buchan, Croson, and Johnson frame the ultimatum bargaining in a buyer-seller context giving richer context to the game than most other studies summarised here.

2 2_{Unlike the other studies cited, Schmitt does not use the strategy method. In her experiment, responders}

reject the 8/12 offer while only 4% reject the 5/15 offer with the difference being significant at the 1%-level. They take this result as a case for the presence of spitefulness which they define as the willingness to sanction in order to increase the payoff difference between two agents.

All ultimatum game experiments, cited above, introduce outside options. However, each of them studies the behaviour in two particular outside option settings only. Moreover, the characteristics of these settings are similar. The (positive) outside options of both players are relatively small, ranging from approximately 7% to 40% of the pie, only in the study by Falk, Fehr, and Fischbacher (2001) does the responder have an outside option of 50% of the pie. Accordingly, the difference in outside options is small, spreading from 7% to 20% of the pie, with the exception of 50% in the Falk, Fehr, and Fischbacher paper. In contrast, the present study varies outside options systematically from no outside option to an outside option of 72% of the pie. The minimum difference in outside options is no difference at all and the maximum is 72% of the pie.

Finally, we report on a study by Güth, Huck, and Müller (2001). They conduct three reduced ultimatum games where the proposers chose between a “fair” and an “unfair” offer. The unfair offer attributes 85% of the pie to the proposer. The three games vary with respect to the fair allocation. In thefirst version, the alternative to the unfair offer is to split the pie exactly equally. In the second version, the alternative is slightly tipped to the favour of the responder, he gets 55%, whereas in the third version the proposer gets the more favourable share of 55%. Güth, Huck, and Müller find that proposers are less likely to make a fair offer if the equal split is replaced by a nearly equal split. Responders reject unfair offers less frequently if the nearly equal split is tipped to the side of the proposer.