Using these assumptions as a basis the behaviour of the players can be predicted. It can be predicted that the proposer according to the first assumption will try to offer as small a share of the money as possible to keep his or her own share at an optimal level. The responder will be willing to accept any offer made to them in light of the fact that even a small amount of money is better than receiving no money at all and in accepting they will still start of better than when they started. If these predictions are correct then it implies what is called a ‘perfect subgame equilibrium’ based on the concept of ‘utility’. Both players are likely to be satisfied with the outcome of the game as a result.
Utility theory as described by Baron, 2000 is a measure of how well our actions meet our goals or values. This theory would point out that by making decisions such as these we aim to maximise our achievement of the goals we set. In the instance of ultimatum bargaining the responder has to consider both his own goals and the goals of the proposer as the responders decision will affect both of their achievements and the outcome of the game. Therefore in accepting the proposer’s offer the responder has satisfied his or her own goals and also maximised the gains of the proposer in accordance with utilitarian theory.
However this theory seems rather idealistic and does not cater for a responder who questions the fairness of receiving a lesser share in a game. Although it may be better to receive a smaller, perhaps unequal share of the money rather than no money at all, it may also be worth considering the fact that the power to maximise or completely abolish both players gains lies in the hands of the responder. Initially the power may appear to be owned by the proposer who makes the offer without the option of negotiation yet they cannot control the outcome of the game in its finality. Murnighan and Pillutla (1995) in their studies say the opposite to this and point out that responders have the least power in the game and as a result look to proposers’ to be fair in their offers.
Findings that dissuade the concepts of perfect subgame equilibrium and utility theory in predicting the behaviour of players are found in experimental study conducted by Straub and Murnighan (1995). Games with complete information about the amount of money being divided, that include one, two, three or more periods, with offers alternating between the players, all generate a strong pull toward 50-50 agreements. Only in games where one of the players has an outside option (Binmore et al., 1985, 1989, 1991) does observed behaviour support game theoretic predictions, and such situations are not consistently supportive (Kahn & Murnighan, 1993).
Responders also reject moneymaking offers 20% of the time (Guth et al., 1982). In addition to this proposers typically demand less that 70% of the total funds for themselves (Guth, Schmittberger & Schwarz, 1982). These findings have been replicated in more recent studies (Murnighan and Saxon, 1998).
Reasons for responders to be turning down offers which is against utility theory have as afore mentioned been studied by questioning players as to why they made such a decision (Straub and Murnighan, 1995) and consistently fairness has been cited as their motives. Fairness may be the main reason why responders may turn down very apparent unfair offers of small amounts of money.
Psychologists have looked into whether it is a desire to be socially desirable that influences the offers proposers make rather than simply fairness, alone. They may wish to appear fair to gain creditability in a social sense (Suleiman, 1996). The results of partial information conditions in the ultimatum bargaining showed proposers offered significantly less money than the complete information conditions used by (Pillutla & Murnighan, 1995). These findings suggest players play strategically rather than fairly and seek to maximise their own gains whilst still trying to appear fair depending on the conditions.
In the experiment we carried out we tried to look at all of these studies and basing the experiment on the complete information conditions we tried to replicate work of Guth and Van Damme (1998) to see what seemed more probable in terms of fairness, utility theory, perfect subgame equilibrium and strategic play.
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Method
Participants
329 participants were chosen using opportunity sampling, which meant they were mainly students from University of Warwick, aged 18-20. The participants had to be tested alone as responses to this game could be affected by the presence of other people. The participants were split in to two groups for the two conditions. With 168 in one condition and 161 in the other condition.
Materials
An instruction sheet was drawn up for the participant that explained to them what they were meant to do and also made sure they were aware that they could withdraw from the experiment at any time they wished.
Design
The independent variable was the percentage of £1000 the participant was offered and the independent variable was whether the participants chose to accept the offer or decline the offer. A between subjects design was used as not all 329 participants were given the same offer. The independent variable provided to different conditions with one really high percentage and one really low percentage of money being offered to the participants depending on which group they fell into.
Procedure
329 participants were told that they were taking part in an experiment involving responding to an offer to divide up a fictional amount of money between themselves and the person offering them the choice. They were told they only have to answer one question either by accepting or declining the offer made to them. They were also reminded that they could withdraw from the experiment at any time if they needed to and the experiment didn’t in any way pass on the information or take any personal information in the first place.
161 participants were offered a chance to split £1000, with the proposer keeping 60% and they would get 40% but if they declined completely then neither of them would get anything at all. The other 168 participants were offered a chance to receive only a 5% share of the £1000 and the proposer getting 95%, if they agreed to take the 5% share or nothing at all for either of them if they declined. The participants were reminded that the offer was an ultimate offer and their was no room for negotiation but only the option of considering the offer and choosing to either accept or decline bearing in mind the outcome. They were also instructed to treat the offer seriously even though it was a hypothetical amount and situation.
Results
The chi square table is in the appendix but the results were as follows.
Table 1. Responses to being offered a 5% share of £1000
a GROUP = 5%
In group A that was offered only a 5% share of the £1000, 82% chose to still accept the offer with only 17.3% choosing to reject it as shown in Table 1 above.
Table 2. Responses to being offered a 40% share of £1000
b GROUP = 40%
In group B that was offered a 40% share of the £1000, 97.5% chose to accept the offer with only 2.5% choosing to reject it as shown in Table 2.
Discussion
The results supported the view of the existence of a perfect subgame equilibrium as the majority of the responders in both the unfair, low offer and higher, fairer offer still chose to take the money. The acceptance rate was higher for both, at least over 80% in both conditions. This would support the findings of Guth & Van Damme (1998) that both players are only motivated by self-interest and as a result responders would rather gain some money than none at all. On the surface it may seem that although 82% of people still accepted an offer of only 5% of £1000, responders did not give much thought to the fairness. Yet this also means that close to 20% of responders would reject the offer. In realising this it can be said on the reverse that the results would support the findings of Guth et al (1982) that responders also reject profitable offers and accept zero approximately 20% of the time. This would mean that the perfect subgame equilibrium is a poor predictor for the behaviour of the players (Straub and Murnighan, 1995) and neither of the players behave in accordance to utility theory.
On the other hand it could be argued that the results overall are let down by the fact that sample was an opportunity sample made up of mainly student participants. This would undermine the results as it would have to be taken into account the financial situation of the students. Being students that by tradition are known as constantly being out of pocket they may not care about fairness because the experiment hypothetically gives them the choice between a little amount of money or none at all and to students even a sum of £50 may seem a lot rather than nothing at all. Perhaps the experiment would have been more reliable and more representative if it had a more selective sample of participants. For example the question would perhaps be answered more objectively who due to have a better income and financial position may place more value in fairness than simply getting as much money as they can rather than none. There are issues of self-esteem as well that may be the reason for the respondents of the lower offer condition to reject the offer. All in all the results may depend heavily on the socio-economic status of the participants as these are factors that may influence a person’s judgement for the reasons cited above.
In explaining the high rate of acceptance for the condition offering £400 of the money, this speaks for itself as this is a large amount of money to anyone and does not seem excessively unfair although not a complete 50/50 divide. Further studies would have to try more than simply two conditions and perhaps incorporate the method of partial information and complete information being given to the responders similar to Pillutla and Murnighan (1995). The design of this version of ultimatum bargaining really only concentrates on a partial information condition and perhaps respondents would be heavily influenced if they were to know that there was the possibility of being offered more under different conditions of the ultimatum they are given. In comparison to people being offered £400 responders being paid £50 would obviously feel inferior and see the unfairness. Yet when only being made of the condition they are offered as an isolated offer it may still seem reasonable and better than no monetary gain at all.
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Appendix 1
Chi square test as completed using SPSS.
Chi-Square Tests
a Computed only for a 2x2 table
b 0 cells (.0%) have expected count less than 5. The minimum expected count is 16.15.
References
Guth, W., & Van Damme, E. (1998). Information, strategic behaviour and fairness in ultimatum bargaining: an experimental study. Journal of Mathematical Psychology, 42, pages 227-247
Murnighan, J.,& Saxon, M. (1998) Ultimatum bargaining by children and adults. Journal of Economic Psychology, 19, pages 415-445.
Suleiman, R. (1996). Expectations and fairness in a modified ultimatum game. Journal of Economic Psychology, 17, pages 531-554
Paul G. Straub & J. Keith Murnighan (1995) An experimental investigation of ultimatum games: information, fairness, expectations, and lowest acceptable offers, Journal of Economic Behavior and Organization, 27 pages 345-364
Guth, W., Schmittberger, R., & Schwarz, B. (1982). An experimental analysis of ultimatum bargainings. Journal of Economic Behaviour and Organization, 3 pages 367-388.
Pillutla, M., & Murnighan, J. (1995) Being fair or appearing fair: Strategic behaviour in ultimatum bargaining. Academy of Management Journal, 38 pages 1408-1426
