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The effect of psychological factors on decision making in ultimatum bargaining games was studied in 329 first year psychology undergraduates at University of Warwick using an opportunity sampling to choose participants. The ultimatum bargaining game was a replication of the studies conducted by Guth and Van Damme (1998). Each participant was made a hypothetical offer of the opportunity to gain a 5% share of �1000 if they split it with the proposer. However if they chose to reject the offer then neither them nor the proposer would get anything at all. The offer was an ultimatum and thus did not allow any negotiation at all. The second condition was the same but offered participants a 40% share of �1000. There was a higher rate of acceptance in the group offered �400 (97.5% accepted) than in the group offered only �50 (82% accepted). This suggests that overall responders would rather gain some money rather than none at all yet there is a high enough rejection rate to the lower offer to imply that the concept of perfect subgame equilibrium is a poor predictor of player behaviour. This would support the claims of Straub and Murnighan, 1995.

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Introduction

Ultimatum bargaining is a game that involves two players locked in a competitive and sometimes also strategic, situation with the role of one person as the proposer and the other as the responder. The purpose of the exercise is to share a fixed amount of money between them depending on the rules set. Guth and Van Damme, 1998 carried out a game method, which meant that the proposer offers the responder a share of a sum of money and gives them the option to either agree to take the offer or refuse it. However they are not allowed to negotiate the offer made to them and if they choose to refuse the offer then neither the responder nor the proposer will get the money at all. This game has been the basis for a lot of experimental study and research examining the psychological factors that affect those playing the game and what power the roles of proposer and responder carry.

Although on the surface this may seem like a simple game it does have great social meanings and an insight into the workings of an everyday skill, negotiation (Murnighan & Saxon 1998). In their study they stated that ultimatums become a possible (and sometimes probable) end game strategy from a very young age for children and these are skills that may have differing characteristics depending on the age range of players of such a game.

In studying ultimatum bargaining predictions are based on two main assumptions. Suleiman, 1996 assumes that the players play with the aim to make a decision that is most beneficial to themselves and thus rational. Also the bargainers are said to only be interested in their own profits and making as much money as they can without any consideration of the monetary recompense of the other player (Guth & Van Damme, 1998). Hence it can be said that in playing such a game the players are self-centred.

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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