Ultimatum bargaining behavior of people affected by schizophrenia

1.2. Decision-making behavior and social cognition in schizophrenia 

The degree to which schizophrenic patients show intact functioning on decision-making tasks is still unclear. Several studies using two different decision tasks — Bechara's gambling paradigm (also known as the Iowa Gambling Task) and the two-choice prediction task— resulted in ambiguous conclusions (Bechara et al., 1994, Shurman et al., 2005, Hutton et al., 2002, Wider et al., 1998, Ludewig et al., 2003).

Beside cognitive deficits such as in working memory and executive function, which are considered a core feature of schizophrenia (Sharma and Antonova, 2003), other deficits belong to the field of social cognition. It was hypothesized that difficulties in social interactions in schizophrenia originate in a deficit in Theory of Mind (ToM), that is, in incorrect interpretation of the intentions and thoughts of others. Various studies were aimed at finding a linkage between the symptomatology of schizophrenia, cognitive deficits, and functioning level in ToM tasks (Corcoran et al., 1995, Stephenson et al., 1996, Pickup and Frith, 1996, Pickup and Frith, 2001).

The crucial difference between a typical task (a ToM task or a decision-making task such as the ones mentioned above) and a game is that the former doesn't take into account interactive considerations; none of the decision alternatives from which a subject chooses a response influence the other subjects. However, in a game such as the UG, each decision alternative has a different effect upon both the player who makes the decision and his or her counterpart.

There is no doubt that a certain ‘mind-reading’ ability is crucial in daily social exchange and social relations, no less than cognitive abilities such as memory and planning ahead. Daily life decision-making processes should take into account other people's response to one's decisions. Therefore, whereas the majority of the literature examined decision-making abilities of schizophrenic patients in non-strategic environments, our study investigates how schizophrenic patients deal with a strategic interaction.

1.3. The Ultimatum Game 

The Ultimatum Game represents a “take it or leave it” negotiation scene: one bargainer makes a final offer to the counterpart and walks away from the table, leaving the other to either sign the deal or not. Personal experience in negotiation might tell us that such a dramatic attitude has a good chance of failing. However, in classical game theory, such an ultimatum should work. Imagine the following situation: you receive a sum of money and are being told to offer an anonymous person a part of it. If this person accepts your offer (for example, of one dollar out of the whole sum), then you end up with the whole sum minus one dollar, and the other person ends up with a dollar. However, the other person has the right to reject your offer, in case it doesn't suit him or her: if that happens — both of you end up with no money at all.

In game theory, this situation is called an Ultimatum Game. In this game there are two players: a Proposer (the one who makes the offer and who has the advantage of the first-goer), and a Responder (who makes the decision whether to accept the offer or reject it, and thus has veto power). If we assume that each player wants to maximize his or her profit in the game, it is clear that the Responder should accept any offer, because any positive amount is better than zero. Therefore the Proposer, knowing this, should offer the smallest amount possible. Thus, in the case of two ‘rational’ players playing for 20 New Israeli Shekels (NIS) — approximately 5 U.S. dollars — the Proposer should offer 1 NIS, the Responder should accept the offer, and the game should end with payoffs (19, 1) — that is, Proposer receiving 19 NIS, Responder receiving 1 NIS. In fact, the Responder should accept even an offer of 0 NIS, because rejection will not negatively effect his or her payoff (either accepting or rejecting the offer, he or she will end up with 0); thus, another possible result of the game is (20, 0). Such a pair of payoffs in called the Nash Equilibrium of the game, and it means that this is how the game should end if the players are both payoff maximizers.(Selten, 1975). However, this equilibrium was rarely realized in any of the numerous experiments that have been conducted throughout the world over the past 22 years (Guth et al., 1982, Guth and Tietz, 1990, Roth et al., 1991, McCabe et al., 2002). Instead, subjects reach a less extreme, more reasonable division of the sum of money at stake, even though the game is played anonymously so that social considerations such as reputation should have no influence. The average Proposer offers 40% of the amount to the Responder. In average, 16% of the offers are rejected. Tiny offers are almost always rejected (Oosterbeek et al., 2003).

Aspects of social exchange in everyday life are represented in this simple game, for example, fairness and punishing for unfairness (even at the price of lowering one's own profit), along with empathy (the Proposer can try to predict the response by putting himself or herself in the place of the Responder). In addition, playing this game more than once involves a learning process, even if one's counterpart changes: for example, one learns which low offers are high enough to be accepted, and which have a high probability of being rejected.

1.4. Hypothesis 

As described above, people affected with schizophrenia tend to misinterpret the intentions and beliefs of others. Hence, we hypothesized that as Proposers, these subjects would:

In addition, we predicted perseveration along trials: after experiencing one round of the game, the offer level would not change dramatically following “accept” responses; a Proposer in the schizophrenic group will not attempt to maximize his or her payoff by reducing their offer after their last one was accepted.

As for the Responder's role, we rely on the article Autism, theory-of-mind, cooperation and fairness (Hill and Sally, 2003). The authors of this unique study investigated the behavior of people with autism in the UG. They conclude that the rejection rate is not necessarily correlated with intact ToM. Therefore, we predicted no substantial difference in rejection rates among the three groups.

2.1. Subjects 

Forty-nine people with a DSM-IV diagnosis of schizophrenia participated in the study. Diagnosis was based on clinical assessment made by two specialist psychiatrists.

All subjects were inpatients in the day care unit of “Shalvata” Mental Health Center, in Hod-HaSharon, Israel. The patients were in various stages of rehabilitation, all attending either the day care ward or a rehabilitation unit. None were fully hospitalized. Based on clinical assessment, none of the patients were in an acute psychotic stage of illness.

The experiment was approved by the local Helsinki committee, and all participants gave their signed informed consent. Subjects were further selected based on functional measures: the patient's ability to cooperate, and autonomously perform his or her part in the game.

Prior to participating in the game, every patient was asked to perform a short preliminary task in order to assess organizational ability and basic arithmetic ability: subjects were given a deck of cards, and were asked to form a combination of cards that would create the number 11. After completing this task successfully, the participants proceeded to the next stage of the experiment.

Two control groups were studied as well. A group of 52 non-clinical controls was recruited from the community and university staff (age and gender matched). A second control group consisted of 19 depressive patients, all inpatients attending a day program at “Shalvata” Mental Health Center at the time of the experiment (Table 1).

Table 1. Participants' demographic and clinical characteristics

		Schizophrenic patients N=49		Depressive patients N=19		Non-clinical controls N=52
		Mean	S.D.	Mean	S.D.	Mean	S.D.
	Age (years)a	36.2	10.8	43.0	18.5	34.9	9.2
	Educationb	0.9	0.6	1.3	0.9	1.5	0.6
	Mean age at onset of illness (years)c	19.4	4.9	27.0	18.0
	Length of current admission (months)d	4.4	5.5	3.5	2.6
	Number of previous admissionse	2.8	2.2	1.8	1.0
	CGI scoref	4.6	1.0	4.3	0.8

a Significant (and typical) difference in age of schizophrenic vs. depressive groups (P=0.03). No significant difference between schizophrenic patients and non-clinical controls (P=0.49). b Education level was assessed using the following scale: 0 — did not complete high school, 1 — completed high school, 2 — high education. The difference between the groups is significant (P<0.01). c No significant difference between the groups (P=0.2). d No significant difference between the groups (P=0.4). e Significant difference between the groups (P<0.01). f Clinical Global Impression (Guy W., ECDEU Assessment Manual for Psychopharmacology. Rockville, MD: US Department of Health and Human Services publication (ADM) 1976; pp. 218–22). No significant difference between the groups (P=0.3).

2.2. Procedures 

Patient sessions included 4, 6, or 8 participants, half of them in the role of Proposers and the other half as Responders. Roles were determined randomly by the instructor. Control sessions included 6, 8, or 18 participants.

Proposers sat in a row facing a row of Responders. All of the participants in a session sat in the same room, so that the experimental procedure would be transparent to them. Each participant was assigned a code number, so that the session would be anonymous: the names of one's counterparts would not be revealed to him or her.

The procedure of each “round” was as follows: The Proposer made an offer by filling in a form (see Appendix 1). The forms were then distributed randomly among the Responders. In this way, every Responder received an offer from an anonymous Proposer. After the Responders filled in their decisions, each form was returned to the Proposer to whom it belonged, so that each Proposer could find out what the response to his or her offer was. Subjects were asked to keep silent during the session.

At the beginning of the session, the subjects were given an oral explanation of the rules of the game by the instructor. Thereafter, a demonstration round was played (with no real payoffs), followed by two “real” rounds (i.e. with payoffs) in a row. The sum of money for each round was 20 NIS (approximately 5 U.S. dollars).

The subjects were told that after these two rounds, they would receive their payoffs according to one of the rounds, which would be randomly chosen. (This was done due to budget limitations.) At the end of the session each subject discreetly received an envelope containing his or her payoff.

The UG can be played, and studied, either as a single-round or a multi-stage game. We have chosen to study a simple two-stage version (two pay rounds). The rationale for this choice was both our interest in the initial behavior rather than the acquired one, and our desire for subjects to fully comprehend the game rules. This is why we address much importance to the last round of the game, the second pay-round, in which we assume subjects to have operated out of comprehension of the game.

2.3. Data analysis 

A Pearson chi-square test was used in order to check whether offer distribution varied with group. To assess order to assess the influence of experience on Proposers' behavior, we applied regression analysis with last (2nd) offer as the dependent variable, and the following variables as predictors: 1st offer (O1), the response to it (R1), group, group•O1, O1•R1.

A Pearson chi-square test was used to determine whether the distribution of Proposer types varied with group.

One- and two-way analyses of variance (ANOVAs) were used to analyze differences in mean offer between the groups, with and without respect to gender.

A series of Pearson chi-square tests was used to examine whether the rejection rate varied with group and round.

3.1. Offers 

3.1.1. Offers by levels 

We divided offers into three categories, with respect to offer level: fair (10 NIS), unfair (less than 10 NIS), and hyper-fair (more than 10 NIS). A significant difference between the groups concerning the final offer was revealed. The distribution of final-round offers by levels is presented in Fig. 1. While the distribution of healthy subjects' offers was approximately even between fair and unfair (none were hyper-fair), that of schizophrenic subjects was significantly different (P=0.016); about 50% of their offers were fair and the rest were more or less evenly divided between unfair and hyper-fair. Thus, for schizophrenic Proposers, the possibility of dividing the money evenly was as reasonable as for healthy Proposers, whereas the option of being hyper-fair appears to be as reasonable as being unfair, in contrast to the pattern for healthy Proposers.

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Fig. 1. Distribution of offers by levels, final round.

3.1.2. Offer fluctuation after acceptance/rejection 

Fig. 2 shows the influence of experience on Proposers' behavior, that is, how the 1st offer and the counterpart's response to it influenced the level of the 2nd offer. It turned out that the nature of this influence varied with group (all P values<0.035).

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Fig. 2. a: A regression model for the 2nd offer, after receiving a rejection of the 1st offer. b: A regression model for the 2nd offer, after receiving an acceptance of the 1st offer.

The adjustment of the 2nd offer after the 1st offer had received a negative response is quite similar in both the schizophrenic and healthy control groups (Fig. 2a). Both figured out that they should raise their 2nd offer after their 1st one was rejected. However, schizophrenic patients were more generous and raised their offer to a slightly higher level than controls. (As can be seen in Fig. 2a, the line representing the schizophrenic group is slightly above the line representing controls, when 1st offer is unfair.) This similarity emphasizes the relative failure in strategic thinking, as demonstrated in the way schizophrenic patients adjust their 2nd offer after their 1st offer had received a positive response. While healthy controls, attempting to maximize their payoff, lower their 2nd offer after a positive response for their 1st offer, schizophrenic patients do not do so. As can be seen in Fig. 2b, their 2nd offer seems independent of the response they had received and is approximately constant (7.7 NIS).

3.1.3. Proposer types 

In order to further examine Proposers' strategic thinking, we divided the entire Proposer population into types, based on how their 2nd offer was affected by the response to their 1st offer: Referring to the two pay-rounds (1st and 2nd), we define ‘strong-strategic’, ‘weak-strategic’ and ‘non-strategic’ types of Proposers as follows:

‘Strong-strategic’ Proposers are those who adjusted their 2nd offer according to the response to their 1st offer, that is, raised their 2nd offer after their 1st one was rejected, or lowered their 2nd offer after their 1st offer was accepted.

‘Weak-strategic’ Proposers are those who perseverated, that is, their 2nd offer was the same as their 1st offer.

Finally, ‘non-strategic’ Proposers are those who unreasonably reduced their offer after a rejection, or raised their offer after an acceptance.

We found that the distribution into types significantly varied with group.

As demonstrated in Fig. 3, the highest proportion of non-strategic Proposers is in the schizophrenic group (P=0.018). Non-strategic Proposers consist as much as 20% of the total in the schizophrenic group, while in the healthy group there are none.

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Fig. 3. Type distribution by group.

3.2. Responses 

3.2.1. Rejection rates 

The rejection rates are presented in Fig. 4.

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Fig. 4. Rejection rates by group and round.

On the demo-round, the rejection rate in the schizophrenic group was significantly lower than in both control groups. (8% vs. 34% and 30% respectively, P=0.077).

A reversed trend was demonstrated in the 1st round, when the rejection rate of patients was significantly higher than that of healthy subjects (P=0.026): the latter rejected only 4% of the offers, while schizophrenic subjects and depressed subjects rejected 20% and 40% of the offers, respectively. By the last round, no significant difference was found in rejection rates between the different groups. Although the rejection rate among schizophrenic subjects remained the highest (29%, vs. 19% of healthy and 20% of depressed patients), this difference was not statistically significant.