Bargaining behavior when profits are unequal and losses are equal

BARGAINING BEHAVIOR WHEN PROFITS ARE UNEQUAL AND LOSSES ARE EQUAL’

by Dan S . Felsenthal

Hebrew University, Jerusalem

This study explores the effect of information about other’s payoffs as well as the power of a mediator in the most difficult bargaining situation: It is clear to both parties that no agreement could benefit them equally, but failing to agree will result in an equal loss.

This situation was investigated in a bilateral monopoly setting where subjects, 172 male undergraduate students, were divided randomly into pairs. One subject in each pair assumed the role of a buyer and the other that of a seller, attempting to complete a transaction involving an imaginary product. Each of the alternative prices which could be agreed upon was associated with a differential profit, and failing to agree resulted in forfeiting a deposit.

The amount of information about the other’s profit schedule was found not to affect the probability of reaching an agreement. It did affect the magnitude of the difference between the parties’ profits, given that an agreement was reached.

An interesting paradox was found concerning the mediator. His availability induced subjects to employ him. Thereafter, they tended to reject his suggestions, incurring a risk that inclined to offset the advantage he seemed to offer.

Despite the possible advantages of intransigence, no party used an intransigent strategy. Hence, no significant difference was found between the proportion of agreements favoring the initiator of the bargaining process and those favoring the party having the last clear chance. The few cases ending in disagreement were all a result of an operation of a random device simulating fatigue. The results are considered to have implications for a wide range of social situations involving both mutuality and opposition of interests.

c*J

MULTITUDE of bargaining studies A (Chertkoff (G. Esser, 1976) have been conducted since Siege1 and Fouraker (1960, 1963) launched the systematic experimental research of bargaining behavior. However, none have tried to investi- gate specifically the most difficult of all bargaining situations, that in which the parties are aware there is no possible agreement that will provide them both with an equal profit. A better bargain for one means less for the other; failing to agree results in an equal loss.

This situation, whether real or perceived as real, is not uncommon in every- day life. It applies to all instances involving objects such as territories, real estate, heirlooms and other property, which either cannot be divided without losing

their value altogether, or are intrinsically indivisible. A simple example of such a dilemma occurs when two trucks meet on a one-lane road. Who backs up? If war is perceived by both sides to be equally dis- astrous but each prefers a different peace- ful solution, which agreement, if any, will finally emerge? If all political parties needed to form a coalition are equally anxious to join it, and if the coalition’s payoffs, e.g., ministries, are perceived not to be divisible among the necessary number of partners in a manner that satisfies them all, which coalition, if any, will form? How will it apportion the payoffs among its members? Who will get the perceived larger payoff?

Such conflict situations are the most difficult to resolve because they involve a

KEY WORDS: bilateral monopoly bargaining, conflict resolution, division fairness, intransigence, mediation. The author wishes to express his gratitude to

Dr. Eliezer Fuchs for his collaboration in the conduct of this study and to Professors Michael Inbar, Thomas C. Schelling and Ira Sharkansky for their

helpful comments. This study was supported by the Social Science Faculty in the Hebrew University and the F. A. Schonbrunn Research Fund. Requests for reprints should be sent to Dan S. Felsenthal, Department of Political Science, Hebrew Univer- sity, Jerusalem 91009, Israel.

334

Behavioral Science, Volume 22, 1977

BARGAINING BEHAVIOR 335

basic dilemma. On the one hand, we would expect the parties to split the profits as equally as the situation permits, since it seems unlikely that they should sustain equal losses just because they cannot divide the profits evenly. On the other hand, if agreement is to be reached, then one party has to concede and both are equally justified in expecting this from the other. Such mutually justified expectations may lead to protracted bargaining. Increasing fatigue, frustration and intransigence may set in during the course of bargaining. This in turn may lead both sides to prefer an equal loss to letting the other side get away with the larger profit (Schelling, 1963; Chertkoff & Baird, 1971; Lamm & Rosch, 1972).

The oldest example of this kind of spite is reflected in the biblical story regarding King Solomon’s judgment of the two har- lots claiming motherhood to the same child. One of them ultimately declared: “Let it be neither mine nor thine, but divide it” (Kings I, 3:26).

Given such a conflict situation, we were interested in determining the probability of reaching an agreement and what the nature of such an agreement would be. These questions were analyzed as a function of two variables: what information each party has about the other’s profit for every possible form of agreement, and whether or not the services of a mediator could be employed. Thus, we have examined four experimental situations of information by mediation.

(1) No information about the other’s profits and mediator unavailable.

(2) No information about the other’s profits and mediator available.

(3) Complete information about the other’s profits and mediator unavailable.

(4) Complete information about the other’s profits and mediator available.

The numerals 1, 2, 3, 4 will be used hereafter to refer to these four situations.

METHOD

Pairs of male undergraduate students who volunteered for the experiment at- tempted to complete a transaction involving the purchase or sale of an imaginary

product. For each pair one student was randomly assigned the role of a single buyer, a monopsonist, and the other that of a single seller, a monopolist. Both were told that they could conduct the transaction only between themselves. As the students arrived for the experiment they were randomly assigned to two rooms, one to the sellers’ and the other to the buyers’ room. Each seller was randomly paired with a different buyer. No seller or buyer knew his partner’s identity. This was a safeguard against illicit deals, e.g., agreeing to split the profits evenly after the experiment ended. They could communi- cate between themselves only in writing by using a negotiation form on which only their code numbers were recorded.

Every seller and buyer were given a table containing a list of 24 prices, ranging in units of I.€ 2.00, from I.€ 2.00 to I.€ 48.00, upon which they could agree fol- lowed by a list indicating the profits for each of those prices. The parties were told that their profit schedules were inversely related but nonlinear and that there was no price in which their profits were equal. In situations 1 and 2, they were not told that for each of the 24 prices their joint profits added up to a constant sum of I.€ 40.00 as depicted in Table 1.

TABLE 1 SELLER’S AND BUYER’S PROFITS AS A FUNCTION OF

PRICE (IS). Price Seller’s Profit Buver’s Profit

2 4 6 8

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 4R

0 1 2 3 6

10 11 14 15 17 18 22 23 24 26 27 29 30 31 33 35 36 39 40

40 39 38 37 34 30 29 26 25 23 22 18 17 16 14 13 11 10 9 7 5 4 1 0


336 DAN S. FELSENTHAL

Before beginning the experiment every participant had to deposit, out of his own pocket, a sum of 1% 10.00. This deposit was returned to him, together with his profit, if he succeeded in arriving at an agreement with his partner. However, if no agreement was reached, this deposit was forfeited. Thus for every feasible form of agreement the parties were to receive an unequal profit and for failing to agree they suffered an equal loss, assuming that their utilities for the sums involved were the same.

For each pair it was randomly decided which party would initiate the bargaining process by first quoting a price. The one selected was allowed five minutes to choose one of the 24 prices and write it down under his column in the negotiation form. This form was then transmitted by the experimenter to the partner who could, also within five minutes, either accept the offer by writing “agree” under his column or reject it by writing a counterproposal. The counterproposal was transmitted to the party initiating the process. This process was repeated until either an agreement was reached or the negotiation process was terminated without agreement.

The negotiation process was terminated, both parties losing their deposits if one of the following situations occurred.

(1) At least one party insisted on the same price for three consecutive rounds, each round being defined as an offer and a response. Subjects were told that such behavior was a clear indication of intransigence. Hence if the other party did not concede by the end of the third consecutive round, it would be pointless to continue the negotiation process.

(2) A random procedure simulating fatigue terminated the negotiation process. This procedure was employed as follows:

(a) When a mediator was unavailable, situations 1 and 3, a die was rolled if no agreement was reached by the end of the third round if no party used a strategy of intransigence. Participants were told that, if the die fell on 1 or 6 (probability 1/31, then a fourth round would not be permitted and the negotiation process would ter-

minate. If it fell on any of the other four numbers (probability 2/3), they would be permitted to negotiate one more round. If no agreement was reached by the end of this additional round and provided that no party used an intransigent strategy in rounds 2, 3, and 4, the die was rolled again to determine whether a fifth round would be permitted, and so on, until either an agreement was reached or the die terminated the negotiating process.

(b) When a mediator was available, situations 2 and 4, participants were told that if no agreement was reached by the end of the third round, despite the fact that no party was intransigent, a fourth round took place. In this round the experimenter assumed the role of a mediator, suggesting to both parties a price which he considered reasonable, If the mediator’s suggestion was rejected by at least one of the parties, the die would be rolled to determine whether the parties should be permitted to resume negotiations between themselves for any additional roundb) as described in (a) above.

The mediator’s suggestion was based on a random selection from the range of prices quoted by the parties in the third round, those prices included. The parties were, of course, unaware of this selection method.

Eighty-six pairs of students participated in the experiment. They were distributed among the four experimental situations as follows: 19 pairs in situation 1, 23 pairs in situation 2, 20 pairs in situation 3, and 24 pairs in situation 4.

HYPOTHESES

Based on previous research and given the experimental design described above, we expected to obtain the following results.

1 . The probability of reaching an agreement: Information effects. One might assume that the probability of reaching an agreement when both parties are ignorant of each other’s possible profits would be greater than if they were completely informed. When both sides are uninformed, each party is more likely to be satisfied with securing a minimal profit than



whether the opponent got a better bargain. However, it could also be argued that bargainers who are uninformed about the other party’s payoff schedule are less likely to concede because they are wary of being exploited. Informed bargainers are less likely to be suspicious because they are aware of the fair agreement price(s) prevailing in the situation and thus are able to reach an agreement more quickly.

Since the second line of reasoning and not the first was supported by previous research (Liebert, Smith, Keiffer, & Hill, 1968; Yukl, 1974) we decided to adopt the hypothesis that informed bargainers have a better chance of arriving at an agreement than uninformed ones.

2. The probability of reaching a n agreement: Mediation effects. There are two conflicting lines of reasoning, both supported by previous research. According to the face-saving theory (Brown, 1971) one might expect greater willingness of bargainers to accept what may appear as less favorable terms if offered by an objective third party, e.g., a mediator, than if offered by the opponent (Pruitt & Johnson, 1970). However, in a later study it was found (Johnson & Pruitt, 1972) that bargainers who anticipated mediation were more likely to concede and reach agreement than bargainers who anticipated arbitration, i.e., binding decisions by a third party. Under the assumption that arbitration represents greater intervention than mediation, these results suggest that bargainers are more likely to reach agreement when they expect less intervention. Moreover, there is reason to assume that in the present study the mediation situations were, from the point of view of the negotiating parties, more like arbitration than genuine mediation since they ran a 1:3 chance of suspended negotiation if at least one of them rejected the mediator’s suggestion. Hence we decided to adopt the hypothesis that the probability of reaching an agreement would be greater when the mediator was unavailable.

3 . The effectiveness of the mediator’s services. Since the mediator could be re- garded as a substitute for information in the no information situation 2, we as-

sumed that his services would be required more often here than in the complete information situation 4. However, given the manner in which the mediator selected his suggestions and based on Hypotheses 1 and 5, we assumed that his suggestions would be rejected more often in the no information situation. 4. The probability of reaching a n agree-

ment. Based on the previous three hypotheses, we expected that the probability for reaching an agreement in the four experimental situations examined would maintain the following ordinal relation- ship from highest to lowest: 3, 1, 4, and 2.

5 . The nature of the agreement reached: Difference in profits. Given that an agreement was reached, we anticipated that the difference between the parties’ profits would be smaller, i.e., they will be closer to the Nash point(s) (Nash, 1950, 1953) in the complete information situations 3 and 4 than in the no information situations 1 and 2.

The rationale underlying this hypothesis is based on Adams’ (1965) equity theory which emphasizes people’s desire to achieve fair outcomes in social exchange, or on Schelling’s (1963) prominent solution theory which suggests that of the possible agreements some are characterized by cer- tain quantitative or qualitative attributes which make them stand out as acceptable solutions to both sides. Accordingly, the price which offers the smallest difference between the parties’ profits constitutes both a fair solution and a prominent one. It should be reached more easily when the parties are fully informed of each other’s payoff schedules. This hypothesis is con- sistent with Siege1 and Fouraker’s (1960) original findings that informed bargainers are more likely to reach a Pareto optimal solution than uninformed ones.

6. The nature of the agreement reached: Who got the better bargain? In those instances where the agreements reached were not based on the mediator’s suggestion, we assumed that the party initiating the bargaining process was more likely to receive the larger profit than the one responding.

The rationale underlying this hypothe-


338 DAN S. FELSENTHAL

sis is based on the last clear chance doctrine (Schelling, 1963; Chertkoff & Baird, 1971). According to this doctrine the party having the last clear chance of preventing disaster, e.g., an automobile collision, will be held responsible if he did not prevent it even if the other party initially was at fault. In the present study, the number of negotiating rounds was limited. In each round the same party made an offer and the other party responded. The responding party confronted a dilemma if negotiations reached the third round: to accept the opponent’s offer or to risk the die-roll and/ or a mediator’s intervention and possibly be responsible for no agreement. Hence we assumed that, if an agreement was reached, it would more likely award the initiator with the larger profit since he would be inclined to take advantage of the responding party’s dilemma.

7. The speed at which an agreement was reached. Based on the rationale underlying Hypotheses 3 and 6, we expected that most agreements in situations 1, 3, and 4 would have been reached no later than the third round. In situation 2 they would not have been reached before the fourth round.

RESULTS

Table 2 presents the data regarding the proportion of agreements reached by situation, as well as the reasons for not reaching an agreement. From the data in this table we observe that the eight cases that ended in no agreement, this disagreement was a result of the negotiations being terminated by the die-roll and not because one party resorted to an intransigent strategy and the other did not concede. A study

of the proportion of agreements reached in each of the four situations indicates that there is no significant difference regarding the probability of reaching an agreement.

This conclusion, however, may be erro- neous since it ignores the specific rounds in which agreements were reached -and thereby ignores the tendency to risk no agreement through the intervention of ex- ternal factors (the die-roll and/or the mediator) -which in our experimental design is the proper measure reflecting the probability of reaching an agreement.

Data regarding the specific rounds in which agreements were reached is pre- sented in Table 3. From this table we observe that most agreements in situations 1 ,3 , and 4 were reached, as expected, during or before the third round. Most agreements in situation 2 were reached, also as expected, during or after the fourth round. In the eight cases that ended in no agreement, we observe that the tendency to risk no agreement was highest in situation 2 (74 percent), lowest in situation 3 (15 percent), with situations 1 and 4 lying in between (31 and 54 percent, respectively).

However, by applying the chi-square significance test we find the differences in the tendency to risk no agreement between situations 1 and 3 as well as between situations 2 and 4 to be insignificant (0.1 < p < 0.25). Applying the same test, the differences are significant between situations 1 and 2 as well as between situations 3 and 4 (0.005 < p < 0.01). We also found the difference in the tendency to risk no agreement between situations 2 and 3 to be highly significant ( p < 0.001),

TABLE 2 NUMBER AND PROPORTION OF AGREEMENTS AND DISAGREEMENTS BY SITUATION.

Pairs not Agreeing Situation Total Pairs Pairs Agreeing

die-roll intransieence n P n P n P

19 17 ,896 2 ,105 - - 23 21 ,913 2 ,087 - - 20 18 ,900 2 ,100 - - 24 22 ,917 2 ,083 - -

Total 86 78 ,907 8 ,093 - -

* Miming values indicate the outcome did not occur.



TABLE 3 AGREEMENTS REACHED BY ROUND AND SITUATION.

___- - Situation

1 2 3 4 Total Round

1st 2nd 3rd 4th 5th 6th 7th 8th 9th

10th

Total 17 21 18 22

3 5

39 17 6 4 1 2

1

78

-

~~

* Missing values indicate the outcome did not occur

but the difference between situations 1 and 4 was insignificant (0.1 < p < 0.25).

These results imply there is no significant difference in the probability of reaching an agreement as a function of the amount of information regarding the opponent’s profit schedule when the effects of mediation are controlled. They also show that there is a significant difference as a function of the availability of a mediator when the effects of information are controlled. Consequently, the probability of reaching an agreement, regardless of information effects, is significantly higher when a mediator is unavailable than when one is available.

In situation 2, 17 of the 21 pairs required mediation. Of these, nine pairs accepted his suggestion. In situation 4, 13 pairs out of 22 required mediation. Of these, there were eight pairs accepting his suggestion. The differences between these two situations were insignificant neither in the extent of requiring the mediator’s services (0.1 < p < 0.25) nor in the extent of accepting his suggestions (0.25 < p < 0.5).

Table 4 shows the nature of agreements reached in the four experimental situations by the price agreed upon. As expected, when the no information situations 1 and 2, are pooled together, significantly fewer agreements are associated with the Nash points (prices 22 or 24) than when the complete information situations 3 and 4 are pooled together (0.05 < p < 0.1). However, contrary to expectation (Table 5 ) , we found no significant difference in any of the four situations between the

proportion of agreements favoring the initiator of the bargaining process and those favoring the respondent, i.e., the party defined as having the last clear chance.

DISCUSSION

We found no support for the assumption that the knowledge of the other party’s profit schedule increases the probability of reaching an agreement. Rather, consist- ent with previous research, we found that such knowledge affects the type of agreement reached, i.e., the magnitude of the difference between the parties’ profits. Consequently, it is suggested that the in- clination to reach an agreement in the conflict situation examined is independent of the amount of information one has about the other party’s payoffs. Instead, agreement may depend on whether the parties prefer an unequal profit to an equal loss or vice versa. If a t least one of the bargaining parties concludes that a smaller profit is preferable to an equal loss, then the knowledge of the precise difference between the parties’ profits will not determine whether an agreement will be reached but rather what kind of agreement will be reached. On the other hand, if the parties are disinclined to agree because both prefer an equal loss to a smaller profit, then this attitude is not likely to be influenced by the amount of information about inequality in profits for every possible form of agreement.

When a mediator is available, there will be no significant difference in the relatively high requirement for his services or in the extent of the relatively low accept-

TABLE 4

SITUATION. TYPES OF AGREEMENTS REACHED BY PRICE AND

Diflerence be- Total Agreements Situation

1 2 3 4 Agreed Price tween Parties’

Profits

4 8 13 14 16 22 or 24 20 or 26 6 4 3 2 1

28 8 2 2 - ’ 3 18 10 1 1 2 -

1 1 - 1 32 14 I - - - 36 20 - 1 - 1

Total 17 21 18 22

16 or 30 12

” Missing values indicate the outcome did not occur.


340 DAN S . FELSENTHAL

TABLE 5

SITUATION. AGREEMENTS REACHED BY FAVORED PARTY AND

_- __ Situation

favors buyer 8 3 6 5 8 4 3 6 favorsseller 2 4 4 6 3 3 7 6 favors Initla- 12 12 11 9

favors re- 5 9 7 13 tor

spondent

ments total agree- 17 21 18 22

~ ___ ~~

* amp and 8 1 8 ~ are acronyms for buyer initiates bargaining process and seller initiates bargaining process, respectively.

ance of his suggestions as a function of the amount of information available regarding payoffs. In fact, the probability of reaching an agreement when a mediator is not available is significantly higher than when one is available. This combination of findings raises an interesting paradox. The presence of a mediator in- duces people to rely on him, supporting the face-saving theory. By doing this, they incur a risk that tends to offset the advantage he seems to offer, thus supporting the intervention theory.

Given that an agreement has been reached, we found no significant difference within each situation or among situations between the proportion of agreements favoring the initiator and those favoring the respondent. We also found that no agreement was reached through the employ- ment of an intransigent strategy. This combination of findings supports the equity theory. This suggests that bargainers inclined to reach agreement are unlikely to use a strategy based on the last clear chance doctrine. They fear that such a strategy might antagonize the opponent to the extent that he would prefer no agreement to an embarassing one. In- stead, such bargainers resort to a step-by-

step strategy where mutual consessions are made in successive rounds. Hence we were unable to determine whether the use of an intransigent strategy improves the party’s bargaining position, or, alterna- tively, reduces the probability of reaching an agreement. This question must be sub- jected to further investigation.

REFERENCES Adams, J. S. Inequity in social exchange. In L.

Berkowitz (Ed.), Advances in experimental socialpsychology, vol. 2. New York: Academic Press, 1965.

Brown, B. R. Saving face. Psychol. Today, 1971, 4, 55-59, 86.

Chertkoff, J. M., & Baird, S. L. Applicability of the big lie technique and the last clear chance doctrine to bargaining. J . pers. SOC. Psychol.,

Chertkoff, J . M., & Esser, J. K. A review of experiments in explicit bargaining. J . exp. S O C . Psychol., 1976, 12, 464-486.

Johnson, D. F., & Pruitt, D. G. Preintervention effects of mediation versus arbitration. J . appl. Psychol., 1972, 56, 1-10,

Lamm, H., & Rosch, E. Information and competi- tiveness of incentive structure as factors in two-person negotiation. Eur . j . SOC. Psychol.,

Liebert, R. M., Smith, W. P., Keiffer, M., & Hill, J . H. The effects of information and magnitude of initial offer on interpersonal negotiation. J . exp. SOC. Psychol., 1968, 4, 431-441.

Nash, J. F. The bargaining problem. Econornetrica, 1950, 18, 155-162.

Nash, J . F. Two-person cooperative games. Econo- metrica, 1953, 21, 128-140.

Pruitt, D. G . , & Johnson, D. F. Mediation as an aid to face-saving in negotiation. J . pers. SOC.

Psychol., 1970, 14, 239-246. Schelling, T. C. The strategy ofconflict. New York:

Oxford Univ. Press, 1963. Siegel, S., & Fouraker, L. E. Bargaining and group

decision making: Experiments i n bilateral monopoly. New York: McGraw-Hill, 1960.

Siegel, S., & Fouraker, L. E. Bargaining behauior. New York: McGraw-Hill, 1963.

Yukl, G. A. Effects of opponent’s initial offer, concession magnitude, and concession fre- quency on bargaining behavior. J . pers. S O C .

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(Manuscript received March 8, 1977)


Bargaining behavior when profits are unequal and losses are equal

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