Department of Psychology
State University of New York at Stony Brook
Stony Brook, New York

This paper was prepared for, and delivered,
on March 7, at the Fortieth Annual Meeting of
the American Orthopsychiatric Association. It
is now being revised for publication; criticisms
and comments, of all kinds, would be most wel-
come.

Bernhardt Lieberman

1
i-Trust

Bernhardt Lieberman

INTRODUCTION

In the many debates about the conduct of internation-
al affairs, though not necessarily in the actual conduct
of such affairs, there is considerable concern with the
notion of trust. A number of questions are often debated.
Among them are the following: Should we trust another
nation or group of nations? Is it important, possible
or sensible to trust a nation, or group of nations, in
the conduct of international affairs? Once a treaty is
signed to limit arms, refrain from arming, or taking or
refraining from some action, can or should a nation or
group of nations be trusted?

Without doing lethal damage to the essence of the
arguments, it is possible to dichotomize the various views
about the above questions. One group argues it is ir-
relevant, and possibly dangerous, to consider the notion
of trust in the conduct of international relations.
Nations, it is said, will act in their own self-interest
and abrogate treaties, agreements, or their word informally

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given, whenever it is believed to be necessary to do so. It is said that a nation that does not act in its own self-interest is difficult to deal with; trustworthy behavior is irresponsible and dangerous. Therefore, there is no point in concerning oneself with such a value-laden notion as trust. Trust is irrelevant in the conduct of international affairs, it is said, and if we seek to resolve conflicts among nations rationally, before they become harmful and mutually destructive, we must not trust our opponents at all; we must not even consider such a notion seriously.

A second group believes that at the root of the difficulty in international affairs is the fact that nations cannot and do not trust each other. Aggressive behavior and conflicts arise not so much from genuinely irreconcilable conflicts, but more from mistrust, suspicion, and untrustworthy acts. They believe that one should impress upon one's opponent one's good intentions. One should take actions that do not endanger one's own security, but show good will. One should sign arms control and disarmament agreements, small ones at first, but agreements that would build mutual trust and positive feeling.

For the sake of contrast, the varying views about the subject have been dichotomized. But even those who

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do not hold such extreme, gross views, those who hold
more sophisticated and delicate opinions have overlooked
what appears to be an essential ingredient in the analysis
of the notion of trust. We do trust other nations but
this trust is not based primarily on moral considerations,
or any notion of the building of positive feelings; it is
based on a sophisticated notion of self-interest.

When an act is clearly contrary to the important
interests of a nation, and when this act requires the
nation to be trustworthy, the nation will, in all likeli-
hood, abrogate the agreement. But it is often in the
interest of a nation or group of nations to keep an agree-
ment, not for immediate gain, even contrary to this con-
sideration, but in the interest of its coalition structure.
A nation may take an action contrary to its immediate
self-interest, or when its own self-interest is unclear,
because, for the sake of the stability of its coalition
structure, it is of value for the nation to do that. It
has long been obvious to statesmen and it was demonstrated
in the particular laboratory experiment I am going to
report on today, that rewards and payoffs come to the
stable alliance and that an alliance has stability when
its members can be reasonably certain that their partners
will not desert them for some temporary gain. No matter

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how amoral some may think the conduct of international
affairs is, some notion of trust, or some similar notion,
is involved. Let us examine an example of trustworthy
behavior among nations.

We rarely have the opportunity to see the actual,
intimate behavior of national leaders when they are con-
sidering the trustworthiness or untrustworthiness of
others; but early in 1961 such an opportunity arose. On
a television program the Kennedy administration showed
excerpts from the activities of the President on a single
day. We have an example of a case in which we did trust
the Russians and they trusted us. The program showed
Kennedy with his advisers, discussing the course and
future of disarmament negotiations. It was early in
1961, the administration had recently taken office and
wanted time to review what had occurred, and prepare
its disarmament policy and programs. One of his ad-
visers indicated to Kennedy that the Soviet Ambassador
had agreed that the Soviets would make no major dis-
armament proposal until the fall; the Russians would
not, in the coming months, exploit the fact that the
United States did not have its position on disarmament
ready. It was agreed, by both representatives, that
neither side would engage in any extensive pro-dis-
armament propaganda for a number of months. As far as

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can be discerned both countries trusted each other and
kept the agreement. We could and did trust the Soviets
successfully. We went about preparing our program for
disarmament proposals. Our officials were probably not
overly concerned about any sudden Soviet propaganda
offensive. The Soviets, had they chosen to, could
have at that time mounted a serious propaganda campaign
for immediate disarmament. Perhaps, they would have made
some gain from such a campaign. However, both sides be-
lieved that it was advantageous to refrain from taking
some action that might bring immediate gain. In a
sense, we and the Soviets had formed a coalition for
these limited purposes.

4

The notion of trust being developed here is some-
what different from the notion that we use in ordinary
conversation. Usually, when we use the word it remains
only vaguely defined, but if we think about it, generally,
some considerations of morality and personal feelings are
involved. When we use the term a person has "pledged
his word" to do or not to do something, there is a
consensus among the parties that it would be improper,
or wrong not to keep the pledge. We believe the person
will fulfill the commitment--we trust the person. If
the person fails to do as he agreed, he is untrustworthy
and, hence, reprehensible. If he behaves as agreed, he

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is believed to be trustworthy and is more likely to be trusted in the future. His behavior is not thought to be particularly virtuous, since trustworthy behavior is expected. It is a thesis of this paper that such a usage of the word trust does not describe the behavior of national leaders in the conduct of international affairs. In such affairs the moral and personal connotations of the term are often absent or suppressed.

The argument is sometimes made that we have international conflicts because statesmen are not trustworthy in the moral and personal sense, and that we will continue to have war and destruction until national leaders either become personally more trustworthy or are induced to be so, by some effective system of enforcible international agreements. Such an argument is answered by statements to the effect that questions of national interest will always outweigh attempts at personal morality, and that often conflicts among nations are provoked by genuine, irreconcilable conflicts.

This paper will not deal with that set of questions. It's purpose is not to argue the normative question but to examine behavior and see where some notion of trust is descriptive. The conception that will be developed in the remainder of this paper will be one involving the *interests* of the persons involved, hence the term _i-Trust_. This notion developed from the results of a laboratory experiment. The experiment examined inter-

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action among three people in a game situation. The situa-
tion was such that the experimental task itself did not
supply the players with standards of behavior; the game
had no solution that would dictate a resolution of the
conflict situation the subjects found themselves in. In
the experimental situation, many of the players developed
a notion of trust similar to the one being offered here.
The puzzling situation the subjects found themselves in,
the details of the experiment, will be presented. We
will then consider the results of the experiment and
see how this notion of trust based on interest helped
some subjects resolve the conflict. We will conclude
with a definition of the notion *i*-Trust.

A Three-Person, Zero-Sum, Matrix Game

The notion *i*-Trust that we have been considering
arose from an experimental study of behavior in a three-
person, zero-sum, majority game situation. In the three-
person, majority game, the players (designated 1, 2, and
3) by a personal move, form coalitions by choosing the
number of one of the two other players. If two choose
each other's number, a couple or coalition is formed.
Three distinct couples are possible; on any one play of
the game only one couple or none at all can occur.
The coalition that forms wins an amount of

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money from the third player. In the game played the characteristic, or payoff, function was:

If coalition (1,2) formed, the coalition received 10 cents from player 3.

If coalition (1,3) formed, the coalition received 8 cents from player 2.

If coalition (2,3) formed, the coalition received 6 cents from player 1.

The two members of the coalition had to divide their earnings in a way agreeable to both. The players were able to communicate by using written messages.

The subjects were twenty-four Harvard College undergraduates. Eight groups of three played forty repetitions of the game which is described in the Accompanying Material.

The study was initially designed to yield information about behavior in a three-person, zero-sum game situation. Some of the questions the study was designed to answer were:

a) Are the various solution notions for three-person, zero-sum games descriptive of actual behavior?

b) Does the size of the payoff to the coalition influence the frequency of the formation of that coalition?

c) How will the subjects divide the payoffs they will receive?

The three-person, zero-sum, majority game played has no precise mathematical solution; the theory of

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games of strategy fails to prescribe an appropriate, specific behavior for each of the subjects. Even if we accept as our definition of rationality, the particular definitions of the mathematical theory, the theory does not offer an unambiguous resolution of the conflict.

The relationships among the three players are quite intricate. One might think that a simple way of resolving the conflict would be for players 1 and 2 to form a permanent coalition and divide their winnings equally. However, when this does occur, it immediately becomes obvious to player 3 that it is advantageous for him to form a coalition with one of the two others. He can make an offer to player 1 to form a coalition with him, from which player 1 can receive more than the 5 cents he can receive together with player 2. It is even advantageous for player 3 to offer 7 cents or even 8 cents to player 1. Thus, player 1 is tempted to break his coalition with player 2 and take the full 8 cents from player 3. Seeing this, player 2 can then make a more attractive offer to 3 or to 1. The process can be repeated.

The three players quickly learned to see the complexities of the situation. What occurred was instability, offer and counter offer, acceptance, rejection, deception, and the "double cross". Coalitions formed

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and were changed; in not one of the eight groups did a
coalition form on the first trial and remain constant through
all the forty plays of the game.

The basic data obtained in the study are presented
in Tables 1 and 2 of the Accompanying Material. These
results have been described in detail elsewhere. Briefly,
the coalition receiving the smallest payoff (2,3) occurred most frequently, and a fifty-fifty split was the
most frequent division of the payoffs between the members
of the winning coalition.

The way in which the subjects came to resolve the
tangled situation facing them is the point of major interest today. The formal situation, the structure of
the game, offered no obvious, readily understandable
solution. Table 3, which shows the number of coalition
changes for each of the eight groups of three subjects
who played the forty repetitions of the game, reflects
this. There was not one group which did not have at
least one coalition change. Five had fewer than ten
changes; the remaining three had more than twenty
changes; the largest number of changes was 33.

The situation the subjects found themselves in
was perplexing. The structure of the game offered no
way to resolve the conflict. Some behavioral standards
or criteria for the resolution of the conflict had to

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develop. The nature of the game made complex negotiations inevitable. The agreements, breaking of agreements, and bargaining that occurred led to an interesting result. From observations of the subjects' behavior, and an analysis of their messages, it became obvious that in a number of games the players came to realize that a maximum return on one or two plays of the game was not important. It was far more profitable to enter into a stable, continuing agreement with one other player. Since defection was not an infrequent occurrence, an intuitive notion of trust was significant in determining which coalitions formed and held together. The subjects stated that they would enter into coalitions with the player they trusted, the one they believed would not be tempted to defect from their coalition for a more attractive offer on a subsequent play of the game.

In five of the eight groups that played the game a notion of trust similar to the one outlined in this paper was raised. The notion of trust contained the element of the desire to maximize one's payoff, and this could be done best by entering into a stable coalition with one other player. The elements of giving a pledge, making a commitment and fulfilling the pledge or commitment were present.

In three of the five groups that developed the

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notion, the actual word trust, or some variation of it
such as trustworthy, was used. In the two games where
the specific word trust was not used, obvious equiva-
lents were present. For example, one player said:

"I have found that I cannot take 1 at his word.
Disappointed as I am, I would be willing to
listen to any offer you make."

A particularly clear example of how the notion
helped to resolve the conflict situation is illustrated
by the following description. Prior to the first play
of the game, player 1 made an offer to 2, and 2 accepted.
Then player 3 made an offer to 1, and player 2 made an
offer to 3. Players 1 and 2 saw the complexities and
the possible dangers, reinstated their initial agree-
ment, and took the 10 cents from player 3, completing
the first play of the game. This coalition occurred on
the second play also. On the third play of the game,
player 3 offered player 1 one cent more than he was re-
ceiving from 2 and formed a coalition with him. On the
fourth play, players 2 and 3 decided to form a coalition
and split the earnings in half. They pointed out to
each other that player 1 had alternated between the two
of them on the initial trials. Before the sixth play,
in response to an offer, player 2 said to 1, "I cannot
trust you". Before the eighth play, 3 said to 1 that
he, 3, and 2 could trust each other. On the eleventh

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trial, player 1 was still trying to destroy the (2,3)
coalition and made the statement, "If you don't trust
me there is no use making further offers. You will note
that I have played 2's every time since my last offer."
This was an attempt on 1's part to have 2 trust him.
Finally on the fourteenth trial, player 1 made a last
attempt to separate the (2,3) coalition. He said to
player 3, "If you trust me I will offer you a four-four
split." This would have enabled player 3 to make more
money than he was receiving with 2. Three declined the
more lucrative offer and continued his coalition with 2.

Another example illustrates the same point: In
another of the games played, the notion of trust per-
vaded the entire bargaining process. By the tenth
trial player 2 had broken an alliance with 1. Player 1
said to 3: "Two broke an alliance. Want the 6-2 now?"
Player 3 responded: "If I broke my alliance with him
(meaning player 2) I'd be no better than him. I owe
him one hand. Next time around I'll consider it." The
subjects, sensing the importance of the stable alliance,
but not wishing to commit themselves for all the re-
maining plays of the game, discovered the technique of
making agreements for two, three, or a larger but limited
number of moves. If a player defected after the agree-

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ment was completed he could still be trusted.

In this game the longest unbroken alliance lasted between trials 15 and 28 when player 3 said to 2: "A long time with you has been doubtful. I _must_ trust 1 and he can trust me. If I leave him, you'll wonder if I might leave you. Then if you two team up, I'll have nowhere to turn." The alliance between 1 and 3 lasted through the 28th trial.

From the 29th to the 38th trial, the coalition (1,2) held together. Player 2 appealed to 1 by saying: "I broke no promises, I merely withdrew proposals." On the last two trials the (1,3) coalition formed, 1 deposed 2, and 2 said, "I can no longer trust you but must offer 3 a deal." That threat was to no avail--- player 3 accepted an offer from 1 and the game concluded. In this case the game concluded with all the players emphasizing the importance of trust, but each making deals with others. However, they did keep their limited agreements.

## THE DEFINITION OF _i_-TRUST

We are now ready to specify just what is meant by the term _i_-trust. Before we do this let me discuss briefly the connotations of the term which are not involved. These are the personal and moral connotations.

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Such elements are present and important when we use the term to describe our personal relations, but they are much less important, and often absent when we consider the relations among nations. We may use the terms, "I trust my young son to tell me the truth about what he plans to do when he goes to visit a friend, even though I may prevent him from visiting that friend." But we do not say I trust that the prime minister will tell me the truth of what he plans to do about the Suez Canal, even if this will defeat his purpose and be contrary to his interests.

Yet we cannot dispense with the notion entirely because certain expectations and obligations that have some striking similarity to the common usage of the term arise among nations; and these expectations and obligations are often fulfilled. The notion i-Trust to be outlined here seems to be descriptive not only of the behavior of the twenty-four college students who played a particular three-person game, but is also characteristic of the behavior of statesmen in the conduct of international affairs.

The elements that comprise the concept seem to be as follows: It is a belief or expectation about behavior in a situation in which the problem of forming a stable coalition structure is important. It is necessary to form a stable, continuing alliance, because

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such a situation yields the greatest payoff to the mem-
bers of the coalition. Without allies, the players will
lose what they value and so they do what will yield the
largest payoff to the coalition. The expectation which
we have named i-trust is the belief that the parties in-
volved in an agreement will actually do what they have
agreed to do, they will fulfill their commitment not
only when it is obviously advantageous for them to do
so, but even when it may be disadvantageous, when the
person must sacrifice some immediate gain.

However, the belief does not require that the person
take an action that is clearly contrary to an important
self-interest. The person who sacrifices some immediate
gain to fulfill a commitment believes he is acting in
his own interest; because his interests transcend the
increased immediate gain he might make should he defect
from a coalition. His interests lie in preserving his
alliance which is what yields him his maximum gain. An
attractive offer may be tempting, but it also may be
ephemeral and dangerous. One keeps agreements so that
he will be trusted and in turn his partner will not de-
sert him and the coalition will grow rich. Often the
present situation is unclear, each person or nation cannot
see clearly what it should do, what actions it should

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take, what behavior will further its interests. In
such a situation, where one's interests are not clear,
an unbreakable alliance with another, which yields some
gain, is preferable to the uncertainty of a swiftly
changing coalition structure, with the possibility
that one may be left alone, without allies. When one
is in such a situation a large single gain is often
not at all attractive.

CONCLUSION

The particular notion of trust, discussed here is
based on a notion of interest, akin to the conception
of maximizing gain taken from game theory. In the
three-person, zero-sum game played, many subjects had
no way of deciding which player to choose. The formal
structure of the game offered clues but gave no answers.
For some the answer seemed obviously to choose the person
who would repeatedly choose him, and not be tempted by
attractive offers. Analogously, in international af-
fairs, payoffs come to stable alliances; and statesmen
do much to maintain these alliances.

MATERIAL ACCOMPANYING THE PAPER

i-TRUST

Bernhardt Lieberman

THE GAME

Subjects played a three-person, zero-sum, majority game. In a majority game, subjects form coalitions by choosing each others' numbers. The subjects are numbered 1, 2, 3 and either no coalition or one of the following three coalitions (1,2), (1,3), (2,3) could occur on any one play of the game. Subjects could communicate by the use of written messages before each play of the game. Twenty-four subjects, eight groups of three, played forty repetitions of the game described by the following characteristic (payoff) function:

NOTES

1

A paper delivered on March 7, 1963 at the fortieth Annual Meeting of the American Orthopsychiatric Associations in Washington, D.C.

2

Work on this research was supported in part by the Public Health Service, when the author was a postdoctoral research fellow of the National Institute of Mental Health in the Department of Social Relations, Harvard University, and by the Center for International Affairs, Harvard University, when the author was a research associate of that Center. Support from the State University of New York at Stony Brook facilitated the completion of the work.

3

For other recent analyses of the notion of trust
see: T. C. Schelling, *The Strategy of Conflict* and M.
Deutsch, *Trust and Suspicion*, *Journal of Conflict
Resolution*, 1958.

4

For an account of the negotiations of this period
see *The New York Times Index*, 1961, Page 68.

5

This study is described more completely in the
paper: Lieberman, *Experimental Studies of Conflict in
Some Two-Person and Three-Person Games*, in *Criswell
et. al.*, *Mathematical Methods in Small Group Processes*,
Stanford University Press, 1962.