Exchange Theory, Equity Theory, and Intrinsic Motivation

Dr. C. George Boeree


There is a side to life that involves a fairly cold, rational calculation of our gains and losses in social interaction:  We weigh the alternatives, balance the anxiety and hopes, contemplate our moves, and so on.  I call this the instrumental side of life, and it has been investigated in depth by researchers working under the name  exchange theory.

The idea is a very old one, and the British philosopher Jeremy Bentham gave it the particularly expressive title "hedonistic calculus."  In modern day theory, it is often expressed as a formula:  MF = E x V.  Motivational force is proportional to the expectancy times the value.  If we are talking about a complex behavior, the motivational force will be equal to the average of the components' "E's x V's."

The expectancy is the subjective likelihood that the desired outcome will happen.  This includes what you believe to be the relationship between your efforts and the results:  "If I'm a good boy, I'll get a cookie;"  "If I work hard, I'll be a success;"  "If I yell at people, they'll work harder for me;" and so on.  Mind you, these beliefs may be wrong and your probabilities way off, but as long as you hold them, they are a part of your motivational formula.

The value is the subjective desirability of the outcome -- what the end is worth to you.  Here we can draw on things like Maslow's hierarchy, or stick with the very idiosyncratic and sometimes weird values that make each one of us unique:  "I want spiritual enlightenment;"  "Money is number one for me;"  "I really love Rocky Road."

Let me show you how you put them together.  What is your motivational force for working hard in this class?   Make a list of possible outcomes, the subjective odds (0 to 1.0) of reaching each outcome, and what each one is worth to you (-1.0 to 1.0).  Then multiply each odds by each worth (E x V).  Then add them up, making sure to keep track of the signs, and divide by the number of outcomes.  You can then compare the motivational force of working hard in this class with other complex behaviors, such as spending the rest of this semester in the south of France.

Up to this point, we really have a theory of motivation.  But we can make it a social theory easily enough, by looking at the "MF's" of two people whose outcomes depend on each other, i.e. by looking at an  exchange.


Most of the research on exchange theory involves playing games.  And the most common game used is based on  the prisoners' dilemma.   You and a fellow criminal are taken in by the cops on suspicion of armed robbery.  The DA needs a confession from at least one of you in order to get an armed-robbery conviction.  Otherwise he can only get the two of you for illegal possession of firearms.  So he takes each of you into the interrogation room one-at-a-time, and makes an offer:

If neither of you confess, he'll get both of you for illegal possession of firearms, carrying a mandatory minimum sentence of one year apiece.

If one of you confesses, that one will be released for turning state's evidence, and the other will have the book thrown at him -- ten years.

If both of you confess, however, he'll be forced to go ahead and prosecute you both, but he'll push for light sentences of five years apiece.

You can arrange this in the form of a matrix:

                               prisoner A (you)

                     not confess       |  confess
                              1 yr.    |         0 yrs.
         not confess                   |
                     1 yr.             |  10 yrs.
prisoner B (him)     ------------------|-----------------
                              10 yrs.  |         5 yrs.
         confess                       |
                     0 yrs.            |  5 yrs

The  cooperative choice  here is to not confess:  You are cooperating with each other (not with the DA), aiming at the best overall results for both of you.  The  competitive choice  is to confess:  You are trying to get the best result for yourself, regardless of your colleague-in-crime.

So this is called a  mixed-motive  game, because you can be altruistic or aggressive.  Most games that we find interesting -- from football to tennis to chess to bridge -- are competitive only.  You cooperate with your teammates, of course, but the scores in a competitive game are "zero-sum:" If I win, you lose; if you win, I lose.

Mixed-motive games, though, are a better model of reality than purely competitive games, and the pattern of the prisoners' dilemma can be found everywhere.  Take international relations, for example:


                 peaceful       | aggressive
                        OK      |         plus
     peaceful                   |
                 OK             |  minus
THEM ---------------------------|--------------
                        minus   |
     aggressive                 |       ?
                 plus           |

Or take the old street game called chicken, where two young gentlemen drive their hot rods straight at each other.  The first one to swerve off the road loses his reputation and his pink slip (car registration).


             swerve     | go-on
                  +1    |       +10
     swerve             |
             +1         | -10
him  -------------------|----------------
                  -10   |        -100
     go-on              |
             +10        | -100

These, of course, are highly subjective:  If you both swerve, you get 1 point of relief each.  If one swerves and the other doesn't, the first loses and the other gains ten "machismo" points, exchangeable locally for the respect and affection of guys and gals alike.  But if both go on, it'll cost each 100 points of pain and suffering.

(Notice that in these games, the "scores" are more negative than positive.  This suggests that these are games you shouldn't play at all!  But there are other games that are much more positive.)

The question comes up:  How do you decide?  In the case of the original prisoners' dilemma, it's a one time deal with the DA, so you have only your opinion of your colleague's character.  But in chicken, and in most real life versions, you can play again and again, so your decision can be based on your experience with or knowledge of your opponent.  And you can use the exchange formula:

If your opponent tends to swerve 50 percent of the time, and go on 50 percent of the time, what is the relative MF of your possible moves?  The MF for you swerving is 50% times +1 (the relief you'll feel if both of you swerve) plus 50% times -10 (your chicken points), which comes to a - 4 1/2.

        (50% x +1) + (50% x -10) = - 4 1/2

The MF for going on is 50% times +10 (your macho points) plus 50% times -100 (your pain and suffering points), which comes to -45.

        (50% x +10) + (50% x -100) = -45

Either choice is negative (so you would have been better off not playing at all), but swerving is definitely your better bet.

If, on the other hand, your opponent swerves 99 out of 100 times, the figures look like this:

        (99% x +1) + (1% x -10) = +.89

        (99% x +10) + (1% x -100) = +8.9

This time, it is worth your while to be macho.

Of course, he's figuring the odds as well, based on your past performance, which changes the odds you'll need to figure your choice, which changes the odds for him....  This is what makes poker -- otherwise a childish game of chance -- such an interesting game.

Theoretically, you can use these matrices to model any social interaction.  Say your boss is heading down the hall towards you.  You've been thinking of asking her for a raise.  In fact, you've just clinched a major deal for her.  As you pass in the hall, you have a number of options:  You could say hello;  You could ask for advice (you know: make her feel smart);  You could introduce the idea of a raise, etc.  Your boss also has a number of options:  She could say hello;  She could compliment you on the deal;  She could ignore you entirely, etc.  Each combination of responses has certain costs and benefits to each of you, and you both may in fact be calculating the MF's for each possible action.


People like to simplify their lives as much as possible.  So many of us, rather than figuring MF's all the time, choose to live by certain principles.  One possibility is to always turn the other cheek, i.e. to consistently play cooperatively.  If the other people in your life are playing rationally (rather than by your high principles), they will choose the competitive choice every time, and you will lose and lose big.  On the other hand, if you decide to live your life aggressively, anyone who begins with an effort at cooperation will soon learn his lesson and begin to respond  with competitive choices, and you will both lose big.  Is there some consistent strategy that works a little better?

The best strategy is very simple and works by encouraging both your partner and you to be cooperative.  It's called the contingency strategy:  You start by cooperating; from then on, you do whatever your opponent did in the previous turn.  Tit for tat.

Some social psychologists actually suggested we start doing this with the Soviet Union in regards to nuclear armament.  They called it GRIT, for graduated reduction in tension.  We never adopted it, but it's the strategy Gorbachev used.

This game model of human interaction becomes much more interesting when you start adding players.  What we see then are the formations of coalitions -- weaker players ganging up on stronger ones.  This is essentially what republics and democracies are all about!


Unfortunately for those of us who would like neat formulas, the exchange formulas are loaded with problems.

First, there are problems with the formula as a whole.  For example, people don't always "optimize" -- they more often "satisfice."  That is, they have a minimum acceptable level of outcome.  We don't wait for perfection, but grab the first thing that is "good enough."  Also, people often function in terms of "short-run" results, without considering the "long-run."  We may take a 10% variable mortgage over a 12% fixed, for example.  And people try to make things more certain, whether that is to their advantage or not.  Most people would rather have $80 guaranteed than a 90% chance at $100, even though the latter has a higher "motivational force."  To summarize, we prefer satisfactory short-run certainties to optimal long-run risks.  This is why most of us do so poorly in the stock market.

Another major difficulty in using the exchange formulas for predicting behavior is that the expectancies and values are all subjective.  For example, they depend a great deal on your personality:  Some people are very optimistic and feel in control of their lives ("internal locus of control," we say); others are more pessimistic and feel as if they were the victims of their environment, society, genetics, or whatever ("external locus of control").

Further, we can distort expectancies like gang-busters, thereby wreaking havoc on the probabilities.  You're doing badly in a "cake" class--so you convince yourself that the material is too stupid to take seriously.  Or you stop studying, so that when you fail it's because you didn't study-- not because you have the IQ of a stalk of celery.  Or you redefine your purpose in attending classes:  It used to be "to learn;"  Now it's "to make the grade."  This makes it possible to take advantage of special educational techniques such as cheating.  This last example actually involves changing values in order to deal with a problem in expectancies!  You can see, I suspect, that expectancies are a bit more slippery than the nice neat letter E would lead you to expect.

Then there are difficulties with values as well.  What you value depends on your needs, obviously.  If you need protein, eating has a high motivational force behind it.  But values also depend on  internal comparisons,  what you are used to getting, both in terms of quality and quantity.  Although we may need protein, that nutritious bowl of gruel may nevertheless be little valued.

It also depends on external comparisons, what you see others getting.  Although that Big Mac may satisfy the need for protein, if everyone around you is sucking up lobster....

Basically, external comparisons have to do with fairness:  If I see you getting more than me, I may consider that unfair.  This is just one more extension of our desire for an orderly world, a  just  world.  Some theorists even suggest that we had to invent an afterlife precisely for this reason:  The good weren't getting sufficiently rewarded, and the evil sufficiently punished, in this life!

Equity theory

This business of fairness is so evident, there is a whole minitheory that addresses it called  equity theory.   It is basically a more sophisticated version of comparison, combined with the idea of dissonance:  We look at the ratio of our outcomes to inputs and compare with others' ratio of outcomes to inputs.  If I work as hard as he does, I expect the same pay; if he gets the same pay, I expect him to work as hard as I do.

         my O              his O
         ----      =?      ------
         my I              his I

If your ratio is better than mine, I will feel dissonance in the form of anger; if mine is better than yours, I will feel guilt.  (Many of you may note that we don't feel quite as guilty when we are doing well than we feel angry when we're not.  No problem for the theory:  The pain of guilt is eased a bit by the fact that we are, in fact, being rewarded by doing well!)

Again, the numbers in the formula are quite subjective, and what is an outcome (or input) to me may not be one to you.

Outcomes, using jobs as an example, might include pay, insurance, other benefits, status, good hours and vacations, nice office, responsibility, no responsibility....

Inputs might include time, effort, sweat, mental sweat, seniority, education required, experience required, amount of brown-nosing required, need to dress-up....

So what is relevant to you goes into your formula, and what is relevant to me goes into mine:  Who should get the promotion first -- the old timer or the young turk?  It depends on who does the figuring.

Of course dissonance often results in dissonance-fixing.  If we have a certain degree of maturity, of course, we could take actions that really change things for the better.  We are, however, as likely to do defensive things:

1.  We can change our own inputs.  If we are angry, for example, we can do less work, take off more often, even sabotage our work.

2.  We can change our outcomes.  We can pad our expense accounts, pilfer supplies, play with the books....

3.  We can cause the others with whom we compare ourselves to change their inputs or outcomes.  We can badger them to work harder, point out their faults to superiors, and generally make their lives a living hell.

4.  We can do any of these things "in our minds" -- i.e. engage in distortion or denial.  "It's lousy pay, but hey!  At least I have a great view from my office.  And at least I have a job.  And I don't really value success the way some people do."

5.  And we can remove ourselves, leave, quit!

The research has been pretty supportive of the theory.  Even regarding the "guilt" aspect:  People thought they were working on an assembly line with another person.  They were told that they did 35% of the work and the other person did 65% of the work.  Then they were asked to divide the reward in any way they thought right.  Lo and behold, most people gave themselves about 35% of the reward!  In other studies, when they were convinced that they were being over-paid, they tried to work harder!

But, in equity theory, we can see some the the same problems as with exchange theory in general, and a few problems even more clearly.  The equity formula says, in essence, "to each according to his inputs."  If we are distributing the luxuries of life, few of us would disagree with the formula:  If you don't work, you don't play.

But what about votes?  Should they only go to those who make an active contribution to society?  To the employed, for example?  Or to land-owners (as some of our founding fathers would have preferred)?  Or to people with titles?  Hardly.  The rule most of us prefer here is "to each, one" or "to each equally."

And what about medicine?  And basic food?  Should the poor do without?  They do, often enough, even in our society.  Most of us would agree, though, that when it comes to the necessities, the rule should read "to each according to his needs."  (Thanks, Karl Marx.)

By altering the formula to fit these different cases, we might be able to salvage equity theory.

Intrinsically valued acts

Despite the problems we've talked about so far, the exchange model remains a useful one  when  the behaviors we are looking at are  instrumental,  that is, means to ends.  These ends are called goals, purposes, values,  or sometimes  meanings (because without them, the behaviors have no meaning!).

So what about behaviors that are not means to ends?  Acts that are  intrinsically  meaningful, intrinsically valued?  Obviously, you can't use the formulas for these things.

An example is bravery:  If you rush into a burning building to save a baby -- that's brave!  But if you did so because someone promised you a million dollars as a reward -- that's just greedy.  It's only bravery if you don't do it as a means to an end.

Or take generosity:  If you give unselfishly, you are generous.  If you give in order to ingratiate yourself to someone, or to get something from someone -- that's just manipulation.  It's only generosity if you have no ulterior motives.

Honesty:  Is it still honesty if it serves your purpose?

Love:  Is it still love if you have conditions on it?

Let's look a little more closely at bravery.  It's not bravery if you act because of a reward.  Neither is it bravery if you act in order to win approval or to go to heaven.  Neither is it bravery if you aren't aware of the danger, or if you're hypnotized or drugged....  You must choose  to do it  knowing  the risks.  A brave person is one who does it because he feels it is the  right thing to do.   He may come by this feeling through intuition, or social learning, or moral reasoning, but as long as he sees it as the right thing to do, and nothing more, it's bravery.

Another way to look at it is that a person behaves bravely because it is a part of who he  is.   It is a part of his  integrity.   He wouldn't feel  right  if he didn't.  He couldn't live with himself.  But don't get confused:  You still don't "act" brave  in order to  feel good about yourself.  Bravery is a  way  of feeling good!

Bravery, for most of us, is a once-in-a-great-while kind of thing.  Let's look at something that occupies much more of our lives:  Work.  Most people spend a third of their lives working or preparing to work (i.e. school).  It is taken for granted that we work  instrumentally,  that is, for money, which in turn will provide us with the necessities of life and, we hope, a few of the luxuries as well.  To this extent, we can look at work through the  exchange  model.

But some work and aspects of work are also intrinsically valuable:  Skill, quality, craftsmanship, invention, discovery, creativity, dedication, duty, service....  These satisfy our sense of self, enhance our lives, enhance other's lives, and generally improve the world.  In other words, work can be a form of actualization, a value in itself, something which gives life meaning.

Copyright 1999, C. George Boeree