Find Enlightenment

Valuing in Games and Life

Edward O'Connor

Forum: Course Essay, Rose-Hulman Institute of Technology, 6 November 2000

Review of Wolff, Robert, "Reflections on Game Theory and the Nature of Value," Ethics, April 1962, vol. 72, no. 3, pp. 171 - 179.

In his article, Robert Wolff intends to demonstrate game theory's inadequacy in dealing with different kinds of value, but he falls short of this lofty goal in several respects. In doing so, he raises issues that are due reflection and consideration.

Wolff begins by introducing the reader to game theory as a discipline by recounting Von Neumann and Morgenstern's findings for the perhaps unfamiliar reader. He describes two player, zero- and non-zero-sum games, as well as the prisoner's dilemma. In doing so, he intends to illustrate for the reader the shortcomings of game-theoretic accounts of human action that he spends the bulk of his article considering in more detail.

His concern lies not in how the field of game theory proceeds, but rather with the field's starting point. He is concerned with the underlying assumptions about the nature of value made by game theorists when they consider rational behavior. He finds these underlying assumptions wanting.

More specifically, economists have long used utility maximization as a standard and defining characteristic of rationality. Wolff is concerned with what kinds of value lend themselves to such economic analysis. He finds that there is a significant class of values, which he calls "social values," that elude game-theoretic analysis.

Wolff defines an egoistic value attitude as "a preference which relates solely to the subjective state of the individual." (173) He uses market goods as traditionally considered in economics as an example of this, because it is the lone consumer who enjoys the value of the good. He points out that this type of value should not be construed as for the selfish only, by offering a characterization of altruism in terms of egoistic value: "The simple altruist also believes that value is egoistic. He merely seeks to maximize someone else's value." (Ibid.)

His major thesis is that game theory is incapable of analyzing situations involving non-egoistic value, and that such values are essential to the human condition. Thus, he concludes that game theory is not a very useful endeavor.

Wolff proposes, very reasonably, that there are many situations in which my "value attitude" is dependent on or is significantly influenced by the value attitude of others. For instance, if my roommate is depressed, my mood is diminished, and this has an effect on how I evaluate that around me. "For want of a better term," Wolff proposes the (clearly loaded) phrase contextual altruism as the name for this category of value attitude. (174)

Contextual altruism points to the possible existence of a particular sort of non-egoistic values, namely those which Wolff calls "social values," and which I call "relational values." Relational values arise in a relationship between multiple persons, and would not exist were the group of persons to not exist. Wolff takes freedom of speech and love as paradigmatic examples of this: for freedom of speech to even be an issue, there have to be at least two people involved, a speaker and a listener. "By social values I mean those states whose realization depends on a reciprocal relation between another's experience and my own." (175)

The groundwork has now been laid to consider Wolff's critique of game theory. Game theory rests on the assertation that "an analysis of rational [...] behavior must be based on a theory of the strategies which the participant[s...] employ[.]" (171) Wolff considers the notion of strategy to be at best inappropriate in the context of social values. He uses this humorous example to illustrate his point: "Any man who seriously debates whether to adopt a competitive or co-operative strategy in his wooing can be sure that he will never know the joys of true love." (176) He considers attempts to explain social values via co-operative strategy to be faulty, because "a co-operative strategy is a joint effort to acquire egoistic values [...] which by accident of the situation cannot as successfully be acquired through competition." (176)

Wolff's critique relies on a conventional and unsympathetic interpretation of what is meant by the word "strategy." He is correct to point out that STRATEGY, as conventionally considered, is a concept generally inapplicable to values like love.1 He fails to grant to the game theorists their specialized use of this term. The game-theoretic STRATEGY is a much, much broader concept than the conventional one: in any situation that an agent is faced with an alternative, the mechanism by which the agent chooses is the agent's strategy. That is all that is stipulated. There is nothing about the game-theoretic STRATEGY that forbids the careful consideration of relational value. The fact that a person in love faces alternative actions and chooses among them is a sufficient condition for there to be a game-theoretic strategy at play.

The critique loses force when we remind ourselves that the act of valuing is both necessary and sufficient for the existence of value. In other words, in order for something to be of value, it must be of value to someone. So, the love Bob feels for his loved one is a value to Bob and to Bob's loved one. The fact that this love arises as a reciprocal relation and would not exist were the relation to fail to obtain does not change the agent-relative nature of valuing.

His critique also depends upon a narrow understanding of agent-relative utility maximization. Humans are complicated, complicated creatures, and any mathematical model which purports to describe their behavior in real-world situations is bound to be oversimplified and easily broken, or alternatively woefully under-specified. The economic model of rational, utility-maximizing agents does a decent job of approximating human action, and this is because it essentially loads all of the complexity of the human condition into each actor's utility function. Wolff recognizes the essential difficulty of modeling utility in his introduction. In fact, this problem as stated here subsumes all three of the major difficulties of choice that Wolff lists at the outset of his article. While the economic model may fall short of what Wolff desires in this case, no other analytical model does any better, because this problem does not go away just by changing terminology.

Game theory can take into account relational values by altering the preconditions of game play and by changing the utility functions of each participant to take into account relational value. As an example of this, consider the game of Love. For our purposes, this is a two-player, non-zero-sum game. Now, if we accept Wolff's characterization of love, unrequited love is not true love, for "love is a relationship and not an egoistic state." (175) Continuing in oversimplifying this most important of human endeavors, each player faces two alternatives: love or do not love. If we take into account the kind of value love is while setting up our game, we can model it like so:

Player 2
don't love love
Player 1don't love (0,0) (0,0)
love (0,0) (L,L)
This model, while clearly inadequate and oversimplified almost beyond recognition, is a model of love. The fact that the experience of love is a relational value is "hidden" in each player's utility function, as was justified earlier and as is usually the case in economic analysis.

By not modeling relational value outside of the utility function, the model becomes less useful than a model which did take such things into account could perhaps be. However, a mathematical model which did explicate such things would be immensely complex, difficult to develop and manipulate, and would not get us much farther along than the results we are already able to obtain by our current methods. "If a thing is worth doing, it's worth doing well - unless doing it well takes so long that it isn't worth doing anymore. Then you just do it 'good enough'." (Programming Perl (second edition), Sebastopol, California: O'Reilly and Associates.)

Wolff goes on to apply his analysis of value and game theory in the political realm. He considers strategy in political discourse and debate, and finds the concept to be inapplicable. He commits the same mistake here as earlier, when he found strategy to be inapplicable in love. He claims that "the man genuinely devoted to the truth will withdraw his ideas as soon as he has been convinced of their falsehood." (176) But surely this itself is a game-theoretic strategy in its own right!

I find it extremely difficult to seriously consider his claim that game theory is inapplicable to the political realm, given the existence and flourishing of public choice theory over the past thirty-five years. It would be unfair to criticize Wolff on this count however, since his article was published just as Gordon Tullock and James Buchanan were beginning their work in this area, years before public choice gained much recognition. Nevertheless, from the modern-day vantage, his argument is all the weaker.

His historical analysis of Locke's and Rousseau's political theories, while interesting, fails to adequately distinguish between political and social contexts. The Lockian conclusion that "there are no distinctively social [...] values which are to be realized by the formation of the polity" doesn't rule out the realization of such values. (177) Indeed, it is the case that most such values should not be realized by the state; most social values are of value to a subset of those in society. Bob and his loved one are more than capable of realizing their love for one another without the state lending a helping hand. Marx makes precisely this mistake as well, in the lengthy passage quoted by Wolff. Marx argues that, because the bounds of one's action are drawn by the existence of others, this is " 'the only bond which holds society together[,]' " yet this is clearly false. Just because the rules of market society prohibit trespass, our interaction with others is not limited to guarding against trespass.

Wolff's characterization of relational value is worth consideration, but he fails to establish his conclusions. Game theory, classical economics, and agent-relative value are all more robust than he makes them out to be, and he should give the literature a more sympathetic reading before attacking its very foundation. However, this should by no means be taken to suggest that his project is devoid of value, for I find his explanation of the nature of relational value to be well written and worth reading.


1Here and elsewhere, I follow the philosopher's convention of writing "strategy" when referring to the word itself, STRATEGY when referring to the concept to which the word refers, and strategy when using the word normally.