Games and Metaphors

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This is a review of Axelrod's book:

Axelrod is at pains to extend his results through powerful metaphors linking games and strategies to the nonexperimental world. One of the more popular sets of metaphors in literature and social science centers around games as general prototypes for other forms of interdependent human behavior. Games ordinarily include activities that we pursue in our leisure time, relatively frivolous amusements perhaps, card games like poker or bridge, board games like chess of checkers, sports. These games are commonly compared with other aspects of life. We may, for example, think of football as war, with different components or teams as analogs to air force or infantry. Writers from different cultures have taken a broader view of games, developing ludic models that seek to illuminate deeper aspects of human existence.

Social scientists have been particularly interested in comparing aspects of social reality with formal structured mathematical games. Axelrod, as we have seen, focuses on one of these games, PD, for theoretical and empirical analysis. He also makes it a metaphor for other aspects of life. A “basic problem occurs,” he says, “when the pursuit of self-interest by each leads to a poor outcome for all.” He goes on:

To make headway in understanding the vast array of specific situations which have this property, a way is needed to represent what is common to these situations without becoming bogged down in the details unique to each. Fortunately, there is such a representation available: the famous Prisoner’s Dilemma game [p. 7].

Axelrod presents us not only with a prototypic game, but also with ideal type decision makers. He describes the winning strategy, TFT, in anthropomorphic terms. TFT has an identity with human qualities. It is not necessarily rations; it is, however, nice, perceptive, and clear. It also has a short memory, and is provocable, forgiving, and patient. Game theory in the social sciences generally assumes a rational decision maker. This has been particularly appealing because it is consistent with the assumption of human rationality associated with western liberal culture. Interestingly and importantly, Axelrod’s decision maker does not necessarily come from this mold. Thus, Axelrod says:

There is no need to assume that the players are rational. They need not be trying to maximize their rewards. Their strategies may simply reflect standard operating procedures, rules of thumb, instincts, habits, or imitations.

He continues, even more daringly: The actions that the players take are not necessarily even conscious choices. A person who sometimes returns a favor, and sometimes does not, may not think about what strategy is being used. There is no need to assume deliberate choice at all [p. 18].

TFT is “nice.” It starts in a friendly way. It cooperates first. It is “never… the first to defect” (p. 67). Moreover, it continues to cooperate if the other player cooperates. TFT is, however, also perceptive. It is “maximally discriminating,” in the sense of being able to recognize “the recent behavior of the other player” (pp. 66, 174). At the same time, it encourages accurate perception by its opponent. TFT is “clear” and “easy to recognize” (pp. 53-54). Being extremely simple, it is easy for the opponent to interpret. And it reacts fast, giving immediate feedback in one move. TFT has a memory, though it is short. Much of the work previously done in game theory assumed no memory. There was only one round of play that either represented a single move or summarized the game’s entire set of moves. In the iterated PD, however, TFT can “recall” what happened in the past, even though the past only extends to the previous move (p. 174). Partly because of its recognition and memory capabilities, TFT is not generally a sucker. By cooperating on the first move against less nice programs, TFT is, of course, suckered when the other program initially defects. If this happens, however, TFT recognizes the fact and responds by defecting on its next move. TFT is thus reciprocal, “nonexploitable,” “provocable,” and “retaliatory.” Axelrod explains that “a rule can be called retaliatory if it immediately defects after an ‘uncalled for’ defection from the other” (pp. 44, 53-54, 69). One defection by its opponent is enough. After that, it gives back what it has received. TFT is, however, “forgiving” (p. 54). Axelrod explains as follows:

Forgiveness of a rule can be informally described as its propensity to cooperate after the other player has defected… TFT is unforgiving for one move, but thereafter is totally forgiving of that defection. After one punishment, it lest bygones be bygones [p.26]

Thus TFT does not hold a grudge, even if the other player defected earlier, on one or a number of occasions. It is “patient” (54) and willing to wait; as soon as the other player resumes cooperation, TFT was willing to do the same.

APPLICATIONS

Axelrod suggests that his results can be applied in a number of important issue areas. These include various sectors of international relations, domestic politics, labor relations, biology, theology. In terms of our earlier discussion of concepts, these are the areas of commonality between the model and political reality.

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LIMITATIONS

Axelrod writes seductively. His general metaphor is compelling because of the many specific examples. Further, his argument resonates in many different corners of our experience. Prisoner’s Dilemma is a well known game that outlines important questions of cooperation, conflict, and choice with deep philosophical, historical, and social scientific roots. Tit-for-tat satisfies our innate desires for reciprocated esteem, material reward, and power or – failing these – revenge. The CC model for coalition formation triggers a whole social scientific index, including segmentary relations within and between tribal societies, Kropotkin’s mutual aid, Riker’s side payments, Olson’s observations on state development and decline, Charles Osgood’s GRIT strategy for international arms reduction. DD, on the other hand, may remind us of duels and feuds, or the dynamics of international escalation described in Schelling’s “slippery slope.” Nevertheless, we may still ask ourselves about the extent to which this experiment contains an adequate metaphor for cooperative society. Going back to our discussion of concepts, we must consider areas of distinctness between the model and political reality. Axelrod refers to these as “complicating” or “potentially relevant factors.” He believes that

the value of an analysis without them is that it can help to clarify some of the subtle features of the interaction – features which might otherwise be lost in the maze of complexities of the highly particular circumstances in which choice must actually be made. It is the very complexity of reality which makes the analysis of an abstract interaction so helpful as an aid to understanding.

At the same time he carefully warns that “no intelligent person should make an important choice without trying to take such compelling factors into account” (p. 19; see Shubik, 1984: 302). To begin with, there are obvious limits to the fit between the structure of any game and other environments. Axelrod’s game is well defined and tidy, a parsimonious, orderly model of social reality with clear definitions of rules, players, strategies, and outcomes. Unfortunately, other parts of the world tend to be more confusing. Life does not usually present itself as a serially ordered set of 2 X 2 tables.