Robert Axelrod

American political scientist (b. 1943)

Robert Marshall Axelrod (born May 27, 1943) is an American political scientist and Professor of Political Science and Public Policy at the University of Michigan, best known for his interdisciplinary work on the evolution of cooperation.

Robert Axelrod, 2019


  • The Cooperation Theory that is presented in this book is based upon an investigation of individuals who pursue their own self-interest without the aid of a central authority to force them to cooperate with each other. The reason for assuming self-interest is that it allows an examination of the difficult case in which cooperation is not completely based upon a concern for others or upon the welfare of the group as a whole. It must, however, be stressed that this assumption is actually much less restrictive than it appears.
    • Chap. 1 : The Problem of Cooperation
  • What makes it possible for cooperation to emerge is the fact that the players might meet again. This possibility means that the choices made today not only determine the outcome of this move, but can also influence the later choices of the players. The future can therefore cast a shadow back upon the present and thereby affect the current strategic situation. But the future is less important than the present-for two reasons. The first is that players tend to value payoffs less as the time of their obtainment recedes into the future. The second is that there is always some chance that the players will not meet again. An ongoing relationship may end when one or the other player moves away, changes jobs, dies, or goes bankrupt. For these reasons, the payoff of the next move always counts less than the payoff of the current move.
    • Chap. 1 : The Problem of Cooperation
  • In fact, in the Prisoner's Dilemma, the strategy that works best depends directly on what strategy the other player is using and, in particular, on whether this strategy leaves room for the development of mutual cooperation. This principle is based on the weight of the next move relative to the current move being sufHciently large to make the future important.
    • Chap. 1 : The Problem of Cooperation
  • Proposition 1. If the discount parameter, w, is sufficiently high, there is no best strategy independent of the strategy used by the other player.
    • Chap. 1 : The Problem of Cooperation
  • In addition, TIT FOR TAT was known to be a powerful competitor. In a preliminary tournament, TIT FOR TAT scored second place; and in a variant of that preliminary tournament, TIT FOR TAT won first place. All of these facts were known to most of the people designing programs for the Computer Prisoner's Dilemma Tournament, because they were sent copies of a description of the preliminary tournament. Not surprisingly, many of them used the TIT FOR TAT principle and tried to improve upon it. The striking fact is that none of the more complex programs submitted was able to perform as well as the original, simple TIT FOR TAT.
    • Chap. 2 : The Success of TIT FOR TAT in Computer Tournaments
  • What accounts for TIT FOR TAT's robust success is its combination of being nice, retaliatory, forgiving, and clear. Its niceness prevents it from getting into unnecessary trouble. Its retaliation discourages the other side from persisting whenever defection is tried. Its forgiveness helps restore mutual cooperation. And its clarity makes it intelligible to the other player, thereby eliciting long-term cooperation.
    • Chap. 2 : The Success of TIT FOR TAT in Computer Tournaments
  • Proposition 2. TIT FOR TAT is collectively stable if and only if, w is large enough. This critical value of w is a function of the four payoff parameters, T; R, P, and S.
    • Chap. 3 : The Chronology of Cooperation
  • Proposition 3. Any strategy which may be the first to cooperate can be collectively stable only when w is sufficiently large.
    • Chap. 3 : The Chronology of Cooperation
  • Proposition 4. For a nice strategy to be collectively stable, it must be provoked by the very first defection of the other player.
    • Chap. 3 : The Chronology of Cooperation
  • Proposition 5. ALL D is always collectively stable.
    • Chap. 3 : The Chronology of Cooperation
  • Proposition 6. The strategies which can invade ALL D in a cluster with the smallest value of p are those which are maximally discriminating, such as TIT FOR TAT.
    • Chap. 3 : The Chronology of Cooperation
  • Proposition 7. If a nice strategy cannot be invaded by a single individual, it cannot be invaded by any cluster of individuals either.
    • Chap. 3 : The Chronology of Cooperation
  • Thus cooperation can emerge even in a world of unconditional defection. The development cannot take place if it is tried only by scattered individuals who have no chance to interact with each other. But cooperation can emerge from small clusters of discriminating individuals, as long as these individuals have even a small proportion of their interactions with each other. Moreover, if nice strategies (those which are never the first to defect) come to be adopted by virtually everyone, then those individuals can afford to be generous in dealing with any others. By doing so well with each other, a population of nice rules can protect themselves against clusters of individuals using any other strategy just as well as they can protect themselves against single individuals. But for a nice strategy to be stable in the collective sense, it must be provocable. So mutual cooperation can emerge in a world of egoists without central control by starting with a cluster of individuals who rely on reciprocity.
    • Chap. 3 : The Chronology of Cooperation
  • Just as important as getting cooperation started were the conditions that allowed it to be sustainable. The strategies that could sustain mutual cooperation were the ones which were provocable.
    • Chap. 4 : The Live-and-Let-Live System in World War I
  • The cooperative exchanges of mutual restraint actually changed the nature of the interaction. They tended to make the two sides care about each other's welfare. This change can be interpreted in terms of the Prisoner's Dilemma by saying' that the very experience of sustained mutual cooperation altered the payoffs of the players, making mutual cooperation even more valued than it was before.
    • Chap. 4 : The Live-and-Let-Live System in World War I
  • The live-and-let-live system that emerged in the bitter trench warfare of World War I demonstrates that friendship is hardly necessary for cooperation based upon reciprocity to get started. Under suitable circumstances, cooperation can develop even between antagonists.
    • Chap. 4 : The Live-and-Let-Live System in World War I
  • The theory of biological evolution is based on the struggle for life and the survival of the fittest. Yet cooperation is common between members of the same species and even between members of different species. Before about 1960, accounts of the evolutionary process largely dismissed cooperative phenomena as not requiring special attention. This dismissal followed from a misreading of theory that assigned most adaptation to selection at the level of populations or whole species. As a result of such misreading, cooperation was always considered adaptive. Recent reviews of the evolutionary process, however, have shown no sound basis for viewing selection as being based upon benefits to whole groups. Quite the contrary. At the level of a species or a population, the processes of selection are weak. The original individualistic emphasis of Darwin's theory is more valid.
    • Chap. 5 : The Evolution of Cooperation in Biological Systems (with William D. Hamilton)
  • In this chapter Darwin's emphasis on individual advantage has been formalized in terms of game theory. This formulation establishes conditions under which cooperation in biological systems based on reciprocity can evolve even without foresight by the participants.
    • Chap. 5 : The Evolution of Cooperation in Biological Systems (with William D. Hamilton)
  • The advice takes the form of four simple suggestions for how to do well in a durable iterated Prisoner's Dilemma:

    1. Don't be envious.
    2. Don't be the first to defect.
    3. Reciprocate both cooperation and defection.
    4. Don't be too clever.

    • Chap. 6 : How to Choose Effectively
  • So in a non-zero-sum world you do not have to do better than the other player to do well for yourself. This is especially true when you are interacting with many different players. Letting each of them do the same or a little better than you is fine, as long as you tend to do well yourself. There is no point in being envious of the success of the other player, since in an iterated Prisoner's Dilemma of long duration the other's success is virtually a prerequisite of your doing well for yourself.
    • Chap. 6 : How to Choose Effectively
  • Will there be anyone out there to reciprocate one's own initial cooperation? In some circumstances this will be hard to tell in advance. But if there has been enough time for many different strategies to be tried, and for some way of making the more successful strategies become more common, then one can be fairly confident that there will be individuals out there who will reciprocate cooperation. The reason is that even a relatively small cluster of discriminating nice rules can invade a population of meanies, and then thrive on their good scores with each other. And once nice rules get a foothold they can protect themselves from reinvasion by meanies.
    • Chap. 6 : How to Choose Effectively
  • The extraordinary success of TIT FOR TAT leads to some simple, but powerful advice: practice reciprocity. After cooperating on the first move, TIT FOR TAT simply reciprocates whatever the other player did on the previous move. This simple rule is amazingly robust. It won the first round of the Computer Tournament for the Prisoner's Dilemma by attaining a higher average score than any other entry submitted by professional game theorists. And when this result was publicized for the contestants in the second round, TIT FOR TAT won again. The victory was obviously a surprise, since anyone could have submitted it to the second round after seeing its success in the first round. But obviously people hoped they could do better-and they were wrong.
    • Chap. 6 : How to Choose Effectively
  • The tournament results show that in a Prisoner's Dilemma situation it is easy to be too clever. The very sophisticated rules did not do better than the simple ones. In fact, the so-called maximizing rules often did poorly because they got into a rut of mutual defection. A common problem with these rules is that they used complex methods of making inferences about the other player-and these inferences were wrong. Part of the problem was that a trial defection by the other player was often taken to imply that the other player could not be enticed into cooperation. But the heart of the problem was that these maximizing rules did not take into account that their own behavior would lead the other player to change.
    • Chap. 6 : How to Choose Effectively
  • Once again, there is an important contrast between a zero-sum game like chess and a non-zero-sum game like the iterated Prisoner's Dilemma. In chess, it is useful to keep the other player guessing about your intentions. The more the other player is in doubt, the less efficient will be his or her strategy. Keeping one's intentions hidden is useful in a zero-sum setting where any inefficiency in the other player's behavior will be to your benefit. But in a non-zero-sum setting it does not always pay to be so clever. In the iterated Prisoner's Dilemma, you benefit from the other player's cooperation. The trick is to encourage that cooperation. A good way to do it is to make it clear that you will reciprocate. Words can help here, but as everyone knows, actions speak louder than words. That is why the easily understood actions of TIT FOR TAT are so effective.
    • Chap. 6 : How to Choose Effectively
  • 1. Enlarge the shadow of the future
    Mutual cooperation can be stable if the future is sufficiently important relative to the present. This is because the players can each use an implicit threat of retaliation against the other's defection-if the interaction will last long enough to make the threat effective. Seeing how this works in a numerical example will allow the formulation of the alternative methods that can enlarge the shadow of the future.
    • Chap. 7 : How to Promote Cooperation
  • 2. Change the payoffs
    A common reaction of someone caught in a Prisoner's Dilemma is that "there ought to be a law against this sort of thing." In fact, getting out of Prisoner's Dilemmas is one of the primary functions of government: to make sure that when individuals do not have private incentives to cooperate, they will be required to do the socially useful thing anyway. Laws are passed to cause people to pay their taxes, not to steal, and to honor contracts with strangers. Each of these activities could be regarded as a giant Prisoner's Dilemma game with many players.
    • Chap. 7 : How to Promote Cooperation
  • 3. Teach people to care about each other
    An excellent way to promote cooperation in a society is to teach people to care about the welfare of others. Parents and schools devote a tremendous effort to teaching the young to value the happiness of others.
    • Chap. 7 : How to Promote Cooperation
  • 4. Teach reciprocity
    TIT FOR TAT may be an effective strategy for an egoist to use, but is it a moral strategy for a person or a country to follow? The answer depends, of course, on one's standard for morality. Perhaps the most widely accepted moral standard is the Golden Rule: Do unto others as you would have them do unto you. In the context of the Prisoner's Dilemma, the Golden Rule would seem to imply that you should always cooperate, since cooperation is what you want from the other player. This interpretation suggests that the best strategy from the point of view of morality is the strategy of unconditional cooperation rather than TIT FOR TAT.
    The problem with this view is that turning the other cheek provides an incentive for the other player to exploit you. Unconditional cooperation can not only hurt you, but it can hurt other innocent bystanders with whom the successful exploiters will interact later. Unconditional cooperation tends to spoil the other player; it leaves a burden on the rest of the community to reform the spoiled player, suggesting that reciprocity is a better foundation for morality than is unconditional cooperation.
    • Chap. 7 : How to Promote Cooperation
  • 5. Improve recognition abilities The ability to recognize the other player from past interactions, and to remember the relevant features of those interactions, is necessary to sustain cooperation. Without these abilities, a player could not use any form of reciprocity and hence could not encourage the other to cooperate.
    • Chap. 7 : How to Promote Cooperation
  • Four factors are examined which can give rise to interesting types of social structure: labels, reputation, regulation, and territoriality. A label is a fixed characteristic of a player, such as sex or skin color, which can be observed by the other player. It can give rise to stable forms of stereotyping and status hierarchies. The reputation of a player is malleable and comes into being when another player has information about the strategy that the first one has employed with other players. Reputations give rise to a variety of phenomena. including incentives to establish a reputation as a bully, and incentives to deter others from being bullies. Regulation is a relationship between a government and the governed. Governments cannot rule only through deterrence, but must instead achieve the voluntary compliance of the majority of the governed. Therefore regulation gives rise to the problems of just how stringent the rules and the enforcement procedures should be. Finally, territoriality occurs when players interact with their neighbors rather than with just anyone. It can give rise to fascinating patterns of behavior as strategies spread through a population.
    • Chap. 8 : The Social Structure of Cooperation
  • The advice in chapter 6 to players of the Prisoner's Dilemma might serve as good advice to national leaders as well: don't be envious, don't be the first to defect, reciprocate both cooperation and defection, and don't be too clever. Likewise, the techniques discussed in chapter 7 for promoting cooperation in the Prisoner's Dilemma might also be useful in promoting cooperation in international politics.
    The core of the problem of how to achieve rewards from cooperation is that trial and error in learning is slow and painful. The conditions may all be favorable for long-run developments. but we may not have the time to wait for blind processes to move us slowly toward mutually rewarding strategies based upon reciprocity. Perhaps if we understand the process better, we can use our foresight to speed up the evolution of cooperation.
    • Chap. 9 : The Robustness of Reciprocity
  • The two-person iterated Prisoner’s Dilemma is the E. coli of the social sciences, allowing a very large variety of studies to be undertaken in a common framework.
    • Preface
  • Throughout the social sciences today, the dominant form of modeling is based upon the rational-choice paradigm. Game theory, in particular, is typically based upon the assumption of rational choice. In my view, the reason for the dominance of the rational-choice approach is not that scholars think it is realistic. Nor is game theory used solely because it offers good advice to a decision maker, because its unrealistic assumptions undermine much of its value as a basis for advice.
    • Introduction
  • A moral of the story is that models that aim to explore fundamental processes should be judged by their fruitfulness, not by their accuracy. For this purpose, realistic representation of many details is unnecessary and even counterproductive.
    • Introduction
  • In complex environments, individuals are not fully able to analyze the situation and calculate their optimal strategy. Instead they can be expected to adapt their strategy over time based upon what has been effective and what has not.
    • Chap. 1 : Evolving New Strategies
    • Adapted from Robert Axelrod, “The Evolution of Strategies in the Iterated Prisoner’s Dilemma,” in Genetic Algorithms and Simulated Annealing, ed. Lawrence Davis (London: Pitman; Los Altos, Calif.: Morgan Kaufman, 1987)
  • Tournament studies, ecological simulation, and theoretical analysis demonstrate: (1) A generous version of tit for tat is a highly effective strategy when the players it meets have not adapted to noise; (2) If the other players have adapted to noise, a contrite version of tit for tat is even more effective at quickly restoring mutual cooperation without the risk of exploitation; (3) Pavlov is not robust.
    • Chap. 2 : Coping With Noise
    • Reprinted from Jianzhong Wu and Robert Axelrod, “How to Cope with Noise in the Iterated Prisoner’s Dilemma,” Journal of Conflict Resolution 39, no. 1 (Mar. 1995): 183–89.
  • A major goal of investigating how cooperative norms in societal settings have been established is a better understanding of how to promote cooperative norms in international settings. This is not as utopian as it might seem because international norms against slavery and colonialism are already strong, while international norms are partly effective against racial discrimination, chemical warfare, and the proliferation of nuclear weapons. Because norms sometimes become established surprisingly quickly, there may be some useful cooperative norms that could be hurried along with relatively modest interventions.
    • Chap. 3 : Promoting Norms
    • Reprinted by permission from Robert Axelrod, “An Evolutionary Approach to Norms,” American Political Science Review 80, no. 4 (Dec. 1986): 1095–1111.
  • Aggregation means the organization of elements of a system into patterns that tend to put highly compatible elements together and less compatible elements apart. Landscape theory predicts how aggregation will lead to alignments among actors (such as nations), whose leaders are myopic in their assessments and incremental in their actions. The predicted configurations are based upon the attempts of actors to minimize their frustration based upon their pairwise propensities to align with some actors and oppose others. These attempts lead to a local minimum in the energy landscape of the entire system. The theory is supported by the results of the alignment of seventeen European nations in the Second World War. The theory has potential for application to coalitions of business firms, political parties in parliaments, social networks, social cleavages in democracies, and organizational structures.
    • Chap. 4 : Choosing Sides
    • Adapted from Robert Axelrod and D. Scott Bennett “A Landscape Theory of Aggregation,” British Journal of Political Science 23 (Apr. 1993): 211–33.
  • In this essay, we have developed and illustrated an approach for predicting the membership of alliances among firms developing and sponsoring products requiring technical standardization. We started with two simple and plausible assumptions, that a firm prefers (1) to join a large standardsetting alliance in order to increase the probability of successfully sponsoring a compatibility standard, and (2) to avoid allying with rivals in order to benefit individually from compatibility standards that emerge from the alliance’s efforts. We then defined the concept of utility as an approximation to profit maximization in terms of size and rivalry, and discussed the influences on incentives to ally in order to develop and sponsor standards. We showed that the Nash equilibria are the local minima of an energy function with this type of utility function.
    • Chap. 5 : Setting Standards
    • Reprinted from Robert Axelrod, Will Mitchell, Robert E. Thomas, D. Scott Bennett, and Erhard Bruderer, “Coalition Formation in Standard-Setting Alliances,” Management Science 41 (Sept. 1995): 1493–1508.
  • In the future it would be good to use these conceptual and statistical developments to answer some new questions suggested by the model. For example, the dynamics we have seen in the tribute model suggest the following interesting questions:
    a. What are the minimal conditions for a new actor to emerge?
    b. What tends to promote such emergence?
    c. How are the dynamics affected by the number of elementary actors?
    d. What can lead to collapse of an aggregate actor?
    e. How can new actors grow in the shadow of established actors?
    • Chap. 6 : Building New Political Actors
    • Reprinted from Robert Axelrod, “A Model of the Emergence of New Political Actors,” in Artificial Societies: The Computer Simulation of Social Life, ed. Nigel Gilbert and Rosaria Conte (London: University College Press, 1995), 19–39.
  • The social influence model illustrates three fundamental points:
    1. Local convergence can lead to global polarization.
    2. The interplay between different features of culture can shape the process of social influence.
    3. Even simple mechanisms of change can give counterintuitive results, as shown by the present model, in which large territories generate surprisingly little polarization.
    • Chap. 7 : Disseminating Culture
    • Reprinted from Robert Axelrod, “The Dissemination of Culture: A Model with Local Convergence and Global Polarization,” Journal of Conflict Resolution 41 (1997): 203–26.

Quotes about Axelrod

  • To be believable, an optimism must first acknowledge fundamental reality, including the reality of human nature, but also the nature of all life. Life as we know it, and probably throughout the universe if there is life elsewhere, means Darwinian life. In a Darwinian world, that which survives survives, and the world becomes full of whatever qualities it takes to survive. As Darwinians, we start pessimistically by assuming deep selfishness at the level of natural selection, pitiless indifference to suffering, ruthless attention to individual success at the expense of others. And yet from such warped beginnings, something can come that is in effect, if not necessarily in intention, dose to amicable brotherhood and sisterhood. This is the uplifting message of Robert Axelrod's remarkable book.
    • Richard Dawkins, Foreword to the New Edition of The Evolution of Cooperation (2006)
  • The first American edition of The Evolution of Cooperation was published in 1984. I read it as soon as it appeared, with mounting excitement, and took to recommending it with evangelical zeal, to almost everyone I met. Everyone of the Oxford undergraduates I tutored in the years following its publication was required to write an essay on Axelrod's book, and it was one of the essays they most enjoyed writing.
    • Richard Dawkins, Foreword to the New Edition of The Evolution of Cooperation (2006)
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