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Axelrod, The Evolution of Cooperation (XXI)

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Matt Domsalla

SAASS 632/5



The Evolution of Cooperation Precis



In The Evolution of Cooperation, University of Michigan Professor of Political Science and Public Policy Robert Axelrod explores under what conditions cooperation will emerge in a world of egoists without central authority. Axelrod investigates “how individuals pursing their own interests will act, followed by an analysis of what effects this will have for the system as a whole.” (6) He develops a theory of cooperation to be used to discovery what is necessary for cooperation to emerge. Axelrod uses an iterative Prisoner’s Dilemma to explore the emergence of cooperation. The possibility of players meeting against makes it possible, though not sufficient, for cooperation to emerge. However, the future is less important than the present for two reasons: (1) players value future payoffs less and (2) there is a change the players may not meet again. The TIT FOR TAT strategy cooperates on the first move and then does whatever the other player did on the previous move. Axelrod ran two strategy tournaments, and TIT FOR TAT won both. Nice strategies would not defect first, and this property separated the more successful rules from the less successful ones. Axelrod concludes the “foundation of cooperation is not really trust, but the durability of the relationship.” (182)



Part I - Introduction

The Problem of Cooperation

· “It pays to defect if you think the other player will defect. This means that it is better to defect if you think the other player will cooperate, and it is better to defect if you think the other player will defect.” (9)

· “Individual rationality leads to a worse outcome for both than is possible. Hence the dilemma.” (9)

· “Two egoists playing the game once will both choose their dominant choice, defection, and each will get less than they both could have gotten if they had cooperated. If the game is played a known finite number of times, the players still have no incentive to cooperate.” (10)

· “The issue then becomes the discovery of the precise conditions that are necessary and sufficient for cooperation to emerge.” (11)

· “What makes it possible for cooperation to emerge is the fact that the players might meet again.” (12)

· “A strategy (or decision rule) is a specification of what to do in any situation that might arise.” (14)

· “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.” (15)

· “The very possibility of achieving stable mutual cooperation depends upon there being a good chance of a continuing interaction, as measured by the magnitude of w.” (16)

· “Saying that a continuing chance of interaction is necessary for the development of cooperation is not the same as saying that it is sufficient.” (16)

· “The analysis of the data from these tournaments reveals four properties which tend to make a decision rule successful: avoidance of unnecessary conflict by cooperating as long as the other player does, provocability in the face of an uncalled for defection by the other, forgiveness after responding to a provocation, and clarity of behavior so that the other player can adapt to your pattern of action.” (20)

· “The evolution of cooperation requires that individuals have a sufficiently large chance to meet again so that they have a stake in their future interaction. If this is true, cooperation can evolve in three states.” (1) Cooperation can get started even in a world of unconditional defection. (2) Strategy based on reciprocity can thrive in a world where many different kinds of strategies are being tried. (3) Cooperation, once established on the basis of reciprocity, can protect itself from invasion by less cooperative strategies. (20 – 21)

Part II – The Emergence of Cooperation

The Success for TIT FOR TAT in Computer Tournaments

· DOWNING is based on “a deliberate attempt to understand the other player and then to make the choice that will yield the best long-term score based upon this understanding. The idea is that if the other player does not seem responsive to what DOWNING is doing, DOWNING will try to get away with whatever it can by defecting. On the other hand, if the other player does seem responsive, DOWNING will cooperate. To judge the other’s responsiveness, DOWNING estimates the probability that the other player cooperates after it (DOWNING) cooperates, and also the probability that the other player cooperates DOWNING defects.” (34)

· Forgiveness of a rule can be informally described as its propensity to cooperate in the moves after the other player has defected.” (36)

· “The real costs [of a defection] may be in the tertiary effects when one’s own isolate defections turn into unending mutual recriminations.” (38)

· “The entries were too competitive for their own good.” (40)

· “A rule can be called retaliatory if it immediately defects after an ‘uncalled for’ defection from the other.” (44)

· “TIT FOR TAT benefits from its own clarity.” (54)

The Chronology of Cooperation

· “A new strategy is said to invade a native strategy if the newcomer gets a higher score with a native than a native gets with another native.” (56)

· “A strategy is collectively stable if no strategy can invade it.” (56)

· “Collectively stable strategies are important because they are the only ones that an entire population can maintain in the long run in the face of any possible mutant.” (56)

· “The advantage of a nice rule in resisting invasion is that it attains the highest score possible in a population consisting of a single type of strategy.” (62)

· “A strategy is maximally discriminating if it will eventually cooperate even if the other has never cooperated yet, and once it cooperates will never cooperate again with ALL D but will always cooperate with another player using the same strategy as it uses.” (66)

· “Nice rules can protect themselves in a way that meanines cannot.” (68)

· “Mutual cooperation can emerge in a world of egoists without central control by starting with a cluster of individuals who rely on reciprocity.” (69)

Part III – Cooperation Without Friendship or Foresight

The Live-and-Let-Live System in Trench Warfare in World War I

· “The live-and-let-live system was endemic in trench warfare.” (74)

· “Demonstrations of retaliatory capabilities helped police the system by showing that restrain was not due to weakness, and that defection would be self-defeating.” (79 – 80)

· “What finally destroyed the live-and-let-live system was the institution of a type of incessant aggression that the headquarters could monitor. This was the raid, a carefully prepared attack on enemy trenches which involved from ten to two hundred men.” (82)

· “The origins, maintenance, and destruction of the live-and-let-live system of trench warfare are all consistent with the theory of the evolution of cooperation.” (84)

· “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.” (85)

· “The very experience of sustained mutual cooperation altered the payoffs of the players, making mutual cooperation even more valued than it was before.” (85)

The Evolution of Cooperation in Biological Systems (with William D. Hamilton)

· “Foresight is not necessary for the evolution of cooperation.” (88)

· “Many of the benefits sought by living things are disproportionally available to cooperating groups.” (92)

· “Cooperation based on reciprocity can thrive in a variegated environment.” (96)

· “Cooperation based on reciprocity can get started in a predominantly noncooperative world, can thrive in a variegated environment, and can defend itself once fully established.” (100)

· Mutualisms – situations of close association of mutual benefit between members of different species. (100)

· “Conditions of free-mixing, and transitory pairing conditions where recognition is impossible, are much more likely to result in exploitation – parasitism, disease, and the like.” (101)

· “Impermanence of association tends to destabilize symbiosis.” (101)

Part V - Conclusions

The Social Structure of Cooperation

· “Four factors are examined which can give rise to interesting types of social structure: labels, reputation, regulation, and territoriality.” (145)

· “These characteristics can allow a player to know something useful about the others player’s strategy even before the interaction begins.” (146)

· “A label can be defined as a fixed characteristic of a player that can be observed by other players when the interaction begins.” (147)

· “Labels can support stereotypes by which everyone suffers, and the minority suffers more than the rest.” (149)

· “A player’s reputation is embodied in the beliefs of others about the strategy that player will use.” (150)

· “When third parties are watching, the stakes of the current situation expand from those immediately at hand to encompass the influence of the current choice on the reputations of the players.” (151)

· “A way to measure the value of any piece of information is to calculate how much better you could do with the information than without it.” (151)

· “The other player may also be trying to establish a reputation, and for this reason may be unforgiving of the defections you use to try to establish your own reputation.” (153)

· “Deterrence is achieved through the establishment of a reputation.” (153)

· “The key [for a government] to maintain compliant behavior from the citizenry is that the government remains able and willing to devote resources far out of proportion to the stakes of the current issue in order to maintain its reputation for toughness.” (155)

· “The trick is to set the stringency of the standard high enough to get most of the social benefits of regulation, and not so high as to prevent the evolution of a stable pattern of voluntary compliance from almost all of the companies.” (157)

· “Territories can be thought of in two completely different ways.” (1) Terms of geography and physical space. (2) Abstract space of characteristics. (158)

· “The territorial system demonstrates quite vividly that the way the players interact with each other can affect the course of the evolutionary process.” (167)

The Robustness of Reciprocity

· “The power of the collective stability approach is that it allows a consideration of all possible new strategies, whether minor variants of the common strategy or completely new ideas. The limitation of the stability approach is that is only tells what will last once established, but it does not tell what will get established in the first place.” (171)

· “The potential for cooperation arises when each player can help the other. The dilemma arises when giving this help is costly. The opportunity for mutual gain from cooperation comes into play when the gains from the other’s cooperation are larger than the costs of one’s own cooperation… But getting what you prefer is not so easy. There are two reasons. In the first place, you have to get the other player to help – even though the other player is better off in the short run by not helping. In the second place, you are tempted to get whatever help you can without providing any costly help yourself.” (173)

· The main results of Cooperation Theory show that “cooperation can get stared by even a small cluster of individuals who are prepared to reciprocate cooperation, even in a world where no one else will cooperate.” (173)

· “What is more interesting is how little had to be assumed about the individuals or the social setting to establish these results.” (173)

o “The individuals do not have to be rational: the evolutionary process allows the successful strategies to thrive, even if the players do not know why or how.” (173)

o “There is no need to assume trust between the players: the use of reciprocity can be enough to make defection unproductive.” (174)

o “Altruism in not needed: successful strategies can elicit cooperation even from an egoist.” (174)

o “No central authority is needed: cooperation based on reciprocity can be self-policing.” (174)

· “The emergence, growth, and maintenance of cooperation do require some assumptions about the individuals and the social setting. They require an individual to be able to recognize another player who has been dealt with before. They also require that one’ s prior history of interactions with this player can be remembered, so that a player can be responsive.” (174)

· “For cooperation to prove stable, the future must have a sufficiently large shadow.” (174)

· “The evolution of cooperation requires that successful strategies can thrive and that there be a source of variation in the strategies which are being used.” (175)

· “There must be some clustering of individuals who use strategies with two properties: the strategies will be the first to cooperate, and they will discriminate between those who respond to the cooperation and those who do not.” (175)

· “TIT FOR TAT’s robust success is due to being nice, provocable, forgiving, and clear.” (176)

· “The importance of future interactions can provide a guide to the design of institutions. To help promote cooperation among members of an organization, relationships should be structured so that there are frequent and durable interactions among specific individuals.” (180)

· “The foundation of cooperation is not really trust, but the durability of the relationship.” (182)

· “It is better to be provocable sooner, rather than later.” (185)



Proposition 1. If the discounter parameter, w, is sufficiently high, there is no best strategy independent of the strategy used by the other player. (15)

Proposition 2. TIT FOR TAT is collectively stable if and only if, w is large enough. (59)

Proposition 3. Any strategy which may be the first to cooperate can be collectively stable only when w is sufficiently large. (61)

Proposition 4. For a nice strategy to be collectively stable, it must be provoked by the very first defection of the other player. (62)

Proposition 5. ALL D is always collectively stable. (63)

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. (66)

Proposition 7. If a nice strategy cannot be invaded by a single individual, it cannot be invaded by any cluster of individuals either. (67)

Proposition 8. If a rule is collectively stable, it is territorial stable. (160)

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