• R > (C+S)/2, i.e., cooperation by both pays more than alternating exploitation; and
• I neither gain nor lose from my opponent’s scoring (e.g., if I were to gain even partially from his gains, then continuous cooperation would be favored).
If one expects to play only a single round against a specific opponent, then the optimum strategy in Prisoner’s Dilemma is to always defect. Similarly, in a population of individuals with no repeat encounters or within a species incapable of recognizing that an encounter is a repeat encounter, constant competition is favored over cooperation. More relevant to interactions among scientists, however, is the case of many repeat encounters where one remembers previous encounters with a given ‘opponent’. It is this situation that Axelrod and Hamilton [1981] modeled by a computer round robin tournament, first among 14 entries and then among 62 entries of algorithm strategies submitted by a variety of people of different professions. Subsequent computer studies by various investigators simulated the process of biological evolution more closely, incorporating variables such as natural selection (higher birth rate among more successful strategies) and mutation.
In nearly all simulations, the winner was one of the simplest of strategies: tit for tat. Tit for tat cooperates on the first move, then on all subsequent moves duplicates the opponent’s preceding move. Axelrod and Hamilton [1981] call tit for tat “a strategy of cooperation based on reciprocity.” When tit for tat encounters a strategy of all defect, it gets burned on its first cooperative move but thereafter becomes a strategy of all defect, the only viable response to an all defecter. Tit for tat does much better against itself than all defect does against itself, and tit for tat also does much better against various other strategies, because mutual cooperation pays off more than mutual defection.
Axelrod and Hamilton [1981] prove that tit for tat meets the success criteria of initial viability, robustness, and stability for Prisoner’s Dilemma, and they argue that tit for tat is also a successful evolutionary strategy in various species from human to microbe (its reactive element does not require a brain). Some of their examples are highly speculative, while others such as territoriality ring true. Individuals in adjacent territories develop stable boundaries (‘cooperation’), but any attempt by one individual to encroach is met by aggression by the other. In contrast to this dominantly tit for tat behavior with the same individual, one-time encounters with encroaching strangers are consistently met by aggression (all defect).
Tit for tat does have two weaknesses. First, a single accidental defection between two tit for tat players initiates an endless, destructive sequence of mutual defections. Second, a tit for tat population can be invaded temporarily by persistent cooperators. An alternative strategy – win-stay, loseshift – copes with these situations more successfully [Nowak and Sigmund, 1993]. This strategy repeats its former move if it was rewarded by a high score (opponent’s cooperation); otherwise, it changes its move. The strength of this strategy stems from the fact that cooperation by the opponent is more beneficial than their defection. Win-stay, lose-shift quickly corrects mistakes, and it exploits chronic cooperators.
It’s incredible that we scientists make decisions – sometimes difficult, sometimes emotion-laden – based on strategies similar to those used by some single-celled organisms. Success of tit for tat and win-stay, lose-shift in computer games of Prisoner’s Dilemma does not imply that these strategies are appropriate guides for interactions with fellow scientists. Experience shows that the extremes of total cooperation and total competition are also viable for some scientists, although the ‘hawks’ do take advantage of the ‘doves’. Some doves react to being repeatedly taken advantage of by becoming either bitter or hawkish. Tit for tat seems like a more mature reaction to being exploited than does rejection of all cooperation.
Which strategy is best for science? Both cooperation and competition are stimulating to scientific productivity, and in different individuals either appears to be able to give job satisfaction by fulfilling personal needs. Communication of scientific ideas is clearly a win-win, or non-zero-sum
