Kind Hearts Rejoice! Evolution Does Not Favor the Jerks – A Game Theory Analysis
An ongoing debate in the evolutionary biological community is whether or not selfish actions are evolutionary favorable. It seems like the answer should be yes right? Survival of the fittest can easily be interpreted as doing everything possible to benefit yourself and to ensure you are living in the best conditions possible. Yet how stable can this mindset be for an entire population under its influence? An article published last August in Nature Communications by Christoph Adami & Arend Hintze provided new evidence for the position that selfish strategies are not evolutionarily preferable.
Adami & Hintze build their argument using a new class of probabilistic and conditional strategies within the realm of two-player iterated games that was recently discovered by Press and Dyson, known as “zero-determinant (ZD)” strategies. Following a ZD strategy allows one to unilaterally fix an opponent’s payoff or extort the opponent to accept an unequal share of payoffs. ZD strategies can be thought of as both “memory-one” strategies, in which a player’s current turn is decided solely by his opponent’s previous move (tit-for-tat), as well as stochastic conditional strategies that are defined by a set number of probabilities that represent the possible outcomes of the last encounter between a player and his opponent. Say we are looking at a game where there are four possible outcomes with respective probabilities of p1, p2, p3, and p4. Outcomes 1 and 4 are instances where the two players make the same move while outcomes 2 and 3 are the cross-terms where they choose different moves. ZD strategies involve fixing p2 and p3 to be a function of p1 and p4. Press and Dyson went on to show that the payoff that an opponent reaps is defined by the payoffs and the two remaining probabilities p1 and p4 only.
It is also possible for a ZD strategist to extort an uneven share of the payoffs from the opponent who could refuse it (Ultimatum game anyone?). In these “extortionate” games, the victim whose strategy is being taken advantage of can increase his own payoff by modifying his own strategy, however this will ultimately increase the extorting player’s payoff. Therefore, Press and Dyson concluded that a ZD strategy will always beat an opponent who adapts his strategy to maximize his payoff. Adami & Hintze show in their paper that these ZD strategies are in fact evolutionarily unstable, are easily beaten by fairly common strategies, and quickly evolve to become non-ZD strategies.
Adami & Hintze measured economic stability by using the steady-state payoffs of two players engaged in an unlimited encounter as the one-shot payoff matrix between their strategies. They went on to apply Maynard Smith’s evolutionary stable strategy conditions to that effective payoff matrix, and showed that ZD strategies are at most weakly dominant. In other words, their payoff against self is equal to what any other strategy receives playing against them. It was also found that those ZD extortionists are not even weakly dominant except in one limiting case. It is important to note that it is possible for ZD strategies to win every single match up against non-ZD strategies, however this situation is evolutionary unstable and eventually driven to extinction.
With respect to the mutation of ZD strategies over time, Adami & Hintze found that ZD strategies are mutationally unstable even when they are the evolutionary stable strategy at zero mutation rate. As the ZD mutants that aren’t necessarily ZD strategists proliferate, they represent an unyielding obstacle to the evolutionary establishment of ZD. Instead of taking over, it was found that the ZD strategy evolves into a harmless cooperating or defecting strategy. The jerks turn into those they were exploiting in the first place!
Adami & Hintze note that there is one situation in which ZD strategies can stably and reliably outcompete other strategies. In order for this situation to come to fruition, the ZD strategists must possess some kind of informational advantage, whether that be a longer-memory strategy that they can use the probe their opponents strategy, or by using a tag to recognize when they are playing against other ZD strategists and conditionally cooperate.
In conclusion, I find it rather reassuring that there is strong evidence that selfish strategies such as the ZD ones described above are not evolutionarily healthy. One can’t help but notice that if Adami & Hintze’s experiments are scientifically valid and accurate, then the existence of the human race today is living proof that we are not collectively (at least over the history of our species) selfish jerks. Though humanity contains a great deal of the “in it for themselves” types, philanthropists and benevolent human beings abound. We can only hope that in our current society the ZD strategists aren’t the majority. According to Adami & Hintze, this would spell out our extinction in the future as the circle of extortion started by the ZD strategist comes full circle and humanity is extorted out of its own existence.
Sources:
http://www.nature.com/ncomms/2013/130801/ncomms3193/full/ncomms3193.html
Adami, C. and Hintze, A. Evolutionary Instability of zero-determinant strategies demonstrates that winning is not everything. Nat Commun. 4. 2193 (2013).