Stewart and Plotkin, the Prisoner’s Dilemma and Generous Strategies

Posted: 10/16/2013 - 08:01

I’ve been a game theory fan for many years, particularly as it relates to showing that cooperative behavior indeed creates true “win-win” situations. So I was excited to read a work of University of Pennsylvania professors Alexander J. Stewart and Joshua B. Plotkin, ‘From Extortion to Generosity, Evolution in the Iterated Prisoner’s Dilemma‘, published recently in the Proceedings of the National Academy of Science (PNAS).

I was even more excited by their findings, which underscores (once again) that the evolution and validity of cooperation is a better approach than using the power of extortion to gain cooperation. It is definitely an academic study worthy of “unpacking.”

The Stewart and Plotkin study sheds some a new light on a classic question concerning human behaviour: is it better to gain a lot at the expense of another person, or to gain slightly less while simultaneously promoting the other’s wellbeing? They explore this question through the application of a spin on the classic Prisoner’s Dilemma game. A Prisoner’s Dilemma is a situation, common in society and business, where the short-term self-interest of each party conflicts with the parties’ long-term interests. Research has shown that over the long term, people (or organisations) are better off if they cooperate. I wrote about the Prisoner’s Dilemma for this column in May, 2011, ‘John Nash, Robert Axelrod, Game Theory and the art of playing nice’.

Stewart and Plotkin’s work is full of rather dense mathematical equations and Venn diagrams that looks at what they reference as “zero determinant (ZD) strategies.” They write: “Recent work has uncovered a remarkable class of extortion strategies that provide one player a disproportionate payoff when facing an unwitting opponent.” This is what is called the zero determinant (ZD) and is typified by a solution where one party “wins” at a much higher rate than the opponent. They identify ZD, as “a new class of probabilistic and conditional strategies” that unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner’s Dilemma no matter the opponent’s strategy, or else determines the ratio between a ZD player’s and their opponent’s expected payoff.

While the math is impressive, it’s their conclusion that excites me. Simply put, they find (like all the other research!) that cooperation and generosity are better modes of behaviour than obstinance and self-interest when it comes to thriving within a society.

While extortion strategies “perform very well in head-to-head competitions,” at least for a brief period of time, Stewart and Plotkin write, “they fare poorly in large, evolving populations.”

Common sense – right?

What is maybe not so common sense is that Stewart and Plotkin look beyond ZD extortion strategies to something they refer to as “generous ZD strategies.” The generous ZD strategy subset involves active cooperation with others and the forgiveness of defection, thus replacing the extortionists.

In general, Stewart and Plotkin continue, “Extortion and ZD strategies are disfavored by evolution in populations. This has led to the view that ZD strategies are of importance only in the setting of classical two-player game theory, and not in evolving populations.”

Their conclusion: when the various Prisoner’s Dilemma strategies are in play, generous strategies are “disproportionately favoured” over extortion strategies. That’s because they “stabilise cooperative behaviour.”

Stewart and Plotkin’s results underscore the value of collaboration and cooperation – major tenets of the Vestedmodel – and help explain the evolution of cooperation in the Prisoner’s Dilemma scenario.

Of course – it makes sense to me. Be nice and cooperate and you will win much more often than not. Be generous and you will really win friends and influence others, which will come back in positive ways in the future. While some would call this good karma, others need the underlying math and science to prove common sense. So I am thankful Stewart and Plotkin took the time to do the math and – yet once again – prove you can indeed win more with a “what’s-in-it-for-we” (WIIFWe) mindset!


About The Author

Kate Vitasek's picture

Kate Vitasek is an international authority for her award-winning research and Vested business model for highly collaborative relationships. She is the author of six books on the Vested model and a faculty member at the University of Tennessee. She has been lauded by World Trade Magazine as one of the “Fabulous 50+1” most influential people impacting global commerce.