We had a great workshop on information and entropy in biological systems, and now you can see what it was like. I think I’ll post these talks one a time, or maybe a few at a time, because they’d be overwhelming taken all at once.
So, let’s dive into Chris Lee’s exciting ideas about organisms as ‘information evolving machines’ that may provide ‘disinformation’ to their competitors. Near the end of his talk, he discusses some new results on an ever-popular topic: the Prisoner’s Dilemma. You may know about this classic book:
• Robert Axelrod, The Evolution of Cooperation, Basic Books, New York, 1984. Some passages available free online.
If you don’t, read it now! He showed that the simple ‘tit for tat’ strategy did very well in some experiments where the game was played repeatedly and strategies who did well got to ‘reproduce’ themselves. This result was very exciting, so a lot of people have done research on it. More recently a paper on this subject by William Press and Freeman Dyson received a lot of hype. I think this is a good place to learn about that:
• Mike Shulman, Zero determinant strategies in the iterated Prisoner’s Dilemma, The n-Category Café, 19 July 2012.
Chris Lee’s new work on the Prisoner’s Dilemma is here, cowritten with two other people who attended the workshop:
• The art of war: beyond memory-one strategies in population games, PLOS One, 24 March 2015.
Abstract. We show that the history of play in a population game contains exploitable information that can be successfully used by sophisticated strategies to defeat memory-one opponents, including zero determinant strategies. The history allows a player to label opponents by their strategies, enabling a player to determine the population distribution and to act differentially based on the opponent’s strategy in each pairwise interaction. For the Prisoner’s Dilemma, these advantages lead to the natural formation of cooperative coalitions among similarly behaving players and eventually to unilateral defection against opposing player types. We show analytically and empirically that optimal play in population games depends strongly on the population distribution. For example, the optimal strategy for a minority player type against a resident tit-for-tat (TFT) population is ‘always cooperate’ (ALLC), while for a majority player type the optimal strategy versus TFT players is ‘always defect’ (ALLD). Such behaviors are not accessible to memory-one strategies. Drawing inspiration from Sun Tzu’s the Art of War, we implemented a non-memory-one strategy for population games based on techniques from machine learning and statistical inference that can exploit the history of play in this manner. Via simulation we find that this strategy is essentially uninvadable and can successfully invade (significantly more likely than a neutral mutant) essentially all known memory-one strategies for the Prisoner’s Dilemma, including ALLC (always cooperate), ALLD (always defect), tit-for-tat (TFT), win-stay-lose-shift (WSLS), and zero determinant (ZD) strategies, including extortionate and generous strategies.
And now for the talk! Click on the talk title here for Chris Lee’s slides, or go down and watch the video:
Abstract. Information theory is an intuitively attractive way of thinking about biological evolution, because it seems to capture a core aspect of biology—life as a solution to “information problems”—in a fundamental way. However, there are non-trivial questions about how to apply that idea, and whether it has actual predictive value. For example, should we think of biological systems as being actually driven by an information metric? One idea that can draw useful links between information theory, evolution and statistical inference is the definition of an information evolving machine (IEM) as a system whose elements represent distinct predictions, and whose weights represent an information (prediction power) metric, typically as a function of sampling some iterative observation process. I first show how this idea provides useful results for describing a statistical inference process, including its maximum entropy bound for optimal inference, and how its sampling-based metrics (“empirical information”, Ie, for prediction power; and “potential information”, Ip, for latent prediction power) relate to classical definitions such as mutual information and relative entropy. These results suggest classification of IEMs into several distinct types:
1. Ie machine: e.g. a population of competing genotypes evolving under selection and mutation is an IEM that computes an Ie equivalent to fitness, and whose gradient (Ip) acts strictly locally, on mutations that it actually samples. Its transition rates between steady states will decrease exponentially as a function of evolutionary distance.
2. “Ip tunneling” machine: a statistical inference process summing over a population of models to compute both Ie, Ip can directly detect “latent” information in the observations (not captured by its model), which it can follow to “tunnel” rapidly to a new steady state.
3. disinformation machine (multiscale IEM): an ecosystem of species is an IEM whose elements (species) are themselves IEMs that can interact. When an attacker IEM can reduce a target IEM’s prediction power (Ie) by sending it a misleading signal, this “disinformation dynamic” can alter the evolutionary landscape in interesting ways, by opening up paths for rapid co-evolution to distant steady-states. This is especially true when the disinformation attack targets a feature of high fitness value, yielding a combination of strong negative selection for retention of the target feature, plus strong positive selection for escaping the disinformation attack. I will illustrate with examples from statistical inference and evolutionary game theory. These concepts, though basic, may provide useful connections between diverse themes in the workshop.