Two conceptions of evolutionary games: reductive vs effective

Abstract

Evolutionary game theory (EGT) was born from economic game theory through a series of analogies. Given this heuristic genealogy, a number of central objects of the theory (like strategies, players, and games) have not been carefully defined or interpreted. A specific interpretation of these terms becomes important as EGT sees more applications to understanding experiments in microscopic systems typical of oncology and microbiology. In this essay, I provide two interpretations of the central objects of games theory: one that leads to reductive games and the other to effective games. These interpretation are based on the difference between views of fitness as a property of individuals versus fitness as a summary statistic of (sub)populations. Reductive games are typical of theoretical work like agent-based models. But effective games usually correspond more closely to experimental work. However, confusing reductive games for effective games or vice-versa can lead to divergent results, especially in spatially structured populations. As such, I propose that we treat this distinction carefully in future work at the interface of EGT and experiment.In my views of game theory, I largely follow Rubinstein (2012): game theory is a set of fables. A collection of heuristic models that helps us structure how we make sense of and communicate about the world. Evolutionary game theory (EGT) was born of classic game theory through a series of analogies. Given this heuristic genealogy of the field, it is usually alright to not worry too much about what exactly terms like strategy, player, or game really mean or refer to. I am usually happy to leave these terms ambiguous so that they can motivate different readers to have different interpretations and subsequently push for different models of different experiments. I think it is essential for heuristic theories to foster this diverse creativity: anything goes.However, not everyone would agree with Rubinstein and me; some people think that EGT isn't "just" heuristics. EGT is also directly empirically useful for questions in both mathematical oncology and the evolution of microorganisms. Microscopic experimental systems in which EGT has been use- (Kaznatcheev et al. 2017b). But when we actually start doing experiments like these, it is no longer acceptable to be willy-nilly with fundamental objects of the theory: strategies, players, and games. The biggest culprit is the player. In particular, I think that a lot of confusion stems from saying that "cells are players".In classical game theory, the concepts of player, strategy, and game are intertwined but relatively straightforward. Players use a rational decision process to select strategies which are then mapped by the rules of the game to payoffsthe utility given to the players. Or, as I say more awkwardly in the first column of table 1: utility is given to a player based on its strategy which results from a rational decision process carried out by the player. All of this is summarized as the game. But, how does this classic pict...

Fibroblasts and Alectinib switch the evolutionary games played by non-small cell lung cancer

“…Previous work has considered games like snowdrift [24], stag hunt [25], rock-paper-scissors [21], and public goods [23,26] alongside experiments. Instead, we experimentally operationalize the effective game (see [15,16]) as an assayable hidden variable of a population and its environment. We define the effective game as the game played by an idealized population that shows the same frequency dynamics as the experimental population under consideration.…”

“…We do this by having each row correspond to a strategy's fitness function with the column entries as the p = 1 and p = 0 intersects of this line of best fit. These payoff matrix entries are abstract phenomenological quantities that could be implemented by various biological or physical processes [15]. If we look at our empirical measurements for DMSO + CAF (upper-right quadrant Figure 4b) we see the Leader game, and Deadlock in the other three cases (we will use DMSO to illustrate the Deadlock game).…”

“…We measured fluorescent area from time-lapse images via python code using the OpenCV package and used this as our units of size for populations. See Kaznatcheev [15] for a discussion of fitness and replicator dynamics under various definition of population size. We cleaned images by renormalizing them (GFP and mCherry intensities vary over different orders of magnitude), removed vignetting with CLAHE, and finally thresholded to identify fluorescent regions.…”

“…All of these microdynamical details are buried in the definition of experimental fitness. This allows us to focus on effective games [15] and avoid potential confusions over aspects like spatial structure [16].…”

“…We aimed to come to a quantitative understanding of how these dynamics were affected by clinically relevant concentrations of Alectinib (0.5µM; see [14]) in the presence or absence of CAFs isolated from a lung cancer. To achieve this, we developed an assay for quantifying effective games [15,16] that is of independent interest to the general study of microscopic systems.…”