Ontology of player & evolutionary game in reductive vs effective theory

In my views of game theory, I largely follow Ariel Rubinstein: 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 was born of classic game theory theory through a series of analogies. These analogies are either generalizations or restrictions of the theory depending on if you’re thinking about the stories or the mathematics. Given this heuristic genealogy of the field — and my enjoyment of heuristic models — I usually do not worry too much about what exactly certain ontic 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 agrees with Ariel Rubinstein and me; some people think that EGT isn’t “just” heuristics. In fact, more recently, I have also shifted some of my uses of EGT from heuristics to abductions. When this happens, it is no longer acceptable for researchers to be willy-nilly with fundamental objects of the theory: strategies, players, and games.

The biggest culprit is the player. In particular, a lot of confusion stems from saying that “cells are players”. In this post, I’d like to explore two of the possible positions on what constitutes players and evolutionary games.

In classical game theory, the concepts of player, strategy, and game are intertwined but relatively straightforward. Players select strategies which are then mapped by the rules of the game to payoffs. But, how does this translate to evolutionary games?

The easiest place to start is payoffs: these are almost always interpreted as changes in fitness. We can take this much as uncontroversial. But fitness itself has a complicated ontology and is part of a more general discussion in biological theory that is beyond EGT. Unfortunately, many in EGT are unaware of these discussions and take their own intuitive views on fitness as definitive.

Since many are computational modelers or think in terms of simulations and agent-based models, they take fitness as a property of an individual organisms. In that case, they can define players as the organisms that receive the payoff. The game then becomes the local interactions that happen between pairs of organisms (or more for multi-player games) — what I would call the reductive game. Since in a the most common EGT setting, what the organisms do in the game is fixed by their genes, this means that under this reductive interpretation players don’t alter their strategies. This is the sort of view of games that many have when studying the evolution of cooperation and that I implicitly had in my old work on the evolution of ethnocentrism (Shultz et al., 2009; Kaznatcheev, 2010b; Kaznatcheev & Shultz, 2011; Hartshorn et al., 2013).

This makes it easy to present classic vs evolutionary game theory as two extremes on the spectrum of decision making. In classic game theory, players are unbounded rational decision-makers. In evolutionary game theory, players are the most bounded possible: they make no decisions at all; their behavior is genetically fixed. For many years, this is how I taught the distinction between classic and evolutionary games to a cognitive science class. From this perspective, it becomes natural for the evolutionary game theorists to gradually build up the decision making capacities of the player. Tag-based models like those for ethnocentrism can be seen as taking a minimal step upwards by allowing the focal to decide to cooperate of defect conditioned on the tag of the alter. Although this characterization behavior is simple, it can allow for a rich analysis as a form of minimal cognition (Beer, 2003). We can even consider a cognitive cost for this extra decision-making ability (Kaznatcheev, 2010a). In Kaznatcheev et al. (2014), I pushed this genotype to behavior map even further by having evolving agents act rationally on their evolved perceptions of the game payoffs and (potentially-biased) estimates of other’s probability to cooperate (for this direction, see also Masel, 2007).

But fitness doesn’t have to be defined individually.

An alternative perspective is to see fitness as defined only for populations. This is the perspective that makes the most sense to me when operationalizing fitness in microscopic systems; especially when using typical fitness measures like growth-rates. In that case, the player is the (sub)population that receives the payoff of fitness. The game then becomes the macroscopic coupling between (sub)populations made up of microscopic agents. It is even misleading to call this coupling an “interaction” since that suggest something too active and direct — but the coupling could be as indirect as two populations feeding on a single resource in batch culture. This population-level description is what I call an effective game. Given its roots in operationalization of microscopic systems, the effective games can be measured directly and we recently developed a game assay for this purpose (Kaznatcheev et al., 2017).

This perspective has some curious consequences. Since the players are populations, the individuals organisms — or behaviorally identical classes of them — are the strategies. The player is not static but carries out a ‘decision making process’ specified by the rules of the evolutionary dynamics. This is usually described by the replicator equation. Make what you will of the correspondence between replicator dynamics and Bayesian inference, reinforcement learning and other forms of rational decision making (Borgers & Sarin, 1997). To me, this seems like both a closer correspondence to the aspirations of classical game theory and easier to link to experiment.

It is also tempting to draw from behavioral ecology and try to walk a middle ground that combines both. Define organisms as (reductive) players, their non-genetically determined behaviors as (reductive) strategies, and the behavior-affecting payoffs of the resultant interactions as the (reductive) game. Based on my debates with him, I think this is how Joel Brown defines games. To this, I would add the population level. Consider the ecological dynamics coupling the populations of organisms as the effective game. This combined would result in a game nested inside a game with two different concepts of fitness. In general, this can be a mess. But if the dynamics of decision making by both the reductive and effective players are described by the replicator equation then maybe we can undo this factoring. This would allow a single level of description as an unfactored effective game with strategies as the behavioral states within individual organisms.

What does this mean for “cells are players”? For the reductive game, each individual cell is a player. For the effective game, the population of cells is a player.

Under both interpretations thought, the motto “don’t treat the player, treat the game” is probably still good advice.


Beer, R.D. (2003). The Dynamics of Active Categorical Perception in an Evolved Model Agent. Adaptive Behavior. 11(4): 209-243.

Börgers, T., & Sarin, R. (1997). Learning through reinforcement and replicator dynamics Journal of Economic Theory, 77 (1), 1-14

Hartshorn, M., Kaznatcheev, A., & Shultz, T. (2013). The Evolutionary Dominance of Ethnocentric Cooperation. Journal of Artificial Societies and Social Simulation, 16 (3)

Kaznatcheev, A. (2010a). The cognitive cost of ethnocentrism. In S. Ohlsson & R. Catrambone (Eds.), Proceedings of the 32nd annual conference of the cognitive science society.

Kaznatcheev, A. (2010b). Robustness of ethnocentrism to changes in inter-personal interactions. Complex Adaptive Systems – AAAI Fall Symposium.

Kaznatcheev, A., & Shultz, T.R. (2011). Ethnocentrism Maintains Cooperation, but Keeping One’s Children Close Fuels It. In L. Carlson, C, Hoelscher, & T.F. Shipley (Eds), Proceedings of the 33rd annual conference of the cognitive science society.

Kaznatcheev, A., Montrey, M., & Shultz, T.R. (2014). Evolving useful delusions: Subjectively rational selfishness leads to objectively irrational cooperation. Proceedings of the 36th annual conference of the cognitive science society. arXiv: 1405.0041v1

Kaznatcheev, A., Peacock, J., Basanta, D., Marusyk, A., & Scott, J. G. (2017). Fibroblasts and alectinib switch the evolutionary games that non-small cell lung cancer plays. bioRxiv, 179259.

Lyon, P. (2006). The biogenic approach to cognition. Cognitive Processing, 7, 11-29.
Shultz, T. R., Hartshorn, M., & Hammond, R. A. (2008). Stages in the evolution of ethnocentrism. In B. Love, K. McRae, & V. Sloutsky (Eds.), Proceedings of the 30th annual conference of the cognitive science society.

Masel, J. (2007). A Bayesian model of quasi-magical thinking can explain observed cooperation in the public good game. Journal of Economic Behavior and Organization, 64(2), 216-231.

Shultz, T. R., Hartshorn, M., & Kaznatcheev, A. (2009). Why is ethnocentrism more common than humanitarianism? In N. Taatgen & H. van Rijn (Eds.), Proceedings of the 31st annual conference of the cognitive science society.

About Artem Kaznatcheev
From the Department of Computer Science at Oxford University and Department of Translational Hematology & Oncology Research at Cleveland Clinic, I marvel at the world through algorithmic lenses. My mind is drawn to evolutionary dynamics, theoretical computer science, mathematical oncology, computational learning theory, and philosophy of science. Previously I was at the Department of Integrated Mathematical Oncology at Moffitt Cancer Center, and the School of Computer Science and Department of Psychology at McGill University. In a past life, I worried about quantum queries at the Institute for Quantum Computing and Department of Combinatorics & Optimization at University of Waterloo and as a visitor to the Centre for Quantum Technologies at National University of Singapore. Meander with me on Google+ and Twitter.

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