Half a century of evolutionary games
Authors: Alger Ingela , Couto Marta , Gardner Andy , Glynatsi Nikoleta , Cleve Jeremy Van , Stein Alexander , Leimar Olof 
Published: May 2023

Evolutionary game theory (EGT) is an indispensable part of modern evolutionary theory. 2023 marks the 50th anniversary of the article by John Maynard Smith and George Price that defined central concepts and became a focal point in the field. EGT can address biological questions where there is no obvious “best thing” that an individual can do, because their payoff depends not only on what they do but also on what their ‘opponents’ do. In the last 50 years, EGT has expanded and become integrated with a range of other theoretical methods. A recent theme issue reviewed the history and methodology of the field and presented novel research. In this seminar, some of the authors from the issue will talk about the topic and their papers.

Evolutionarily stable preferences

The 50-year old concept of an evolutionarily stable strategy provided a key tool for theorists to model ultimate drivers of behaviour in social interactions. For decades, economists ignored ultimate drivers and used models in which individuals choose strategies based on their preferences—a proximate mechanism for behaviour—and the distribution of preferences in the population was taken to be fixed and given. This article summarizes some key findings in the literature on evolutionarily stable preferences, which in the past three decades has proposed models that combine the two approaches: individuals inherit their preferences, the preferences determine their strategy choices, which in turn determine evolutionary success. One objective is to highlight complementarities and potential avenues for future collaboration between biologists and economists.

Cooperation and coordination in heterogeneous populations

One landmark application of evolutionary game theory is the study of social dilemmas. This literature explores why people cooperate even when there are strong incentives to defect. Much of this literature, however, assumes that interactions are symmetric. Individuals are assumed to have the same strategic options and the same potential pay-offs. Yet many interesting questions arise once individuals are allowed to differ. Here, we study asymmetry in simple coordination games. In our set-up, human participants need to decide how much of their endowment to contribute to a public good. If a group’s collective contribution reaches a pre-defined threshold, all group members receive a reward. To account for possible asymmetries, individuals either differ in their endowments or their productivities. According to a theoretical equilibrium analysis, such games tend to have many possible solutions. In equilibrium, group members may contribute the same amount, different amounts or nothing at all. According to our behavioural experiment, however, humans favour the equilibrium in which everyone contributes the same proportion of their endowment. We use these experimental results to highlight the non-trivial effects of inequality on cooperation, and we discuss to which extent models of evolutionary game theory can account for these effects.

The rarer-sex effect

The study of sex allocation—that is, the investment of resources into male versus female reproductive effort—yields among the best quantitative evidence for Darwinian adaptation, and has long enjoyed a tight and productive interplay of theoretical and empirical research. The fitness consequences of an individual's sex allocation decisions depend crucially upon the sex allocation behaviour of others and, accordingly, sex allocation is readily conceptualized in terms of an evolutionary game. Here, I investigate the historical development of understanding of a fundamental driver of the evolution of sex allocation—the rarer-sex effect—from its inception in the writing of Charles Darwin in 1871 through to its explicit framing in terms of consanguinity and reproductive value by William D. Hamilton in 1972. I show that step-wise development of theory proceeded through refinements in the conceptualization of the strategy set, the payoff function and the unbeatable strategy.

The future of theoretical evolutionary game theory

volutionary game theory is a truly interdisciplinary subject that goes well beyond the limits of biology. Mathematical minds get hooked up in simple models for evolution and often gradually move into other parts of evolutionary biology or ecology. Social scientists realize how much they can learn from evolutionary thinking and gradually transfer insight that was originally generated in biology. Computer scientists can use their algorithms to explore a new field where machines not only learn from the environment, but also from each other. The breadth of the field and the focus on a few very popular issues, such as cooperation, comes at a price: several insights are re-discovered in different fields under different labels with different heroes and modelling traditions. For example, reciprocity or spatial structure are treated differently. Will we continue to develop things in parallel? Or can we converge to a single set of ideas, a single tradition and eventually a single software repository? Or will these fields continue to cross-fertilize each other, learning from each other and engaging in a constructive exchange between fields? Ultimately, the popularity of evolutionary game theory rests not only on its explanatory power, but also on the intuitive character of its models.

Evolutionarily stable strategy analysis and its links to demography and genetics through invasion fitness

Evolutionarily stable strategy (ESS) analysis pioneered by Maynard Smith and Price took off in part because it often does not require explicit assumptions about the genetics and demography of a population in contrast to population genetic models. Though this simplicity is useful, it obscures the degree to which ESS analysis applies to populations with more realistic genetics and demography: for example, how does ESS analysis handle complexities such as kin selection, group selection and variable environments when phenotypes are affected by multiple genes? In this paper, I review the history of the ESS concept and show how early uncertainty about the method lead to important mathematical theory linking ESS analysis to general population genetic models. I use this theory to emphasize the link between ESS analysis and the concept of invasion fitness. I give examples of how invasion fitness can measure kin selection, group selection and the evolution of linked modifier genes in response to variable environments. The ESSs in these examples depend crucially on demographic and genetic parameters, which highlights how ESS analysis will continue to be an important tool in understanding evolutionary patterns as new models address the increasing abundance of genetic and long-term demographic data in natural populations.

Stackelberg evolutionary game theory: how to manage evolving systems

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest control). Often the worst strategy for the leader is to adopt a constant aggressive strategy (e.g. overfishing in fisheries management or maximum tolerable dose in cancer treatment). Taking into account the ecological dynamics typically leads to better outcomes for the leader and corresponds to the Nash equilibria in game-theoretic terms. However, the leader’s most profitable strategy is to anticipate and steer the eco-evolutionary dynamics, leading to the Stackelberg equilibrium of the game. We show how our results have the potential to help in fields where humans try to bring an evolutionary system into the desired outcome, such as, among others, fisheries management, pest management and cancer treatment. Finally, we discuss limitations and opportunities for applying SEGs to improve the management of evolving biological systems.

Game theory in biology: 50 years and onwards

Game theory in biology gained prominence 50 years ago, when Maynard Smith Price formulated the concept of an evolutionarily stable strategy (ESS). Their aim was to explain why conflicts between animals of the same species usually are of a ‘limited war’ type, not causing serious injury. They emphasized that game theory is an alternative to previous ideas about group selection, which were used by ethologists to explain limited aggression. Subsequently, the ESS concept was applied to many phenomena with frequency dependence in the evolutionary success of strategies, including sex allocation, alternative mating types, contest behaviour and signalling, cooperation, and parental care. Both the analyses of signalling and cooperation were inspired by similar problems in economics and attracted much attention in biology. Here we give a perspective on which of the ambitions in the field have been achieved, with a focus on contest behaviour and cooperation. We evaluate whether the game-theoretical study of the evolution of cooperation has measured up to expectations in explaining the behaviour of non-human animals. We also point to potentially fruitful directions for the field, and emphasize the importance of incorporating realistic behavioural mechanisms into models.