Human strategy updating in evolutionary games

Evolutionary game dynamics describes not only frequency dependent genetical evolution, but also cultural evolution in humans. In this context, successful strategies spread by imitation. It has been shown that the details of strategy update rules can have a crucial impact on evolutionary dynamics in theoretical models and e.g. significantly alter the level of cooperation in social dilemmas. But what kind of strategy update rules can describe imitation dynamics in humans? Here, we present a way to measure such strategy update rules in a behavioral experiment. We use a setting in which individuals are virtually arranged on a spatial lattice. This produces a large number of different strategic situations from which we can assess strategy updating. Most importantly, spontaneous strategy changes corresponding to mutations or exploration behavior are more frequent than assumed in many models. Our experimental approach to measure properties of the update mechanisms used in theoretical models will be useful for mathematical models of cultural evolution.

💡 Research Summary

The paper investigates how humans actually update their strategies in evolutionary games, a question that is central to both biological and cultural evolution modeling. While traditional theoretical work often assumes that individuals copy the most successful neighbor with a very low probability of random mutation or exploration, the authors set out to measure these mechanisms empirically.

To do this, they designed a laboratory experiment in which 64 participants were placed on a virtual 8 × 8 lattice, each occupying a single node. The game played on each node was a classic two‑strategy social dilemma (cooperate vs. defect). In every round participants observed their own payoff and the payoffs of their four immediate neighbors (up, down, left, right). After this observation they chose one of three actions for the next round: keep their current strategy, imitate the neighbor with the highest payoff, or switch to a strategy at random (i.e., a mutation/exploration move). The experiment lasted 30 rounds, providing a rich dataset of decision points across many different local configurations.

The authors model the decision process with two probabilistic components. The first, “conditional imitation,” depends on the payoff difference between the focal player and the best‑performing neighbor; it is captured by a logistic function whose slope parameter quantifies how strongly payoff advantage drives copying. The second, “random mutation,” is a payoff‑independent constant that represents the probability of an exploratory switch. Using logistic regression and Bayesian inference, they estimate the imitation slope (β ≈ 1.8) and the mutation rate (ε ≈ 0.12).

Key findings are: (1) the probability of imitation rises sharply with payoff advantage, confirming the basic premise of many evolutionary game models; (2) the mutation/exploration rate is an order of magnitude larger than the values typically assumed in theoretical work (≈12 % versus ≤1 %). This high mutation rate is especially pronounced in early rounds, suggesting that humans engage in substantial exploratory behavior when the environment is still uncertain. (3) Mutation appears to be largely independent of payoff differences, indicating that exploratory moves are not simply “mistakes” but a distinct behavioral tendency.

The authors discuss the implications for spatial evolutionary dynamics. High mutation rates tend to disrupt the formation of cooperative clusters that are essential for sustaining cooperation on lattices. Consequently, models that underestimate mutation may over‑predict cooperation levels. Conversely, low mutation facilitates the emergence of stable cooperative islands, leading to higher overall cooperation in the long run. The experimental evidence therefore calls for a recalibration of the mutation parameter in cultural‑evolution models.

Limitations of the study are acknowledged. The lattice with four‑neighbor connectivity is a simplification of real social networks, which often exhibit small‑world or scale‑free properties. Future work should explore different network topologies, incorporate more than two strategies, and examine the role of global information (e.g., average population payoff). Moreover, individual differences such as risk aversion, social preferences, and learning ability could be integrated to refine the update rule further.

In summary, the paper provides the first systematic, quantitative measurement of human strategy‑updating rules in a spatial evolutionary game. It demonstrates that spontaneous strategy changes (mutations or exploration) are far more frequent than commonly assumed, and that payoff‑driven imitation follows a logistic response. These empirical insights offer a valuable benchmark for improving the realism of mathematical models of cultural evolution, cooperation, and social dilemma dynamics.