Students and researchers from HSE University and the Landau Institute for Theoretical Physics have examined the widely known ‘Prisoner’s Dilemma’ game using methods from statistical physics. They used the mean-field concept, a common tool for studying the physics of many-particle systems, to describe human decision-making processes. Researchers suggest that this model may be helpful for understanding systems with many participants. The results of the study are published in the September issue of the Physics Review Research journal.
The paper’s authors looked at the spatial variation of the ‘Prisoner’s Dilemma’ game—the Nowak-May game—from a new perspective. In particular, they included statistical physics methods in the game’s rules. ‘In the classic version of the dilemma, there are two “players.” We used a modified version with a large number of agents,’ said Lev Shchur, Professor, Department Head and Chief Research Fellow at MIEM HSE.
The game is played with participants’ ‘nearest neighbours’, just like communicating with family and co-workers in real life. The players’ individual opinions sum up to a kind of average opinion, which in the suggested model directly impacts the decisions made by the players. Then an individual’s behaviour is determined by this ‘mean-field,’ formed by the behaviour of all individuals in the population. This construction is successfully used in statistical physics, which studies the emergent behaviour of large numbers of interacting particles.
The main feature of the model is that it considers both the structure of the population and the mean-field impact. The authors believe that the model might play a key role in the study of social systems. For example, in the paper, the presence of a mean-field is interpreted as the media’s impact on personal decisions, something that previous models of this kind haven’t considered.
It has been established that the spatial version of the Prisoner’s Dilemma game features sharp transitions between different steady states. The authors find that the new approach allows for a smoothening of these transitions. This is the first indication of the co-existence of two types of transitions—sharp and smooth—in deterministic systems.
The scholars believe that this model may help understand how systems with large numbers of participants behave or how the media impacts individual choices.
Evgeni Burovski, Associate Professor at the HSE School of Applied Mathematics‘We have obtained some exciting results. In classical evolutionary game models, Darwinian processes are described in terms of well-mixed populations, and the information on the structure of the population is lost,’ explained Evgeni Burovski, Associate Professor at the HSE School of Applied Mathematics. ‘We are suggesting an alternative approach — games both with a local neighborhood and the self-consistent mean-field opinion. This approach helps consider the impact on decision making that the closest environment (colleagues and friends) has, as well as the things that people hear or read in the news.’
The suggested approach can be applied to a broad class of spatial evolutionary games with both deterministic and stochastic rules. Given the interdisciplinary nature of the study, the researchers hope to collaborate with their colleagues working in sociology and economics to further develop and apply the model in trials.
Mean-field interactions in evolutionary spatial games
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