Thermodynamics of evolutionary games

• How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperators is given by the expectation value of a thermal observable akin to a magnetization. We apply the formalism to the public goods game with three players and show that a phase transition between cooperation and defection occurs that is equivalent to a transition in one-dimensional Ising crystals with long-range interactions. We then investigate the effect of punishment on cooperation and find that punishment plays the role of a magnetic field that leads to an "alignment" between players, thus encouraging cooperation. We suggest that a thermal Hamiltonian picture of the evolution of cooperation can generate other insights about the dynamics of evolving groups by mining the rich literature of critical dynamics in low-dimensional spin systems. © 2018 American Physical Society.

Subject headings

NATURVETENSKAP  -- Biologi -- Evolutionsbiologi (hsv//swe)

NATURAL SCIENCES  -- Biological Sciences -- Evolutionary Biology (hsv//eng)

Keyword

Biology

Defects

Dynamics

Phase transitions

Spin dynamics

Thermodynamics

Evolution of cooperation

Evolutionary games

Expectation values

Hamiltonian dynamics

Long range interactions

Low-dimensional spin systems

Public goods games

Unsolved problems

Hamiltonians

article

expectation

human

magnetic field

mining

phase transition

punishment

Publication and Content Type

ref (subject category)

art (subject category)