Outcome (game theory)

Mechanism (biology)

Gene

Quantum mechanics

Transition (genetics)

Demography

Philosophy

Social dilemma

Biology

Inclusive fitness

Microeconomics

Social psychology

Dynamics (music)

Expression (computer science)

Pedagogy

Selection (genetic algorithm)

Economics

Computer science

Simple (philosophy)

Phenomenon

Evolutionary biology

Non-cooperative game

Social evolution

Genetics

Physics

Psychology

Repeated game

Evolutionarily stable strategy

Epistemology

Population

Sociology

Artificial intelligence

Prosocial behavior

Evolutionary dynamics

Mathematical economics

Evolutionary game theory

Game theory

Programming language

Strong reciprocity

Natural selection

Proceedings of the National Academy of Sciences

The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals' behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds [Formula: see text], where k is the average number of neighbors of an individual and [Formula: see text] captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.

Evolutionary dynamics with game transitions