Changing rewards reshape strategies in classic game-theory models

Researchers used a mathematical model to examine how randomly changing rewards affect the evolution of strategies in classic game-theory models. The study covers the prisoner’s dilemma, chicken and rock-paper-scissors.

Traditional models keep the payoff for each outcome fixed. The new model adds external changes unrelated to player behavior and finds that even small payoff fluctuations can create new stable states.

Cooperation emerges in the prisoner’s dilemma

Under fixed conditions, the prisoner’s dilemma quickly converges on a state where everyone defects. When payoffs vary, a second stable point appears, allowing cooperators and defectors to coexist.

With greater variation, the defector state becomes unstable and only cooperation remains in the model. That differs from the standard result that cooperation is a losing strategy.

Chicken shifts between two outcomes

In chicken, fixed payoffs produce a stable outcome in which everyone swerves. A small change in rewards creates a population that does not swerve, while stronger noise produces switching between survival and crashing.

Rock-paper-scissors develops cycles

Standard rock-paper-scissors has no stable point: choices continually rotate among the three strategies. Random payoffs introduce stable and unstable points, while uneven rewards can produce predictable cycles in the frequencies of rock, paper and scissors.

The authors say such models may help in studying economic behavior. The research was published in Physical Review Letters in 2026, DOI: 10.1103/3yby-qq2n.