Researchers have used a mathematical model to study how classic game-theory contests, such as the prisoner's dilemma, the game of chicken and rock-paper-scissors, behave when rewards fluctuate randomly over time rather than remaining fixed. Traditional versions of these games assume static payoffs, which limits their usefulness for modelling real-world behaviour, where the risks and rewards of a given strategy are shaped by external, uncontrollable factors, such as weather affecting a rabbit's food supply. By adding randomly varying returns to the models, the researchers found that these simple games develop far richer and sometimes more precarious dynamics than previously understood.

In the standard prisoner's dilemma, the model converges on a single stable outcome in which everyone betrays everyone else. Introducing even small random variation in rewards creates a second stable point where cooperators and defectors coexist, and with greater variation the "everyone defects" outcome becomes unstable, leaving only cooperators. In the game of chicken, no variation produces universal survival, but adding noise causes a non-swerving population to emerge, and further variation produces a bistable state that flips between survival and collision. Rock-paper-scissors, which normally cycles endlessly with no stable point, develops new stable and unstable points under random rewards, altering how quickly the population settles into cycling behaviour.