Evolutionary games with variable payoffs

Matrix games, defined by a set of strategies and a corresponding matrix of payoffs, are commonly used to model animal populations because they are both simple and generate meaningful results. It is generally assumed that payoffs are independent of time. However, the timing of contests in real populations may have a marked effect on the value of rewards. We consider matrix games where the payoffs are functions of time. Rules are found which hold in this more general situation, and the complexity of possible behaviour is underlined by demonstrating other conditions which do not hold and an illustrative game.