Autocratic strategies for iterated games with arbitrary action spaces

Games with two actions ("cooperate" and "defect") have been extremely useful in modeling biological interactions. Despite their utility, however, there are many naturally occurring encounters that these games cannot fully capture. For example, the effort expended in animal grooming or the rate of siderophore production by microbes can take on a continuous range of values. Such interactions are better modeled by games with more general (continuous) action spaces. In this setting, we prove the existence of autocratic strategies that unilaterally enforce linear relationships on the payoffs for repeated games. In particular, we show that a player can often enforce such a relationship by playing only two actions throughout the repeated game.