Statistical measures for defining an individual's degree of independence within state-dependent dynamic games

For organisms living or interacting in groups, the decision-making processes of an individual may be based upon aspects of both its own state and the states of other organisms around it. Much research has sought to determine how group decisions are made, and whether some individuals are more likely to influence these decisions than others. State-dependent modelling techniques are a powerful tool for exploring group decision-making processes, but analyses conducted so far have lacked methods for identifying how dependent an individual's actions are on the rest of the group.

Here, we introduce and evaluate two easy-to-calculate statistics that quantify how dependent an individual's actions are upon the state of a co-player in a two-player state-dependent dynamic game. We discuss the merits of these statistics, and situations in which they would be useful.

Our statistical measures provide a means of quantifying how independent an individual's actions are. They also allow researchers to quantify the output of state-dependent dynamic games, and quantitatively assess the predictions of these models.