Background
In evolutionary game theory, one can what kinds of different strategies yield the most payoff to players that play the same game repeatedly. Consider, for instance, the iterated Prisoner's Dilemma.
In any given interaction, individuals can choose to cooperate, which yields a fixed benefit $b$ on their partner at a fixed cost $c$ to themselves, or to defect, bestowing no benefit and paying no cost. Here we will consider only conditional strategies that modify their cooperation in response to their partner’s cooperation.
The players may choose to adopt one of three strategies: 1. cooperate conditionally (CC), 2. deceive tactically (TD), or 3. defect honestly (HD). The CCs aim to cooperate only with other cooperative individuals and not cooperate with defectors, whereas HDs simply always defect. Moreover, the TDs always defect, but attempt to hide that defection from others (by, for instance, waiting until they are unobserved or manipulating their reputation by lying). This deception carries a cost $d$. The CCs will cooperate with HDs in proportion $s$ of their interactions, and will fail to recognize TDs as defectors with probability $q$.
Questions
One could analyse this particular game and show that the evolution of cooperation creates selection pressures that favour adopting tactical deception as a strategy, as McNally et al. (2013) have done in the article linked above.
(Question 1) What I wonder, however, is something different. Suppose one would observe the payoffs of two players playing this game repeatedly, without knowing their strategies beforehand. Are there any methods that would allow you, the observer, to infer (with high probability) which strategies they employ in this iterated Prisoner's Dilemma?
(Question 2) This was a particular example of a game in which players can choose some types of strategies. I am curious whether there is any literature in general - possibly on other games - in which methods are described to reveal the strategies of the players, based on the sequence of payoffs one sees as an outside observer.
Literature and thoughts
With the exception of this paper by Lehre Seip et al. (2016), I have found few examples of articles that focus on identifying strategies by analyzing a sequence of payoffs. Moreover, the aforementioned paper focusses on two quite particular roles in a game: those of leaders and followers.
The subject of leaders and followers in game theory may prompt one to consider the class of Stackelberg games, which also follows a hierarchical dynamic. With regards to question two, I am also interested in identifying leaders and followers, and wonder how the methods to do so differ from those employed in games that are not Stackelberg (so non-hierarchical). So I am interested in role detection in both hierarchical and non-hierarchical games.
Finally, something relevant to consider may be the concept of (Granger) casuality. An example of leader detection employing this concept is described here. However, here technique is applied in the context of time series. I am not sure it has relevance in the context of game theory.
