Learning, teaching and sophistication in a strategic game

The present study would like to show - among other things - in the spirit of Hyndman, Terracol and Vaksmann (2009), that learning and teaching are still observed in an environment where there is no pure strategy Nash equilibrium (but still, as in any finite game, a mixed strategy Nash equilibrium), which is the case in the majority of real-life situations. The main objective in this paper is to test experimentally the following hypotheses: - First, we want to know if players believe that their opponents can be learners and that their actions might influence their opponent's beliefs. - Second, we would like to investigate the idea that players do use this awareness of their opponent's ability to learn to manipulate their opponents' beliefs. - Third, we want to know if there are other explanations we can provide for the way players behave in our game: "cyclic behaviour", "learning of correlated strategies"? - Last, we think that Inequity and Risk aversion might play a role but that doesn't undermine our teaching strategy hypothesis mentioned above. The paper is organized as follows. Section II introduces our game and experimental procedure. Section III gives some preliminary results and descriptive statistics. Section IV-V and VI shows that subjects might be more sophisticated than the standard theories predict. Section VII-VIII-IX explore the possibility of "cyclic playing behaviours", the existence of a learning of "correlated strategy" and examines the effect of "inequity and risk aversion". Section X concludes the paper