Learning in experimental games

Experimental games typically involve subjects playing the same game a number of times. In the absence of perfect rationality by all players, the subjects may use the behavior of their opponents in early rounds to learn about the extent of irrationality in the population they face. This makes the problem of finding the Bayes-Nash equilibrium of the experimental game much more complicated than finding the game-theoretic solution to the ideal game without irrationality. We propose and implement a computationally intensive algorithm for finding the equilibria of complicated games with irrationality via the minimization of an appropriate multi-variate function. We propose two hypotheses about how agents learn when playing experimental games. The first posits that they tend to learn about each opponent as they play it repeatedly, but do not learn about the population parameters through their observations of random opponents (myopic learning). The second posits that both types of learning take place (sequential learning). We introduce a computationally intensive sequential procedure to decide on the informational value of conducting additional experiments. With the help of that procedure, we decided after 12 experiments that our original model of irrationality was unsatisfactory for the purpose of discriminating between our two hypotheses. We changed our models, allowing for two different types of irrationality, reanalyzed the old data, and conducted 7 more experiments. The new model successfully discriminated between our two hypotheses about learning. After only 7 more experiments, our approximately optimal stopping rule led us to stop sampling and accept the model where both types of learning occu