Chapter 63 The Effect of Message Space Size on Learning and Outcomes in Sender-Receiver Games

As documented in the dynamics (figures) and outcomes (tables), agents learn to attach meaning to "a priori" meaningless messages. For the common interest game, Game 1, we observe the efficient separating outcome, although the learning process is gradual. For the partial common interest game, Game 2, the outcomes and dynamics vary with the size of the message space. With two messages, we observe a partial pooling outcome with a minimal amount of non-equilibrium play. Again, the dynamic adjustment (learning) process is gradual. For three and four messages, the highest frequency of play is the fully separating equilibrium, although there is a significant amount of partial pooling play in both treatments and, consistent with theory, there is more partial pooling play in the four message treatment than in the three message treatment. Finally, while there is less non-equilibrium play in the four message treatment than in the three message treatment, the dynamic adjustment (learning) process in both treatments is gradual and incomplete.