Generalizing Lewis Signaling Games
- Cochran, Calvin Thomas
- Advisor(s): Barrett, Jeffrey
David Lewis's 1969 account of convention formation broke ground through its use of game theory to model how these patterns of behavior might emerge without prior explicit agreement. Of particular interest to us are Lewis's ``signaling games'', a how-possible model for the evolution of a primitive language. Recent work by philosophers and economists applies evolutionary game theory techniques to Lewis's signaling games and demonstrates how a range of cognitively diverse species might learn to communicate. The current manuscript is written in the same spirit: we use evolutionary game theory to investigate how players might reach a successful convention in more generalized signaling game structures.
After a brief introduction in the first chapter, chapter 2 gives results for a simple learning rule, probe and adjust, on three natural extensions of Lewis's original model: the chain game, multiple sender game, and multiple receiver game. The chapter concludes by defining signaling network chains as a particularly flexible generalization of signaling games and with a discussion of probe and adjust on this new model. We show that probe and adjust users converge to a signaling system with probability 1 in all of these signaling game variants. Chapter 3 is an empirical investigation into the effects of extra or too few signals on human subjects' success and learning in Lewis signaling games. Finally, chapter 4 investigates Win-Stay/Lose-Shift with Inertia, a new learning dynamic in which players only change strategies after repeated failure and which seems to characterize some subjects' behavior in chapter 3. We show that this dynamic converges to a signaling system in the limit with probability 1 for all inertia levels and game sizes, with one exception. Our simulations also suggest that a moderate dose of inertia helps agents' speed to convergence in the short and medium run.