9. Brian Skyrms: The Evolution of Signalling Systems

The speaker begins by setting the scene for a talk on signaling games, reminiscing about past experiences with Bill and their shared interest in game theory. They introduce the concept of equilibrium selection in signaling games, which is the focus of the discussion. The talk aims to explore dynamic considerations in equilibrium selection, using signaling games as a framework. The basic structure of a signaling game is explained, involving a sender and a receiver with different states of the world, signals, and acts, highlighting the importance of common interest in these games.

The speaker generalizes the basic signaling game by considering various factors such as unequal profitability of states, different numbers of states, signals, and acts, and the introduction of costly signaling. They delve into equilibrium selection, discussing the concept of evolutionary stable strategies and states, as introduced by John Maynard Smith. The talk covers the equilibria in simple signaling games, including isolated signaling system equilibria and pooling equilibria, and touches on the challenges of selecting among these equilibria using evolutionary stability.

The speaker explores the dynamics of equilibrium selection, discussing the use of replicator dynamics and learning dynamics in understanding how equilibria emerge over time. They mention the work of Donaldson and Lman in analyzing the structure of equilibria in signaling games and the challenges of finding evolutionary stable states in complex games. The talk also covers scenarios with a mismatch between the number of states, signals, and acts, and how this can lead to various equilibrium configurations, including perfect information transfer and unused signals.

The speaker discusses scenarios where the interests of the sender and receiver are not aligned, leading to equilibria with no information transfer. They suggest that dynamics, rather than static concepts, are the key to understanding equilibrium selection. The talk briefly touches on different types of dynamics that could be used to model the evolution of signaling systems, including replicator dynamics and learning dynamics, and the importance of considering these dynamics in the context of game theory.

The speaker examines the effects of different dynamics in signaling games with varying levels of complexity. They discuss how both evolutionary and learning dynamics can converge to a signaling system in the simplest signaling games. However, as the games become more complex, with more states and signals, the dynamics can lead to partial pooling equilibria, which are not evolutionarily stable. The talk also explores the persistence of synonyms and unused signals in these games, highlighting the limitations of using evolutionary stable strategies for equilibrium selection.

The speaker delves into the impact of mutation on evolutionary dynamics in signaling games. They discuss how introducing mutation can collapse a line of equilibria to a single point, which could either be an unstable point or an attractor, depending on the probability of states. The talk highlights the importance of considering mutation in the dynamics of signaling games and how it can influence the emergence of signaling systems.

The speaker introduces a model of reinforcement learning with invention, where senders can invent new signals and receivers learn to associate signals with correct actions. They discuss the potential for this model to explain the evolution of complex signaling systems, such as natural languages, by allowing for the continuous creation and learning of new signals. The talk also touches on the challenges of analyzing this model and the need for further research.

The speaker engages in a discussion about the implications of different dynamics and learning rates in signaling games. They explore the idea that reinforcement learning can converge to mean field dynamics, which can be used to predict the outcomes of these games. The talk also considers the impact of varying the initial probabilities and reinforcement weights on the learning process, highlighting the potential for different learning rates to influence the stability and outcomes of signaling games.

The speaker contemplates the role of context in signaling games, where a single signal can have multiple meanings depending on the situation. They consider the possibility of modifying the basic signaling games to account for contextual meaning and the challenges of modeling such complexities. The talk also discusses the potential for different attitudes toward inductive risk to affect the learning process and the stability of equilibria in signaling games.