Network formation by reinforcement learning: the long and medium run

We investigate a simple stochastic model of social network formation by the process of reinforcement learning with discounting of the past. In the limit, for any value of the discounting parameter, small, stable cliques are formed. However, the time it takes to reach the limiting state in which cliques have formed is very sensitive to the discounting parameter. Depending on this value, the limiting result may or may not be a good predictor for realistic observation times.Comment: 14 page

Reinforcement learning in signaling game

We consider a signaling game originally introduced by Skyrms, which models how two interacting players learn to signal each other and thus create a common language. The first rigorous analysis was done by Argiento, Pemantle, Skyrms and Volkov (2009) with 2 states, 2 signals and 2 acts. We study the case of M_1 states, M_2 signals and M_1 acts for general M_1, M_2. We prove that the expected payoff increases in average and thus converges a.s., and that a limit bipartite graph emerges, such that no signal-state correspondence is associated to both a synonym and an informational bottleneck. Finally, we show that any graph correspondence with the above property is a limit configuration with positive probability.Comment: 6 figure

PROPOSITIONAL CONTENT in SIGNALS

Propositional content arises from the practice of signaling with information transfer when a signaling process settles into some sort of a pattern, and eventually what we call meaning or propositional content crystallizes out. We give an evolutionary account of this process

Hierarchical Models for the Evolution of Compositional Language

We present three hierarchical models for the evolution of compositional language. Each has the basic structure of a two-sender/one receiver Lewis signaling game augmented with executive agents who can learn to influence the behavior of the basic senders and receiver. With each game, we move from stronger to weaker modeling assumptions. The first game shows how the basic senders and receiver might evolve a compositional language when the two senders have pre-established representational roles. The second shows how the two senders might coevolve representational roles as they evolve a reliable compositional language. Both of these games impose an efficiency demand on the agents. The third game shows how costly signaling alone might lead role-free agents to evolve a compositional language