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

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

An observation on Carnapʼs Continuum and stochastic independencies

We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single predicate