The creation of a language can be understood, in a simplified setting, as a dynamics arising from a repeated game with two players: Sender and Receiver. Both have a limited number of States of Nature that can be communicated (say M), and of Signals available to transmit them (say N). At every time step, Nature imposes a State of Nature to the Sender, who when chooses a Signal she transmits to the Receiver. He interprets it as a certain State of Nature, and both players receive a payoff if the interpretation coincides with the initial State of Nature.

Several evolutionary dynamics have been studied towards the understanding of that game, in biology, economics and social sciences, starting with the replicator dynamics introduced by Fisher and Wright in the 1920's.

We have considered, with Hu and Skyrms (2011), the so-called reinforcement learning dynamics, and have shown that it leads to the creation of a language for which no State of Nature/Signal connection can be both synonymic and polysemic. We have generalized that result with Kious in 2016 to a reinforcement learning dynamics for the evolution of social networks.