Vagueness and Imprecise Imitation in Signalling Games

Signalling games are popular models for studying the evolution of meaning, but typical approaches do not incorporate vagueness as a feature of successful signalling. Complementing recent like-minded models, we describe an aggregate population-level dynamic that describes a process of imitation of successful behaviour under imprecise perception and realization of similar stimuli. Applying this new dynamic to a generalization of Lewis’s signalling games, we show that stochastic imprecision leads to vague, yet by-and-large efficient signal use, and, moreover, that it unifies evolutionary outcomes and helps avoid sub-optimal categorization. The upshot of this is that we see ‘as-if’-generalization at an aggregate level, without agents actually generalizing. 1 Introduction 2 Background   2.1 Sim-max games and conceptual spaces   2.2 Vagueness in sim-max games and conceptual spaces   2.3 Vagueness, functional pressure, and transmission biases 3 Imprecise Imitation   3.1 Replicator dynamic in behavioural strategies   3.2 Noise-perturbed conditional imitation 4 Exploring Imprecise Imitation   4.1 Setting the stage   4.2 Simulation set-up   4.3 Measures of interest   4.4 Results 5 Discussion   5.1 Levels of vagueness   5.2 Evolutionary benefits of imprecision   5.3 Related work 6 Conclusion Appendix  1 Introduction 2 Background   2.1 Sim-max games and conceptual spaces   2.2 Vagueness in sim-max games and conceptual spaces   2.3 Vagueness, functional pressure, and transmission biases   2.1 Sim-max games and conceptual spaces   2.2 Vagueness in sim-max games and conceptual spaces   2.3 Vagueness, functional pressure, and transmission biases 3 Imprecise Imitation   3.1 Replicator dynamic in behavioural strategies   3.2 Noise-perturbed conditional imitation   3.1 Replicator dynamic in behavioural strategies   3.2 Noise-perturbed conditional imitation 4 Exploring Imprecise Imitation   4.1 Setting the stage   4.2 Simulation set-up   4.3 Measures of interest   4.4 Results   4.1 Setting the stage   4.2 Simulation set-up   4.3 Measures of interest   4.4 Results 5 Discussion   5.1 Levels of vagueness   5.2 Evolutionary benefits of imprecision   5.3 Related work   5.1 Levels of vagueness   5.2 Evolutionary benefits of imprecision   5.3 Related work 6 Conclusion Appendix