The Evolution of Conjectures

Huw Dixon and Ernesto Somma
University of York, UK
hdd1@york.ac.uk
es10@york.ac.uk

Abstract

We model the evolution of conjectures in an economy consisting of a continuum of firms which meet in duopolies according to a random matching technology. The duopoly game is modelled by conjectural variation duopoly, where each firm's belief (conjecture) about the other firms behaviour determines its own behaviour. An evolutionary process occurs, by which conjectures that give rise to larger profits (on average) become more common. This is modelled by the replicator dynamics, and can be seen as occurring due to imitation, propagation, and natural selection. In the context of homogeneous good Cournot duopoly, the conjectures resulting from the noiseless replicator dynamics are the the consistent conjectures. We also derive a variety of analytic and simulation results for noisy replicator dynamics.