The evolution of beliefs and strategic behaviour

Daniel Opolot, UNU-MERIT

This dissertation theoretically studies how evolutionary game theory and observational learning can be used to model three aspects of economic and social interactions: repeated interactions, experimentation and communication. These three aspects influence individual decisions and in turn social welfare. The first part focuses on the aspects of repeated interactions and experimentation when agents behave strategically. It starts by developing computational methods for identifying long-run stable outcomes. The solution concept introduced is that of epsilon stability. We use this concept to show that if probabilities of mistakes depend on payoff losses, then risk-dominant strategies are the most likely to be played in the long-run. Risk-dominant strategies however need not be epsilon stable in general.

Secondly, it studies how restrictions on available information may influence outcomes in such evolutionary processes. Here, individuals are assumed to observe the behaviour of those in their social network. We then focus on large decentralized societies. We show how payoff gains and network topology interactively determine long-run stable outcomes. What matters for stability is whether or not an action can spread by best-response once it is initially played by a small fraction of the population. That is, whether or not an action is contagious.

Thirdly, we study the convergence rates for evolutionary processes in networks. A distinction is made between expected waiting times from any state to the long-run stable outcome and the convergence time to the stationary distribution. The main result is that the speed of evolution is influenced by three main factors: the payoff gains, the topology of interactions and the level of experimentation. For a given level of experimentation, what matters is whether or not epsilon stable outcomes are contagious. Whenever contagion is feasible, expected waiting times are shorter for highly than sparsely connected networks.

The last part of the thesis studies evolution of individual beliefs through repeated interactions and word-of-mouth communication. Three factors are modelled as relevant in determining the structure of beliefs over time: historical factors (prior beliefs), the learning mechanism (rational or bounded-rational learning), and the topology of communication structure governing information exchange. Heterogeneity in public beliefs resulting from such interactions is more likely when individuals are rational than when they are not. This could result from heterogeneity in historical factors, topology of interactions or both. We also examine conditions under which the resulting public beliefs correctly aggregate decentralized private information.

Venue: Aula, Minderbroedersberg 4-6, Maastricht

Date: 03 June 2015

Time: 12:00 - 13:30