Investigating Learning Schemes in Game Theory With an Application to a Model of Entry in a Regulated Market
by
Iqbal Adjali
BT Laboratories
Coauthors: David Collings, Michael Lyons, Adrian Varley

Since its inception in the early 1940’s, game theory has had a long tradition as an analytical modelling tool for strategic decision models in economic systems. Two main phases can be identified in the development of game theory. The theory first developed following the basic principles of neoclassical economics (utility maximising agents, rational agent behaviour and general equilibrium). The key concept in neoclassical game theory is the Nash equilibrium and the main preoccupation of the theory is with static game analysis. In the second phase of its development (from the 1970’s onwards), game theory has embraced the principles of evolutionary biology and more recently agent-based simulation techniques. Evolutionary game theory (EGT) has addressed two main shortcomings of its traditional form, namely the lack of dynamics and the strong, unjustified assumption of rational agent behaviour. EGT has been successful in analysing many biological systems and is rapidly gaining interest in the economics community. In particular, EGT seems to fit rather naturally within the framework of evolutionary economics. However the question of how to use learning mechanisms in evolutionary game theory for economic applications is still an open question, as the biological metaphor although powerful has some limitations.

In this paper we investigate different learning schemes in dynamic game theory and consider their relative importance when constructing strategic decision models for economic applications. The different models of learning dynamics we have formulated fall into three main categories: repeated games, discrete-time replicator games and discrete-time best-response games. Repeated games are a basic repetition of one-shot games, replicator games are inspired from applications of EGT to evolutionary biology and best-response games combine to some extent many of the desirable properties of evolutionary learning with a more realistic economic interpretation of the decision making process. In all three approaches taken, the models built are considered in their basic deterministic form as well as when stochastic behaviour is added. Synchronous and asynchronous updating and the effects of a variable memory of past moves and discounting are included.

To take a specific economic example in which to conduct the analysis and compare the various dynamic games formulated, we run computer simulations of a simplified market entry model in the context of the telecommunication industry. There are four players in the game: the incumbent, the market follower, the potential entrant and the regulator. Each player has its own strategy set and characteristics such as extent of adaptation and uncertainty about the environment. One important conclusion is that the choice of learning mechanism in the formulation of dynamic games has a drastic effect on the results obtained and is likely to be highly context dependent. Our results show that each approach has its merits and shortcomings. In particular, best-response games with mixed strategy updating seems to offer a richer behavior range than its repeated game counterpart and a more realistic (short term) evolution of the players’ behaviors than the equivalent replicator game. We conclude by summarizing the main points and suggesting directions for future work.

Keywords: evolutionary game theory, stochastic modelling, computer simulations, market entry models, telecommunications industry.

Date received: June 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafk-75.