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Modelling Bounded Rationality In Agent-Based Simulations using the Evolution of Mental Models
Among evolutionary techniques, the paradigm of GP  is particularly appropriate, due to the structure of the genome*1. In GP the genes are tree-structures, which conform to a pre-defined syntax but otherwise can be of any shape or size. This makes them appropriate for representing a very wide range of models including expressions in formal languages and networks. These techniques, however, can not be blindly applied. For example, the efficiency of the learning process is only a secondary concern when seeking to model economic agents by their software cousins, but many of the other features of this approach for modelling learning in an economic agent are appropriate, namely:
In using the evolutionary paradigm in this sort of modelling we tend to:
- the population of programs can represent a collection of multiple, competing models of the world with which it is concerned;
- there is always at least one maximally fit individual model that can be used to react to events and from which appropriate deductions can be made - so that agents can `flip' between models as appropriate;
- the models are incrementally developed by the learning mechanism;
- the fitness measure can be tailored to include aspects such as cost and complexity as well as the extent of the agreement with known data;
- the language of representation of the models can be very general and expressive.
This paradigm needs to be integrated with an agent-based approach and adapted to relate to credible models of economic agents. In particular the cross-over operator is somewhat arbitrary when simulating the development of models in economic agents (although undeniably efficient). Also, when applied to large populations this introduces a globality to the search which is unrealistic.
- represent the agent by a whole evolving population - each gene corresponding to one of its alternative models;
- populations of agents are thus modelled as populations of evolving populations (i.e. populations of populations), with an intended agent to evolving population correspondence (e.g. );
- give the agents only small populations of models, representing limited memory;
- base the fitness function on either its error in modelling known past data or the utility the agent would have gained in the past if it has used this model but also with other factors such as the size of model and its predictivity (precision and range of applicability);
- restrict the variation operators so towards an exploitative learning process, for example by restricting to such as generalisation, specialisation, averaging, combining and mutating;
- and give them only a limited inferential ability to use its best model to choose its action.
The fundamental difference between these agents and, say, logic-based agents, is that the updating of internal belief structures is done in a competitive evolutionary manner using a continuously variable fitness measure rather than in a "crisp" consistency preserving manner. This is appropriate in situations of great uncertainty caused by a rationality that is not able to completely "cope" with its environment but is more restricted in its ability.
In the first example presented below (Section 5.2) we use a process of combining old models together as branches from a new node and introducing randomly generated small new models. This produces more realistic results, for example it allows for better fitting by parameterisation. The second application (Section 5.3) uses a more traditional GP setup using the cross-over operator, but with a low level of cross-over compared to propagation, applied to very small populations and with the addition of some new random models each generation.
Modelling Bounded Rationality In Agent-Based Simulations using the Evolution of Mental Models - 17 MAR 98
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