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5.2 Example 1- utility learning agent facing structural change

5.2.1 General Description

A simple application of the above approach is that of an economic agent that seeks to maximise its utility by dividing its spending of a fixed budget between two goods in each time period. Unlike classical economic agents, this one does not know its utility function (even its form) but tries to induce it from past experience. To do this it attempts to model its utility with a function using the following nodes: +, -, *, % (division unless divisor is zero), max, min, log, exp, average, ifle1thenelse (a three-argument function which takes the second value if the first value is less than 1 and the third value thereafter, i.e. it is a graft of two functions at a point determined by a third - a sort of functional cross-over.), and terminals: a selection of random constants and variables representing the amounts bought of the two products.

The advantage in this model is that we can introduce a severe structural change in the agent's utility function and observe the result (imagine the agent has suddenly developed an allergy to the combination of the two products concerned).

Initially, each agent is given a population of randomly generated models using the above nodes and terminals to a given fixed depth.

Each subsequent time period it:

  1. carries over its previous functional models;

  2. produces some new ones by either combining the previous models with a new operator or by growing a new random one;

  3. it then evaluates all its current models according to the minimum error of past data against what they would have predicted using past known data on amount it spent and the utility it gained (considerations such as the depth of the model are also factors in the fitness function);

  4. it then selects the best models in terms of fitness for carrying over in the next period

  5. it finds the fittest such model;

  6. the action is determined by a limited binary search for the spending pattern that the model predicts will return the best utility, the cost of action inference is thus represented by the number of binary search refinements.;

  7. finally it takes that action and observes its resulting utility.

Modelling Bounded Rationality In Agent-Based Simulations using the Evolution of Mental Models - 17 MAR 98
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