The El Farol Bar Problem for next generation systems

Chapter 3
Analysis and Extension of the
Stochastic Algorithm
3.1 Overview
None of the previous three variations was proved to be fair and efficient. Fairness
and efficiency seem to be contradicting terms. In this chapter, new variations
of the stochastic adaptive learning algorithms that were presented in subsection2.2.3,
are examined. The variations could be divided into two categories: the
taxing/payoff algorithms which have to do with an adaptive change of µ and
the budget algorithms, where the agents are forced not to attend the bar after
having attended it consecutively for a number of weeks, as a result of inadequate
resources.
3.2 Taxing/Payoffs Algorithms
3.2.1 Overview
The basic idea behind this algorithm is that in the system there are three types
of agents. The ‘selfish’ who attend a bar regardless if it is crowded or not, those
who attend an uncrowded bar and those who never attend the bar. ‘Partial information’
maximises the probability of attendance incrementing a small quantity
to the original probability when the bar is uncrowded or subtracting it from the
original probability when the bar is crowded. This quantity depends on µ which
is constant. In this version (equations: 3.2.1), the parameter µtax is inserted so
that selfish behaviour can be penalised. When a selfish agent attends a crowded
bar, the quantity that is subtracted from the original probability is ctax times
greater than in the ‘partial information’ algorithm.
Simulations indicated that for rather large values of ctax (ctax ≥ 8) the bar
is underutilised (mean ≤ 58). The behaviour of this algorithm is summarised in
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