Gossip, Sexual Recombination and the El Farol Bar--论文代写范文精选

去酒吧的人数明显是随机振荡的,但这并不是由于任何单一的行为模式,不同组的特工交换他们的首选模式，虽然每个代理应用不同模型，在任何时候选择不同的菜单模式。下面的essay代写范文进行详述。

Abstract 
Brian Arthur’s ‘El Farol Bar’ model is extended so that the agents also learn and communicate. The learning and communication is implemented using an evolutionary process acting upon a population of mental models inside each agent. The evolutionary process is based on a Genetic Programming algorithm. Each gene is composed of two tree-structures: one to control its action and one to determine its communication. A detailed case-study from the simulations show how the agents have differentiated so that by the end of the run they had taken on very different roles. Thus the introduction of a flexible learning process and an expressive internal representation has allowed the emergence of heterogeneity.

Introduction
In 1994, Brian Arthur introduced the ‘El Farol Bar ’ problem as a paradigm of complex economic systems. In this model a population of agents have to decide whether to go to the bar each thursday night. All agents like to go to the bar unless it is too crowded (i.e. when more that 60% of the agents go). So in order to epitomise its own utility each agent has to try and predict what everybody else will do. The problem is set up so that any model of the problem that is shared by most of the agents is self-defeating. For if most agents predict that the bar will not be too crowded then they will all go and it will be too crowded, and vice versa. Brian Arthur modelled this by randomly giving each agent a fixed menu of potentially suitable models to predict the number who will go given past data (e.g. the same as two weeks ago, the average of the last 3 week, or 90 minus the number who went last time). Each week each agent evaluates these models against the past data and chooses the one that was the best predictor on this data and then uses this to predict the number who will go this time. It will go if this prediction is less than 60 and not if it is more than 60. 

As a result the number who go to the bar oscillates in an apparently random manner around the critical 60% mark, but this is not due to any single pattern of behaviour - dif ferent groups of agents swap their preferred model of the process all the time. Although each agent is applying a dif ferent model at any one time chosen from a dif ferent menu of models, with varying degrees of success, when viewed globally they seem pretty indistinguishable, in that they all regularly swap their preferred model and join with dif ferent sets of other agents in going or not. None takes up any particular strategy for any length of time or adopts any identifiably characteristic role. V iewed globally they seem to be acting stochastically and homogeneously , despite the fact that the whole system is completely deterministic and each agent is initialised with a dif ferent repetoire of models [12]. 

The purpose of this paper is to report on the dif ference in their behaviour when these agents are given a suitably powerful learning and communicative mechanisms and the whole system is allowed to co-evolve. It can thus be seen as an extension of the work in [2] The approach taken is to endow each agent with a form of bounded rationality in the form of an evolutionary process among a population of competing mental models inside each agent. This is described in section 2. Then in section 3 I describe how this is applied to the El Farol Bar problem in a way which will allow social relations to emerge among the agents. The results are considered in section 4 at the macroscopic level as well as in detail in the form of a case study of the interactions in the model at the last date of a particular (but representative) run.

Modelling Boundedly Rational Agents
The purpose of the model is to explore some of the possible ways that emer gent social structures in an agent community might effect the overall behaviour of that collection of agents. The agent modelling approach adopted broadly follows [5]. Each agent has a population of mental models, which broadly correspond to alternative models of its world. This population develops in a slow evolutionary manner based on what its past success at gaining utility might be. Each notional week, the new population of models is produced using a genetic programming (GP) algorithm (Koza 1992). In GP each ‘gene’ is a tree structure, representing a program or other formal expression of arbitrary complexity. 

A population of such genes is evolved using a version of crossover that swaps randomly selected sub-trees and propagation. Selection of genes for crossover and propagation is done probilistically with a likelihood of selection in proportion to its fitness. I have slightly modified this here by only using some tree crossover but with a high degree of propagation and also some new random genes introduced each time. Then the best model is selected and used to determine first its communicative action and subsequently whether to go to El Farol’s or not. Thus the evolution of mental models is a rough representation of learning. The cross-over operation is not very realistic but does as a first approximation. For a critique of cross-over and further discussion of the philosophy of agent design for the purposes of the credible modelling of human agents, see [5]. This model of learning fits into the wider framework of modelling economic learning as modelling described in [9].

Extending the El Farol Bar Model with Learning and Communication
In this extension of the model agents have a chance to communicate with other agents before making their decision whether to go to El Farol’ s Bar. Each of the agents’ models of their environment is composed of a pair of expressions: one to determine the action (whether to go or not) and a one second to determine their communication with other agents. The action can be dependent upon both Gossip, Sexual Recombination and the El Farol Bar - Bruce Edmonds page 3 the content and the source of communications received from other agents. Although the beliefs and goals of other named agents are not explicitly represented, they emer ge implicitly in the effects of the agents’ models. The two parts of each model are expressions from a two-typed language specified (by the programmer) at the start 1 . A simple but real example is shown in figure 1 below. Translated this example means: that it will say that it will go to El Farol’ s if the trend predicted over observed number going over the last two weeks is greater than 5/3 (the total population was 5 in this example); but it will only actually go if it said it would go or if barGoer-3 said it will go.

The formal languages indicated in figure 2 allow for a great variety of possible models, including arithmetic projections, stochastic models, models based on an agents own past actions, or the actions of other agents, logical expressions and simple trend projections. The utility that agents get is 0.4 if they go when it is two crowded, 0.5 if they stay at home and 0.6 if they go when it is not too crowded (where too crowded means greater than 60% of the total population). The best (and hence active) genes of each agent are summarised above in figure 3. I have simplified each so as to indicate is logical effect only. The actual genes contain much logically redundant material which may put in an appearance in later populations due to the activity of cross-over in producing later models. Also it must be remembered that other alternative models may well be selected in subsequent weeks, so that the behaviour of each agent may ‘flip’ between different modes (represented by dif ferent models) depending on the context of the other agent’ s recent behaviour.

The effect of the genes is tricky to analyse even in its simplified form. For example agent-1 will tell its friends it will go to El Farol’ s if the average attendance over a previous number of time periods (equal to the number who went last time) is greater than the predicted number indicated by the trend estimated over the same number of time periods but evaluated as from the previous week! However its rule for whether it goes is simpler - it goes if it went last week1 . You can see that for only one agent what it says indicates what it does in a positive way (agent 4) and one which will do the exactly the opposite of what it says (agent 2). It may seem that agents 1 and 3 are both static but this is not so because figure 3 only shows the fittest genes for each agent at the moment in terms of the utility they would have gained in previous weeks. During the next week another gene may be selected as the best. The interactions are summarised in figure 4, which shows the five agents as numbered circles. It has simple arrows to indicate a positive influence (i.e. if agent-2 says she is going this makes it more likely that agent-4 would go) and crossed arrows for negative influences (e.g. if agent-2 says she will go this makes it less likely she will go). The circles with an “R” represent a random input.

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