On the advantages of non-cooperative behavior in agent populations
Introduction
Multi-agent systems include any computational system whose design is fundamentally composed of a collection of interacting parts. Agent based models are simulations based on the global consequences of local interactions of members of a population. Agent based modelling systems are now widely used in many disciplines such as Humans and Artificial Societies [6], [8], [14] , Ecology and Biology [5], [15] , Economics [9], [18], [24] , Traffic simulations [4], [26] and Environmental modelling [7], [12], [20], [21]. We investigate the behavior of a collective systems of agents that are able to communicate locally. The aim is to analyze how communication between agents can be optimized to fulfill a larger common goal such as the minimization of time taken to search for and collect randomly distributed rewards. We begin with a definition of the terminology we will be using in Section 2 which enables us to formulate a generic description of the problem in Section 3. Section 4 then introduces the parameter values we investigate followed by presentation of the results in Section 5. The discussion of the results contained in Section 6 is followed by Section 7 were we suggest the existence of naturally occurring examples. Finally, we conclude by offering some closing remarks in Section 8.
Section snippets
Definitions
We use the generic term agentfor an artificial or biological entity playing a part in the behavior of a population. An agent can be a gene or an animal such as an insect or human being, or an artificial entity such as a software-agent, a router in a communications network, a central processor in a multi-CPU cluster or a mechanical robot, to just name a few examples. We also use the word population as a generic term for a collection of agents in a defined environment. A population can be
Problem description
Located in a d-dimensional world of size , at each trial are K targets with a total of R equally distributed rewards so that each individual target consists of rewards. The size of the targets, , is chosen so that an arbitrary ratio is achieved. A population of agents of zero extent (i.e. point-size agents) are uniform-randomly placed into this world at each iteration (cf. Fig. 1 for configuration). If an agent happens to be placed in a target area, the agent
Simulations
Since our bandit-searchproblem can not be satisfactorily analyzed anymore using a simple mathematical approach, we investigate the effects and influences of a variation in parameter values via computer modelling as follows. We select a varying number of targets (bandits) and agents with a fixed ratio for the number of rewards per agents to exclude the likely influence of total number of rewards on the results (we did not separately investigate the influence
Results
The results of these runs are represented in graphic form in Fig. 2 for and agents. The significant points of those graphs, namely mean total collection times T for and , are summarized in a single graph, Fig. 3, for better comparison.
From these results we draw the following conclusions.
- (1)
The optimum rate of assistance (or successful information transfer) that minimizes the total collection time T, changes with the number of agents N and number of targets K.
- (2)
With an
Discussion
The power law relationship of the collection time with both variables, number of agents and number of rewards K displayed in Fig. 4 , is reminiscent of the Danish theoretical physicist Per Bak’s self-organized criticality[3]. “Self-organized” is often associated with the word “emergent” [11, p. 99]. It seems that if a population of agents would be able to regulate its own standard deviation via a feedback loop to tune it optimally, it could lead to the emergent ability of the system to
Examples
Deneubourg [10] noticed an “error” (as he called it) during communication among ants of the location of a food source. Some ants would not follow the instructions given to them by other ants to help exploit a known source, and wander away instead. Those ants were however free to discover new sources and Deneubourg showed, via computer simulations, that this behavior maximizes the total intake of scattered food for the colony over time. The standard deviation of this communication error can
Conclusion
Using a simple computer simulation of an interacting population of reward collecting agents, we have shown that there exists an optimum amount of cooperation between agents that minimizes the population’s reward collection time. We investigated some parameters for the number of agents and the number of rewards and found that the optimum is sensitive to those parameters and located somewhere between agents providing no assistance and full assistance. Our simulations have also highlighted the
Acknowledgement
The author would like to thank Piero Giorgi for discussions and comments on the manuscript.
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