On the advantages of non-cooperative behavior in agent populations

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Abstract

We investigate the amount of cooperation between agents in a population during reward collection that is required to minimize the overall collection time. In our computer simulation agents have the option to broadcast the position of a reward to neighboring agents with a normally distributed certainty. We modify the standard deviation of this certainty to investigate its optimum setting for a varying number of agents and rewards. Results reveal that an optimum exists and that (a) the collection time and the number of agents and (b) the collection time and the number of rewards, follow a power law relationship under optimum conditions. We suggest that the standard deviation can be self-tuned via a feedback loop and list some examples from nature were we believe this self-tuning to take place.

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 Aworld, at each trial are K targets with a total of R equally distributed rewards so that each individual target consists of R/K rewards. The size of the targets, Atarget, is chosen so that an arbitrary ratio a=Aworld/Atarget is achieved. A population of N 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) K=1,5,20,50 and agents N=1,50,100,500 with a fixed ratio r=2 for the number of rewards per agents r=R/N 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 1,5,20 and 50 agents. The significant points of those graphs, namely mean total collection times T for σ=0,σ=σopt and σ=∞, 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 σopt (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 Nand 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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