An evolutionary model of multi-agent systems

Abstract

A multi-agent system can be viewed as an evolutionary system where each individual (agent) acts on a basis of population dynamics and stability under the criterion of Darwinian fitness. This “survival of the fittest” or “best for individual (or gene or agent)” argument can be used to find evolutionary stable strategies within the multiagent system. The aim of this paper is to introduce some of these evolutionary ideas to the multi-agent society.

The differences between a product maximising mechanism (PMM) and an evolutionary stable strategy (ESS) are discussed. In a PMM the utility for an agent, in a mixed joint plan, is the positive difference between the maximum expected cost that the agent is willing to pay in order to achieve his goal, and his expected part of the outcome. In an ESS the fitness of the utility function does not have to be positive because zero fitness is a state which can be both improved and weakened. Both PMM and ESS are, according to game theory, individual rational and pareto optimal but they address different kinds of problems. If we know the maximum expected costs that each agent is willing to pay to achieve his goal, it is possible to use a PMM. If we instead know the agent's zero fitness, which is assumed to be the same for all agents, it is possible to use an ESS.

As an example, a solution to the telephone call competition among two agents with an overbid-underbid strategy (or hawk-dove strategy in the terminology used by evolutionary biologists) is demonstrated by using an ESS. This solution is compared with one in which the best bid wins and is paid the second price.

In an extended asymmetric game between two competing agents, one mixed and one pure evolutionary stable strategy are found. It is proposed that both these strategies will bring the competing agents near the “real” value and accordingly can be alternatives to the best bid wins, get second price idea.