Fairness, Stability and Optimality of Adaptive Multiagent Systems: Interaction Through Resource Sharing

An argument for stability is derived for multiagent systems characterized by resource sharing and algorithm selection. These multiagent systems reflect the trends of modern information systems and the argument made here can serve as a guide to designing robust multiagent systems. The argument is that fairness leads to stability and consequently optimality. The fairness is allocating resources according to the utilities achievable by individual agents. On the other hand, unfairness arises when resources are allocated strictly equally or as reserved beforehand. The source of instability is identified as excess resources resulting from the unfairness. Since excess resources of some agents can be utilized by others, a system becomes vulnerable to instability due to the interactions from resource sharing. The fairness eliminates excess resources and agents become securing definite valuations of resources, as a result of utility-maximizing behaviors. As a consequence, the system reaches an optimal equilibrium voluntarily after any perturbation.