On the stability of a dynamic stochastic capacity pricing scheme for resource allocation in a multi-agent environment

Abstract

Following the view point of Evolutionary Dynamics, we have built a multi-agent system to study resource allocation in a heterogeneous network of resources. The class of systems we are looking at are systems facing structural uncertainties (supply structure and growth, concentration level, substitute products, ...). In our approach [1,2] resources are modeled as strategies, and agents distribute processing requirements onto resources using imperfect information and local decision making. Our agents are endowed with bounded rationality [8] and have to face the challenge of dealing with imperfect understanding of the feedback structure from resources which use unintendedly rational heuristics to set resources' unit prices. Our intent is to achieve cooperative equilibrium using competitive dynamics by controlling congestion through capacity pricing. To achieve this, a distributed differentiated pricing scheme has been used to improve loose coupling between agents and resources. The dynamics of this pricing scheme has been studied in [3]. This required a loosely coupled interaction model that adequately reflects the autonomy of the involved parties and provides the necessary spatial and temporal decoupling [4]. However, the benefits of greater decentralization and increased local decision-making come at the expense of greater stochastic dynamics which can have unpredictable effects on the stability of the system. Because such non-functional properties (stability, performance, etc) depend upon the system's underlying design and implementation [5], we had to come up with an appropriate approach for its stability analysis. This paper first describes the system under study. Following, we describe the procedure we use to analyze its stability and then show its concrete application.