Modelling Cooperative Behaviour for Resource Access in a Compositional Multi-Agent Environment Frances Brazier, Pascal van Eck and Jan Treur Artificial Intelligence Group Department of Mathematics and Computer Science Vrije Universiteit Amsterdam De Boelelaan 1081a NL-1081 HV Amsterdam, The Netherlands Email: {frances,patveck,treur}@cs.vu.nl Tel: +31 20 44 47730 Fax: +31 20 44 47653 Abstract Modelling and formally specifying agent knowledge required to deal with limited access to resources in a multi-agent situation, is the focus of this paper. Not only the static elements involved but also the dynamic element, namely the behaviour of the system, is explicitly modelled and specified. It will be shown how this results in a flexible, compositional specification that is applicable to real-world domains. DESIRE, a formal framework for the design and specification of compositional architectures, is employed for this purpose. A task model of an arbitrary participating competitive agent is presented, together with a model of interaction between agents, the formal specifications and a comparison of this knowledge-based approach and other approaches. 1 Introduction Modelling interaction between autonomous agents requires insight in the types of knowledge and cooperation strategies agents employ. To formally specify interaction between agents, a framework is required in which interaction between agents is explicitly modelled. DESIRE [LPT92, BTWW95ab, TW93], a formal framework for the design and specification of compositional architectures (with tools for prototype implementation generation), has been successfully used to design and specify single agent systems in which interaction with users was explicitly specified [BT94, BPT92]. Recently the framework has been extended to formally model and specify multi-agent systems, illustrated in a real-life situation for cooperative agents in [BDJT95a,b]. The aim of this paper is to show how a compositional, knowledge-based approach to specifying both the static and dynamic aspects of multi-agent systems results in a flexible specification. In particular, this is done by analysing, modelling and specifying competitive interaction between agents, within one single framework. The advantages of the approach will become apparent: the reflective nature of the specification enables easy adaptation to other strategies and assumptions regarding for instance communication are explicitly modelled. The generic agent model used in [BDJT95a,b] is reused and extended in the current paper. The competitive interaction used to describe the approach focuses on the interaction required for the acquisition of a limited resource. In Section 2, an example of a domain in which such interaction is required, is presented. The DESIRE framework, a framework which supports a compositional approach to declarative multi-agent system specification, is introduced in Section 3. An abstract task model of an arbitrary participating agent is presented in Section 4, together with a description of the additional knowledge and tasks agents require to be able to perform the basic task of acquiring a resource. Section 5 shows how limited resource acquisition has been formally modelled and specified in DESIRE, illustrated for the example presented in Section 2. A non-knowledge-based approach to this type of interaction can be found in algorithms for mutual exclusion (see for example [RA81]) in the domain of operating systems. Such algorithms correspond, in principle, to specific implementation of the interaction described in this paper, for which additional assumptions must be made to define a fixed protocol. These assumptions are included in the discussion in Section 6. Section 6 also includes a comparison of the DESIRE framework with other formal specification frameworks, such as Object-Z [DKRS91] and Concurrent MetateM [FW94]. Discussion and further research are presented in Section 7. 2 Task description A common phenomenon in many real life situations is the phenomenon of limited availability of resources. Resources can be tangible such as books in libraries, seats in aircraft, frequencies for transmission, articles produced by manufacturers, but also time and space are often resources upon which restrictions are placed. To model situations in