The cooperative problem-solving process

The Cooperative Problem-Solving Process MICHAEL WOOLDRIDGE and NICHOLAS R. JENNINGS, Department of Electronic Engineering, Queen Mary and Westfield College, University of London, London E1 4NS, UK. E-mail: fM.J.Wooldridge, Abstract We present a model of cooperative problem solving that describes the process from its beginning, with some agent recognizing the potential for cooperation with respect to one of its goals, through to team action. Our approach is to characterize the mental states of the agents that lead them to solicit, and take part in, cooperative action. The model is formalized by expressing it as a theory in a quantified multi-modal logic. Keywords: Multi-agent systems, cooperation, modal logic, temporal logic. 1 Introduction Agents — both human and artificial — can engage in many and varied types of social interaction, ranging from altruistic cooperation through to open conflict. However, perhaps the paradigm example of social interaction is cooperative problem solving (CPS), in which a group of autonomous agents choose to work together to achieve a common goal. For example, we might find a group of people working together to move a heavy object, play a symphony, build a house, or write a joint paper. In short, the aim of this paper is to develop a formal model of such cooperative problem solving. Researchers working with the tools of game and economic theory have developed a number of models that attempt to explain various aspects of the cooperative problem-solving process. Relevant examples include the circumstances under which cooperation can occur in a society of self-interested autonomous agents [1] and how negotiation protocols can be designed to ensure that (for example) truth-telling is the optimal strategy [23]. However, these models typically make assumptions that render them of limited value in many practical situations (we discuss the limitations of game-theoretic models in more detail in Section 2.2). One of our aims in this article is, therefore, to present a formal model of CPS that is inherently more suitable as a computational model — we elaborate on this issue in Section 7. Moreover, we wish the model to be comprehensive, in that it should cover the entire CPS process — from recognition of the need for cooperation through to completed team action. In more detail, the model consists of four stages:  recognition — in which an agent identifies the potential for cooperation;  team formation — in which the agent solicits assistance;  plan formation — in which the newly formed collective attempts to construct an agreed joint plan; and finally,  execution — in which members of the collective play out the roles they have negotiated. The remainder of this article is structured as follows. Section 2 introduces the idea of CPS J. Logic Computat., Vol. 9 No. 4, pp. 563–592 1999 c Oxford University Press 564 The Cooperative Problem-Solving Process by way of some simple motivating examples. In order to formally express this model, a new quantified multi-modal logic had to be devised, for representing the beliefs, goals, and actions of agents and groups of agents. This logic is informally introduced in Section 3 (a complete formal definition of its syntax and semantics is given in Appendix A). The logic is used to formalize the notions of conventions, commitments, and intentions in Section 4. These definitions are subsequently used in our model of CPS, which is presented in Section 5. Section 6 discusses the properties of the model, and some conclusions and open issues are presented in section 7. 2 Modelling CPS: issues and scope Many aspects of CPS have been investigated by researchers from distributed artificial intelligence, economics, philosophy, organization science, and the social sciences. These models can be divided into two broad categories:  implementation-oriented models for realising cooperative systems, managing cooperative activities, and achieving coordination in cooperative systems at run-time [7, 27]; and  formal theories of cooperation and related issues; examples include economic and gametheoretic models of cooperation and negotiation [23], formal models of communication based on speech act theory [6], and models which typically use a multi-modal logic to describe the mental state of agents engaged in social activities [11, 18, 22]. Implementation-oriented models are useful in that they help to identify the various steps of the CPS process. For example, consider the Contract Net protocol [27]. This protocol contains the following steps: (i) task announcement: an agent (the manager) finds it has a problem that it does not have the resources to solve locally, and broadcasts an announcement to this effect; (ii) bidding: those agents that receive the announcement, and have the appropriate skills to help, send a bid to the manager, representing an offer to help; (iii) awarding: the manager awards the task to the most appropriate bidder, thus establishing a manager–contractor relationship between the two agents; and finally, (iv) expediting: the contractor carries out the task it has been awarded (which may involve generating sub-tasks, and further, hierarchical manager–contractor relationships). On completion of the task, the contractor informs the manager of the final result. On examination, the Contract Net protocol reveals the following stages of CPS: (i) there is a point at which a manager recognizes the potential for social action; (ii) there is an announcement stage, during which the prospective manager attempts to solicit assistance with respect to the task; (iii) there is a negotiation stage, during which potential managers and contractors engage in a dialogue, with the aim of agreeing which agent will do what; and (iv) there is a subsequent execution stage, during which participants play out the roles they have negotiated. Examination of other models of CPS (e.g. partial global planning [7]) indicates the same basic stages. Given this commonality, these are the four stages that our CPS model must cover. Now that we have a broad understanding of the key steps that appear to be common to most forms of CPS, we can begin to identify the key properties that our model must satisfy. Such desiderata are presented in Section 2.1. We then go on to discuss the purpose of our model, and discuss why formalization in symbolic logic is appropriate in Section 2.2. In Section 2.3, we discuss the different perspectives that such a model may take, and justify our choice of an internal perspective. The Cooperative Problem-Solving Process 565 2.1 Desiderata for a theory of cooperative problem solving We can identify the following desiderata for an adequate theory of the cooperative problemsolving process:  Agents are autonomous. Perhaps the most important requirement for a theory of CPS is that it cannot require benevolence (i.e. an a priori disposition to be helpful) on the part of agents. Agents are autonomous problem solvers (...truncated)