Admissible Agreements among Goal-directed Agents Guido Boella Dipartimento di Informatica Universit` a di Torino - Italy guido@di.unito.it Luigi Sauro Dipartimento di Informatica Universit` a di Torino - Italy sauro@di.unito.it Leendert van der Torre CWI and TU Delft - Amsterdam The Netherlands torre@cwi.nl Abstract We study admissible coalitions in goal-directed multia- gent systems. We define a qualitative criterion of admissibil- ity in which a coalition has itself all the necessary informa- tion to check admissibility. We show also that, under some assumptions on preference relations of the agents, this ad- missibility criterion can be used to reduce the search space in a game theoretical approach. 1. Introduction It is desirable that artificial agents can help each other when they cannot achieve their goals, or when they profit from cooperating. Cooperative game theory [6, 1] focuses on collusive behaviors, supported by enforced agreements, that involve the formation of coalitions. In collusive behav- iors, agents have the possibility to decide how to coordi- nate themselves without imposition by anyone. An agree- ment is enforced if the involved parties cannot deviate from the agreement, once they decide to enter it. Sandholm et al. [7] distinguish two phases to establish which coalitions can be formed. In the first phase a struc- ture describing all the possible coalition configurations is defined. In the second phase a quantitative method is used to prune those configurations that cannot occur, under the assumption of self-interested agents. It is reasonable to use game theoretical criteria as pruning method, but, unfortu- nately, it has been shown that several solution criteria de- fined in cooperative game theory are computationally in- tractable [8, 9]. Sandholm et al. [7] therefore define some approximation algorithms to search the space of possible coalitions. In [3] we have introduced the do-ut-des property as a qualitative criterion of admissibility for coalition formation in goal-directed multiagent systems. This criterion has been defined by means of a balance between the set of goals of an agent achieved in a coalition and the tasks it is burdened to perform if it agree to enter the coalition. In this way the formalization of do-ut-des property is based on a not com- pelling mixture of two aspects, the goals achieved and the tasks executed to achieve them, that should correspond to two different level of abstractions. In this paper we consider an alternative approach that removes this weakness. More- over if in [3] the do-ut-des property was defined starting from a multiagent system representation that directly de- scribes the achievement power of sets of agents. Here we face the problem to define a typology of these achievement powers starting from the capabilities of the single agents. This notion of power presents an analogy with the one we developed in [2]. The main difference is that in [2] we de- fined a notion of power requiring to a set A of agents to be minimal with respect the achievement of a goal g, in this way we formalized the fact that all the agents in A have to be necessary for the satisfaction of g. In this work the notion of power requires a minimalization of the tasks assigned to A and not a minimalization on the set itself. Therefore in this case we formalize the notion of relevance of the tasks executed by A with respect to the achievement of g. In this work we face the problem to cut off from the space of all possible coalitions the ones that cannot occur by us- ing a qualitative admissibility criterion to be applied before a quantitative game theoretical criterion. The methodology used is on one hand to abstract from the specific preference relations of the agents by focusing on the goals represent- ing the advantages an agent gains entering a coalition. On the other hand we do not simply represent a coalition by means of the goals it can attain, as done in Dunne et al. [9], we represent a coalition as an agreement describing for each set of agents the goals it is burdened to achieve. In Section 2 we define a multiagent system and provide the notion of goals assurable by a set of agents. In Section 3 we define the cooperative game relative to a multiagent system. In Section 4 the do-ut-des property is defined. Sec- tion 5 shows under which conditions the do-ut-des coali- tions can be employed as a qualitative reasoning on prof- itability of coalitions. Section 6 shows the relation between solution concept of core and the do-ut-des property. Proceedings of the 2005 IEEE/WIC/ACM International Conference on Intelligent Agent Technology (IAT’05) 0-7695-2416-8/05 $20.00 © 2005 IEEE