Competition, cooperation, and authorization

Multi-agent systems considered in the paper consist of a finite number of agents, positions of which can be changed by system actions, and of an evaluation function which assigns to each agent a value of its current position (as e.g. the distance from the intended target). The set of all possible values is ordered; the intention of each agent is to reach a position with the minimum value. Any system action can decrease position values of some agents (the winners) and increase those of the others (the losers); consequently, an action execution can create conflicts among its participants (winners and losers); arbitrary resolutions of such conflicts can prevent some agents of reaching their goals. The present paper is aiming to formulate conditions that must be fulfilled by actions to guarantee each agent reaching its intended final situation.