ON THE CORE OF THE COALITIONAL GAMES WITH TRANSFERABLE PAYOFF AND FINITE SET OF PLAYERS

A dynamic game where agents "behave cooperatively" is postulated: At each stage, current nontrading agents can trade and the payoffs from transactions done are maintained in the subsequent stages. The game ends when no interaction is able to benefit the agents involved (case in which a core outcome is reached) or when any new interaction requires that some of the agents involved do not "behave cooperatively" (case in which the core is empty). The gains in terms of insights, obtained with this approach, allow us to identify a new condition, which is proved to be necessary and sufficient for the non-emptiness of the core. The proof of this result is elementary, in the sense that it avoids specialized mathematical tools, and only uses simple combinatorial arguments.