Formation of coalition structures as a non-cooperative game 1: theory

The paper defines a non-cooperative simultaneous finite game to study coalition structure formation with intra and inter-coalition externalities. The novelty of the game is that the game definition embeds a coalition structure formation mechanism. This mechanism portions a set of strategies of the game into partitionspecific strategy domains, what makes every partition to be a noncooperative game with partition-specific payoffs for every player. The mechanism includes a maximum coalition size, a set of eligible partitions with coalitions sizes no greater than this number (which ∗This paper comes as a further development of the 3-rd and the 4-th chapters of my PhD Thesis ”Essays on Trade and Cooperation” at Ca Foscari University, Venezia, Italy. Acknowledge: Nick Baigent, Phillip Bich, Jean-Marc Bonnisseau, Alex Boulatov, Emiliano Catonini, Giulio Codognato, Sergio Currarini, Luca Gelsomini, Izhak Gilboa, Olga Gorelkina, Piero Gottardi, Roman Gorpenko, Eran Hanany, Mark Kelbert, Ludovic Julien, Alex Kokorev, Dmitry Makarov, Francois Maniquet, Igal Miltaich, Stephane Menozzi, Roger Myerson, Miklos Pinter, Ariel Rubinstein, Marina Sandomirskaya, William Thompson, Konstantin Sonin, Simone Tonin, Dimitrios Tsomocos, Eyal Winter, Shmuel Zamir. Special thanks to Fuad Aleskerov, Shlomo Weber and Lev Gelman. Many thanks for advices and for discussion to participants of SI&GE-2015, 2016 (an earlier version of the title was ”A generalized Nash equilibrium”), CORE 50 Conference, CEPET 2016 Workshop, Games 2016 Congress, Games and Applications 2016 at Lisbon, Games and Optimization at St Etienne. All possible mistakes are only mine. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. E-mail for correspondence: dlevando (at) hse.ru.