Competition and cooperation in non-centralized linear production games

In this paper we analyze how to improve the benefits of n producers when: (1) each producer i faces a linear production problem given by max {cⁱxⁱ : Aⁱxⁱ ≤ bⁱ,xⁱ ≥ 0}, and (2) maintaining the production capabilities of each producer is mandatory. In order to maximize the benefits, the producers decide to trade their resources while ensuring their initial individual gains. We study the games which describe this non-centralized linear production when players do not cooperate (section two), when players cooperate and side payments are possible (section three), and when players cooperate and side payments are not possible (section 4).