Competition and cooperation in linear production and sequencing processes

We analyze applications of biform games to linear production (LP) and sequencing processes. Biform games apply to problems in which strategic decisions are followed by some cooperative game, where the specific environment of the cooperative game is in turn determined by these strategic decisions. In biform LP-processes, we allow firms to compete for resources, rather than assuming the resource bundles are simply given. With strategy dependent resource bundles that can be obtained from two locations, we show that the induced strategic game has a (pure) Nash equilibrium, using the Owen set or any game-theoretic solution concept that satisfies anonymity to solve the cooperative LP-game. In biform sequencing processes, we no longer assume an initial processing order is given. Instead, this initial order is strategically determined. Solving the second-stage cooperative sequencing game using a gain splitting rule, we fully determine the set of Nash equilibria of the induced strategic game.