Cooperation and Competition in Linear Production and Sequencing Processes

We analyze applications of biform games to linear production (LP) and sequencing processes. Biform games, as introduced by Brandenburger and Stuart (2007), apply to problems in which strategic decisions are followed by some cooperative game, where the specific environment of the cooperative game that is played, is in turn determined by these strategic decisions. We extend the work on LP-processes by allowing firms to compete for resources that are scarce or hard to produce, rather than assuming these 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. To analyze competition in 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.