The main purpose of this paper is to make a game-theoretical formulation of model that can represent interactions among local governments (each of which will plan some project independently each other), firms (each of which will determine where and what to produce and his production-capacity, given projects of local governments) and consumers of firms' products. This game-theoretical formulation can help us to represent explicitly a situation where an information of a decision maker on others' decisions is significant for his decision and where his outcome is a result of not only his own decision but also others' decisions.
If there are interactions among projects of local governments, it may be difficult for local governments to evaluate outcomes of their decisions, for their decisions may not result in a unique outocome. Adopting Nash equilibrium as solution of non-cooperative game, this difficulty corresponds to multiple Nash equilibria, but it is likely that a non-cooperative game has multiple Nash equilibria.
Using hypothetical and simple examples, we analyze a 2 regions-1 potential entrant case, a 2 regions-competitive entrants case, and a 2 regions-2 potential entrants case and show that an option (any local government can withdraw his published project if there is no entrant in his region) can reduce his difficulty mentioned above.
Game theory requires all players know completely the game in which they take part, but local governments not only take part in a given game, but also each of them can design some part of the game in which he can not avoid to take part in. If we can assume all local governments know all alternatives, then we can formulate their game in full. But the representation of the game in extensive form is too complex for us to deal with. So piece-meal modifications of their game can be justified if each of their modifications is acknowledged as reasonable by every participant. In this context, the above result is meaningful, though underlying assumptions are very restrictive.
