Governments often divide operations into separate branches that face different constraints and have limited information. Such separation is feasible if each can operate by solving a simple optimization problem using limited information without requiring game-theoretic calculations about others?...

In this paper, we show that the correspondence discovered by Koshevoy ([18]) and Johnson and Dean ([15],[16]) between anti-exchange closure operators and path independent choice operators is a duality between two semilattices of such operators. Then we use this duality to obtain results...