This paper obtains cooperative games in characteristic function form by allowing players to exercise partial control over the constraints of a controlled programming problem (CPP). A CPP is defined as follows: Maximise f(x), subject to \(x\in R^ N_+\), \(g_ j(x)\leq a_ j\) for \(j\in C_ 1\), \(g_ j(x)=a_ j\) for \(j\in C_ 2\). Additionally, there exists a system of controls given by a map d:C\(\to P\cup \{0\}\), \(C=C_ 1\cup C_ 2\), where \(C_ 1\) and \(C_ 2\) represent the constraints sets and P is the set of controllers (players). The quantities \(a_ j\) are interpreted as resources. If d(j)\(\in P\), then the controller has a veto on the use of the resource; he has the power to replace the number \(a_ j\) by 0. Thus, this system of variable constraints can be regarded as resources that the player brings to the enterprise. The optimised value of f(x) for each coalition represents the worth of that coalition. The resulting set function can be interpreted as te characteristic function of a cooperative game. Conditions are given under which the CPP game is totally balanced, and hence has a nonempty core. So, the optimised value of the CPP is a core allocation. Applications of this method are made to a variety of economic models.

Reviewer: B.Dutta

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