The generalized data envelopment analysis model and the convex cone constrained game

This study extends the research on relating the data envelopment analysis (DEA) with the game theory context. We propose a generalized model for the two-person zero-sum finite game with closed convex cone constraints. We prove that the strategy of the closed convex cone constrained two-person zero-sum finite game is equivalent to the solution of the corresponding cone constrained programming problem. We show the existence of an optimal strategy of closed convex cone constrained two-person zero-sum finite game. As a special case of this, we give the optimal strategy of a polyhedral constrained game. In this case, the corresponding dual programming problems are a pair of linear dual programming problems. We then build up the connection between the proposed convex cone constrained game model and the generalized DEA model. With this relationship, a more robust correspondence between game family and the DEA family is established.