A Cooperative Based Algorithm to Compute Solutions in the Assignment Game
Abstract
Based on some recent results about non-balanced TU-games (games with transferable utilities) we propose a new procedure to get optimal assignments for the assignment game of Shapley and Shubik (1972). The method exhibits some particular features that could be exploited to obtain a highly parallelizable competitive algorithm. The key fact todevelop the scheme is a strong relationship between some cycles of pre-imputation which appear in connection with non-balanced games, and the matching associated to optimalassignments. In this note we relate the solutions of an assignment game with some kind of cycles used previously to characterize non-balanced TU-games. This relationship is thenused to develop a practical method to compute solutions of the assignment game with an approach which seems to be new.Downloads
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