Asymmetry of Strategies in Proposal: Gale-Shapley Algorithm on Diagrams

AbstractThis paper proposes a new diagram for a specific matching problem: the stable marriage problem. The diagram allows us to elicit not only the structure of with a blocking relation among the nodes representing pairs, but also asymmetry in the actions of the DA algorithm (Gale-Shapley algorithm). Symmetry and asymmetry of the stable marriage problems permit us to deduce strategies of whether or not and when proposals should be made. Some implications to the asymmetry in rewarding and penalty in the game theoretic model are also discussed