We study provably effective and efficient data reduction for a class of NP-hard graph modification problems based on vertex degree properties. We show fixed-parameter tractability for NP-hard graph completion (that is, edge addition) cases while we show that there is no hope to achieve analogous results for the corresponding vertex or edge deletion versions. Our algorithms are based on transfor...

1. The following four books are all reviewed together by William Gasarch. Fair Division: From Cake Cutting to Dispute Resolution) , by Brams and Taylor, Cake Cutting: Be Fair if You Can by Robertson and Webb, The Win-Win Solution by Brams and Taylor, and Fair Allocation (Proceedings of Symposia in Applied Mathematics, Vol 33) Edited by H. Peyton Young. These books all deal with the problem of f...

We prove that for any constant k and any < 1, there exist bimatrix win-lose games for which every -WSNE requires supports of cardinality greater than k. To do this, we provide a graphtheoretic characterization of win-lose games that possess -WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight [8] to construct win-lose games that do not satisfy the...

The Minority Game is a model of interacting agents, who try to choose between two options every day, and those who are in the minority are winners. In an earlier paper, efficient stochastic strategies for this game was analyzed when the number of agents is 3, 5, 7. When the number of agents is large, the behaviour is qualitatively different, and as the discount parameter is varied, there is a s...