Sergey Norin

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In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that there is no tournament with a partition A,B of its vertex set, such that every transitive subset of A is in the out-neighbour set of some vertex in B, and vice(More)
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(More)
An important instance of the Caccetta-Häggkvist conjecture asserts that an n-vertex digraph with minimum outdegree at least n/3 contains a directed triangle. Improving on a previous bound of 0.3532n due to Hamburger, Haxell, and Kostochka we prove that a digraph with minimum outdegree at least 0.3465n contains a directed triangle. The proof is an(More)
In an -approximate Nash equilibrium, a player can gain at most in expectation by unilateral deviation. An -well-supported approximate Nash equilibrium has the stronger requirement that every pure strategy used with positive probability must have payoff within of the best response payoff. Daskalakis, Mehta and Papadimitriou [8] conjectured that every(More)
We examine strategy-proof elections to select a winner amongst a set of agents, each of whom cares only about winning. This impartial selection problem was introduced independently by Holzman and Moulin [5] and Alon et al. [1]. Fisher and Klimm [4] showed that the permutation mechanism is impartial and 1 2 -optimal, that is, it selects an agent who gains,(More)
We study the structure of the stable coefficients of the Jones polynomial of an alternating link. We start by identifying the first four stable coefficients with polynomial invariants of a (reduced) Tait graph of the link projection. This leads us to introduce a free polynomial algebra of invariants of graphs whose elements give invariants of alternating(More)