Bimatrix Equilibrium Points and Mathematical Programming

Lemke, C. E.

doi:10.1287/mnsc.11.7.681

Cited by 878 publications

(288 citation statements)

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“…Such a point is called an almost complementary point for the augmented problem (3). The algorithm follows a path from one almost complementary basic solution to the next, until z 0 is pivoted out to be a nonbasic variable or LCP(q, M ) is shown to be infeasible [13]. During the branch-and-bound procedure, we want to resolve a new subproblem starting with the basic solution of the parent subproblem.…”

Section: Lemke's Methods As Underlying Quadratic Optimizermentioning

confidence: 99%

Algorithm for cardinality-constrained quadratic optimization

2007

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This paper describes an algorithm for cardinality-constrained quadratic optimization problems, which are convex quadratic programming problems with a limit on the number of non-zeros in the optimal solution. In particular, we consider problems of subset selection in regression and portfolio selection in asset management and propose branch-and-bound based algorithms that take advantage of the special structure of these problems. We compare our tailored methods against CPLEX's quadratic mixed-integer solver and conclude that the proposed algorithms have practical advantages for the special class of problems we consider.

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Section: Lemke's Methods As Underlying Quadratic Optimizermentioning

confidence: 99%

Algorithm for cardinality-constrained quadratic optimization

2007

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“…We give a way of passing from a given symmetric two person game to an imitation game whose Nash equilibria are in one-to-one correspondence with the symmetric Nash equilibria of the given symmetric game. Lemke (1965) …”

Section: Introductionmentioning

confidence: 99%

Imitation games and computation

McLennan¹,

Tourky²

2010

Games and Economic Behavior

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An imitation game is a finite two person normal form game in which the two players have the same set of pure strategies and the goal of the second player is to choose the same pure strategy as the first player. Gale et al.(1950) gave a way of passing from a given two person game to a symmetric game whose symmetric Nash equilibria are in oneto-one correspondence with the Nash equilibria of the given game. We give a way of passing from a given symmetric two person game to an imitation game whose Nash equilibria are in one-to-one correspondence with the symmetric Nash equilibria of the given symmetric game. Lemke (1965) Imitation Games and ComputationAndrew McLennan * and Rabee Tourky † December 31, 2007Abstract: An imitation game is a finite two person normal form game in which the two players have the same set of pure strategies and the goal of the second player is to choose the same pure strategy as the first player. Gale et al. (1950) gave a way of passing from a given two person game to a symmetric game whose symmetric Nash equilibria are in oneto-one correspondence with the Nash equilibria of the given game. We give a way of passing from a given symmetric two person game to an imitation game whose Nash equilibria are in one-to-one correspondence with the symmetric Nash equilibria of the given symmetric game. Lemke (1965) portrayed the Lemke-Howson algorithm as a special case of the Lemke paths algorithm. Using imitation games, we show how Lemke paths may be obtained by projecting Lemke-Howson paths.

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“…Thus we obtatn the follewing lefnma, which was Qbserved by Yamamoto [25]. Lemma 7 ([O, w] + F(J')) × F(J)'"' for some F(J') < F(J).…”

Section: Introductionmentioning

confidence: 83%