National Workshop on Matrix Analysis and Game Theory

Theory of non-negative matrices and its generalization has its application not only in the theory of the games and graphs, it has a greater significance in every branch of science, such as economics, ranking in information technology, population dynamics, etc. Game theory is another important subject area of mathematics having applications in different branch of science like economics, commerce, management, health and technological sciences (particularly in the area of information science). Linear complementarity problem, from the topic of operation research, is yet another topic having strong applications in game theory which connects game theory with theory of non-negative matrices. These topics are considered to be of higher priority for the research in the area of mathematics and has industrial importance.

Participants attending all the sessions and on having completion of assignments in the tutorial will earn a certificate of completion of course on Matrix Analysis and Game Theory with 3 credits.

Contents of workshop include lectures and tutorials on non-negative matrices and their applications in Game theory and Graphs, Game theory and Linear Complementarity Problem (LCP). Topics covered under matrix analysis are Positive Semidefinite matrices, Matrix functions, Nonnegative matrices, Perron theorems, Cones, Generalization of Nonnegative matrices such as 𝑄, 𝑄₀-matrices, 𝑍-matrix, 𝑆-matrix, Positive subdefinite matrix, 𝑃₀-matrix and its subclasses, Copositive, Copositive plus, Copositive star matrix, Eaves and Garcia class of matrices etc. with applications in Game theory and Graphs. The LCP starts with introduction, Complementary cone, existence and multiplicity of solutions to LCP, Matrix class useful in complementarity and Game theory, various generalizations of LCP, application of LCP in Game theory. Topics under game theory start from Introduction, LPP, Bimax games, Lemke’s algorithm, Generalization of Lemke’s Algorithm.

This national workshop will be held in response to the feedback obtained from the young participants of ICLAA 2017 which was held in sequel to CMTGIM 2012 and ICLAA 2014. Prof T.E.S. Raghavan from University of Illinois at Chicago, is one among leading game theorist in the world and we have great pleasure in having his association in the conduct of the present workshop which could benefit the young mathematicians around the region and nations.