Prof. T E S Raghavan, Professor of Emeritus, University of Illinois, Chicago, gave a talk on A note on Linear Complementarity via zero sum two person games on 17 February.
A summary of Prof. Raghavan’s talk:
The matrix M of a linear complementarity problem can be viewed as a payoff matrix of a two-person zero-sum game. Lemke’s algorithm can successfully reach a complementary solution or infeasibility when the game satisfies the following conditions: (i) Value of M equals zero. (ii) For all principal minors of MT (transpose of M) value is nonnegative (iii) For any optimal mixed strategy y of the maximize, either yi > 0 or (My)i > 0 for each coordinate i.
Prof. Raghavan has made many fundamental contributions to the field of game theory and equilibrium computations. He has worked with many renowned mathematicians, game theorists, and Nobel laureates. Since the last few years, he has been running a Gurukulam in Game theory in Pulavanur, Tamil Nadu. Professors from IIT Bombay, IIT Madras, TIFR Bangalore, IISC Bangalore, Dibrugarh University Assam, NIT Surat, etc have sent their best Ph.D students to attend his Gurukulam. Prof. Raghavan plans to continue running the Gurukulam for students serious about entering game theory.