Urban Larsson (IIT Bombay, India) – The Fundamental Theorem of Normal Play

Combinatorial Game Theory is the branch of Mathematics and Computer Science that studies two-player games (the players areLeft/Positive and Right/Negative) with perfect and complete information; there is no chance, and there are no hidden moves. In the 1970s John Conway defined normal play game comparison via the rule G > H if Left wins G-H playing second. He understood that normal play games constitute a group structure, with respect to the disjunctive sum operator. Nowadays we rather define this inequality by G > H if, for all games X, the perfect play outcome of  G + X is no worse than that of H + X, with respect to player Left. And we call Conway’s discovery, that the notions are equivalent, the “fundamental theorem of normal play”. We explain the relevance of this result, and as an illustration, compute game values of some classical ruleset positions, such as Hackenbush, Domineering, Toppling Dominoes, Toads and Frogs and more.

Urban Larsson is an Associate Professor at Dept. of IE&OR, IIT Bombay, India, and before that he was a Research Fellow at National University of Singapore, and before that he was a postdoctoral fellow at the Industrial Engineering and Management dept. at the Technion, Israel (and awarded an Aly Kaufman fellowship). Before that he was awarded a Killam postdoctoral fellowship at Dalhousie University, Canada, 2014-2016, which included lecturing, and before that he was a responsible lecturer in mathematics 2013-2014 and Ph.D. student (ending 2013) at Chalmers & University of Goteborg (Sweden). His main research areas are Game Theory, Number theory, Computer Science and Algorithms, and some of his main contributions find bridges between Combinatorial games and neighboring fields. He publishes regularly (with about 20 peer reviewed published papers in international journals in 2018-2023). Urban has presented his research at more than 100 international conferences and seminars, he is an Associate Editor for International Journal of Game Theory, and he is the Editor of Games of No Chance 5 (in press), and of the next issue, Games of No Chance 6. He has co-organised several workshops in Combinatorial Game Theory–twice Games at Dal (Dalhousie University, Canada) with Nowakowski, Games at Carmel (Technion, Israel), once at Ohio State University with Roldan Roa, and once at IIT Bombay–and he is a member of the program committee for CGTC I, II, III and IV, the fourth was held at the Azores in January 2023, organized by Prof. C. P. dos Santos. He co-organised, with Prof. Mallikarjuna Rao, et al., the CGT conference Games at Mumbai in January 2024.

Zoom Link: https://sutd-edu-sg.zoom.us/j/97509427360?pwd=RyqtxKI90XB7c77W2VJwkkhOc7abeQ.1

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg