Preface to the Special Issue on Gtora 2012

This special issue of the International Game Theory Review contains selected and refereed papers, invited from the speakers at the Game Theory, Operations Research and Applications (GTORA) conference held during 5–7 January, 2012. The conference was organized by Indian Statistical Institute, Chennai Centre and conducted in the SETS campus of ISI’s Chennai Centre. The papers in this special issue have been logically grouped into four areas: game theory, logic, operations research and mathematical programming. Out of the eight papers in the first section on game theory, the authors Dongshuang Hou and Theo Driessen prove an interesting result on the convexity of Owen’s “Airport Profit Game” (inclusive of revenues and costs). They further classify the class of 1-convex Bankruptcy Games by solving a minimization problem of its corresponding gap function. The second paper by Amit Biswas deals with k-convex symmetric games and provides characterizations of the largeness of the core of such games. The paper shows that the totally balanced symmetric k-convex games possess a large core if and only if the game is convex. With growing interest in evolutionary game theory, the third paper by Mallikarjuna Rao and Shaiju revisits evolutionary stability in matrix games with special reference to evolutionary stability against multiple mutations. The next paper by Singh, Hemachandra, and Rao explores the Blackwell–Nash equilibrium property in two-player finite state-action discounted stochastic games. The existence of a stationary deterministic Blackwell–Nash equilibrium is shown for Single Controller-Additive Reward stochastic game, along with sufficiency conditions for general stochastic games. Prasenjit Mondal and Sagnik Sinha’s paper also deals with stochastic games. By adding an additional condition of state independence of transition times, they show that a subclass of finite SER-SIT-PT semi-Markov games (both discounted and undiscounted) have the ordered field property. The last three papers in this section deal with cooperative games. The paper by Sugumaran, Thangaraj, and Ravindran propose a new single valued rule, based on the concept of fair division for all cooperative transferable utility games. In addition, they also define a linear average rule and discuss some of its properties.