This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It...

This paper first establishes a new core theorem using the concept of generated payoffs: the TU (transferable utility) core is empty if and only if the maximum of generated payoffs (mgp) is greater than the grand coalition’s payoff v(N), or if and only if it is irrational to split v(N). It then...

We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a von...

A coalitional matching is a two-sided matching problem in which agents on each side of the market may form coalitions such as student groups and research teams who - when matched - form universities. We assume that each researcher has preferences over the research teams he would like to work in...