A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the...

In this paper which will appear as a chapter in the Handbook ofGeneralized Convexity we discuss the basic ideas ofconvex and quasiconvex analysis in finite dimensional Euclideanspaces. To illustrate the usefulness of this branchof mathematics also applications to optimization theory...

Many economic and social situations can be represented by a digraph. Both axiomatic and iterativemethods to determine the strength or power of all the nodes in a digraph have been proposed inthe literature. We propose a new method, where the power of a node is determined by both thenumber of its...

There is an increasing awareness of the potential of nonlinear modeling in regional science, which can partly be explained by the recognition of the limitations of conventional equilibrium models in complex situationsand partly by the easy availability and accessibility of sophisticated...

These notes review two simple heterogeneous agent models in economics and finance. The first is a cobweb model with rational versus naive agents introduced in Brock and Hommes (1997). The second is an asset pricing model with fundamentalists versus technical traders introduced in Brock and...