It is difficult to overemphasize the contribution of Francis Ysidro Edgeworth (1845-1926) to modern economics. His general research program was indeed ambitious: the application of mathematics and statistics to economics (or, better, to the ‘moral sciences’).’ This program remains very much in the agenda of social science today. In this short paper I will concentrate on Edgeworth’s contribution...

We modify the epistemic conditions for Nash equilibrium only to accommodate Gilboa and Schmeidler’s [Journal of Mathematical Economics, 18 (1989), 141–153] maxmin expected utility preferences, and identify the equilibrium concept in n-player strategic games that characterizes the modified epistemic conditions. The epistemic characterization supports the equilibrium concept as a minimal generali...

The equilibrium problem defined by the Nikaidô–Isoda–Fan inequality contains a number of problems such as optimization, variational inequality, Kakutani fixed point, Nash equilibria, and others special cases. This paper presents picture for relationship between points Moreau proximal mapping solutions that satisfies some kinds monotonicity Lipschitz-type condition.

The Complexity of Nash Equilibria by Constantinos Daskalakis Doctor of Philosophy in Computer Science University of California, Berkeley Professor Christos H. Papadimitriou, Chair The Internet owes much of its complexity to the large number of entities that run it and use it. These entities have different and potentially conflicting interests, so their interactions are strategic in nature. Ther...

A methodology of comparative analysis of evolutionary models is proposed. The main aim of this proposition is to identify to what extend different models can be called ‘evolutionary ones’. Each model is analysed by searching for answers to following questions: • Is the model dynamical one? • Is it focused on far-from-equilibrium analysis? • What are a unit of evolution and a unit of selection? ...