Path independence and Pareto dominance

A choice function on a finite set is path independent if and only if it can be represented as the choice of undominated alternatives taking into account mixed strategy domination.Choice function Path independence Pareto domination

Spectral properties of fractional differentiation operators

We consider fractional differentiation operators in various senses and show that the strictly accretive property is the common property of fractional differentiation operators. Also we prove that the sectorial property holds for differential operators second order with a fractional derivative in the final term, we explore a location of the spectrum and resolvent sets and show that the spectrum is discrete. We prove that there exists a two-sided estimate for eigenvalues of the real component of operators second order with the fractional derivative in the final term.Comment: The research results were discussed and presented at the 8th International Conference on Differential and Functional Differential Equations. Moscow, Russia, August 13-20, 201

On continuous ordinal potential games

If the preferences of the players in a strategic game satisfy certain continuity conditions, then the acyclicity of individual improvements implies the existence of a Nash equilibrium. Moreover, starting from any strategy profile, an arbitrary neighborhood of the set of Nash equilibria can be reached after a finite number of individual improvements.potential game; compact-continuous game; finite improvement property

Shapley's "2 by 2" theorem for game forms

If a finite two person game form has the property that every 2-by-2 fragment is Nash consistent, then no derivative game admits an individual improvement cycle.

On the existence of maximal elements: An impossibility theorem

Most properties of binary relations considered in the decision literature can be expressed as the impossibility of certain ``configurations.'' There exists no condition of this form which would hold for a binary relation on a subset of a finite-dimensional Euclidean space if and only if the relation admits a maximal element on every nonempty compact subset of its domain.Binary relation; Maximal element; Necessary and sufficient condition; Potential games