We construct an index theorem for smooth infinite economies that shows that generically the number of equilibria is odd. As a corollary, this gives a new proof of existence and gives conditions that guarantee global uniqueness of equilibria.

We present a simple proof of existence of subgame perfect equilibria in games with perfect information.

Lévy driven term structure models have become an important subject in the mathematical finance literature. This paper provides a comprehensive analysis of the Lévy driven Heath–Jarrow–Morton type term structure equation. This includes a full proof of existence and uniqueness in particular, which seems to have been lacking in the finance literature so far.

We study the problem of estimating the mean of a multivariate distribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions satisfying some mild moment assumptions.

This paper gives a proof of existence of price equilibria under certain parameters for a model of product differentiation commonly used in the empirical geographic differentiation literature. This proof is needed because the assumptions of Caplin and Nalebuff (1991) are not generally satisfied once data is introduced to geographic models. The theorem also has implications for existence in mixed...

in his recognition of being and achievement of truth, man has two instruments in his constitution and two ways before him: intellect and heart; reasoning and intuition. some have opted the way of reasoning and underestimated intuition because of its lack of reasoning, and some have preferred intuition over reasoning because of its being presential (intuitive). with their research on philosophy ...