An infinity series involving the Smarandache-type function

In this paper, we using the elementary method to study the convergent property of one class Dirichlet series involving a special sequences, and give several interesting identities for it

Information Structures with Unawareness

I construct a state space model with unawareness following Aumann (1976). Dekel, Lipman and Rustichini (1998a) show that standard state space models are incapable of representing unawareness. The model circumvents the impossibility result by endowing the agent with a subjective state space that differs from the full state space when he has the unawareness problem. Information is modeled as a pair, consisting of both factual information and awareness information. The model preserves the central properties of the standard information partition model.unawareness, information, information partition, state space models

Modeling Unawareness in Arbitrary State Spaces

I develop a set-theoretic model of unawareness without making any structural assumptions on the underlying state space. Unawareness is characterized as a measurability constraint that results in players' reasoning about a “coarse" subjective algebra of events. The model is shown to be essentially equivalent to the product model in Li (2007), indicating that such a measurability constraint can be captured by restrictions on the dimensions of the state space without loss of generality. I use a variant of the partition model to examine the case of partial unawareness, where the player is aware of a question but unaware of some possible answers to that question, and characterize the player's knowledge hierarchies from his subjective perspective.unawareness, partial unawareness, information, information partition, the state space