Currently more and more agents are involved in human routine activities and a mixed human-agent society is thus formed by the humans and the agents involved. The relationship between humans and agents in this mixed society is subtle and it is vital to explore the influence that agents bring into the society. In this paper, we try to investigate a few questions: will humans act differently towar...

Let X1,X2, . . . , be independent random variables with EXi = 0 and write Sn = ∑ n i=1 Xi and V 2 n = ∑ n i=1 X i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum S...

A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envyfree, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by ...