Most work on the evolutionary approach to the iterated prisoner’s dilemma (IPD) game uses a binary model where the choice of each player can only be cooperation or defection. However, we rarely commit ourselves to complete cooperation or defection in the real world. This paper examines the continuous IPD game and similarities and differences between the discrete and continuous games. The paper ...

We prove genuinely sharp estimates for the Jacobi heat kernels introduced in context of multidimensional cone Vd+1 and its surface V0d+1. To do so, we combine theory polynomials on explored by Xu with recent techniques Nowak, Sjögren, Szarek, developed to find spherical kernel.

The purpose of this note is to point out some simple mathematical errors in the article "Indirect reciprocity with optional interactions" (Journal of Theoretical Biology 365 (2015) 1–11) by Whan Ghang and Martin Nowak, which a¤ect their results and conclusions. We note various ways that these errors could be …xed, but all require fundamental revisions of their model and lead to counterintuitive...

In an anonymous 4-person economic game, participants contributed more money to a common project (i.e., cooperated) when required to decide quickly than when forced to delay their decision (Rand, Greene & Nowak, 2012), a pattern consistent with the social heuristics hypothesis proposed by Rand and colleagues. The results of studies using time pressure have been mixed, with some replication attem...

The presented in (Gruverman & Kholkin, 2006; Scott, 2006) advances in the quickly developing field of nanoscale ferroelectrics are made because they are important for many applications as well as for the fundamental physics questions. This review summarizes results of investigations of nanowires of antimony sulfoiodide (SbSI) -type materials (i.e. SbSI, antimony selenoiodide (SbSeI), and antimo...

The southern pine beetle (SPB), Dendroctonus frontalis Zimmermann, has been the most economically important forest insect in timber industry United States. From 1960 through 1990, bark caused economic losses estimated at $900 million (Price et al. 1992). 1998 to 2002, a four-year outbreak Appalachian Mountains affected more than 1 acres with an loss of $1 billion (Clarke and Nowak 2009). In 200...