The traditional economics and queueing literature typically assume that customers are fully rational. In contrast, in this paper, we study canonical service models with boundedly rational customers. We capture bounded rationality using a framework in which better decisions are made more often, while the best decision needs not always be made. We investigate the impact of bounded rationality on ...

has infinitely many solutions in rational numbers p/q. It follows from the theory of continued fractions that μ(ξ) is always greater than or equal to 2, and an easy covering argument shows that μ(ξ) is equal to 2 for almost all real numbers ξ (with respect to the Lebesgue measure). Furthermore, Roth’s theorem asserts that the irrationality exponent of every algebraic irrational number is equal ...

This note collects the formal proof sketches that I have done. 1 Algebra: Irrationality of √ 2