We consider a two player simultaneous-move game where the two players each select any permissible n-sided die for a fixed integer n. A player wins if the outcome of his roll is greater than that of his opponent. Remarkably, for n > 3, there is a unique Nash Equilibrium in pure strategies. The unique Nash Equilibrium is for each player to throw the Standard n-sided die, where each side has a dif...

Throughout the post-war period there have been many attempts to reform the UK education system, often with an explicit intention to try and make it more productive. The list of education policy reforms that have been attempted over the last 50 years is quite extensive, and recently the UK (and in particular England and Wales) has introduced many innovative market-oriented reforms to its educati...

Growth and differentiation signals mediated by different regions in the cytoplasmic domain of granulocyte-stimulating factor receptor. Touw IP: Distinct cytoplasmic regions of the human granulocyte colony-stimulating factor receptor involved in induction of proliferation and maturation.: The clonal proliferation of normal mouse hematopoietic cells: Enhancement and suppression by colony-stimulat...

We observe that non-transitivity is not the most general way that Arrow’s impossibility theorem is re‡ected in dice games. Non-transitivity in dice games is a well-known phenomenon. It was described in several Scienti…c American columns in the 1970s, beginning with [3], and has since become a popular topic, discussed in articles like [4, 5] and textbooks on elementary mathematics and probabilit...

We show that infinitesimal probabilities are much too small for modeling the individual outcome of a countably infinite fair lottery.