Report of the Legalized Games of Chance Control Commission of the State of New Jersey.

Report year ends June 30.

The compleat strategyst, being a primer on the theory of games of strategy;

Mode of access: Internet.

Traité des applications de l'analyse mathématique au jeu des échecs, précédé d'une introduction à l'usage des lecteurs soit étrangers aux échecs, soit peu versés dans l'analyse.

Available on demand as hard copy or computer file from Cornell University Library.

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

Introduction to the theory of games.

Bibliography: p. 361-367.

Osztozkodási játékok (Games of fair division)

In this survey we presented several proportional and envy-free cake-cutting algorithms. We also mentioned some interesting open problems.

Recent developments : loss of chance in medical litigation : Tabet v Gett [2010] HCA 12.

Following the judgement of the High Court in Tabet v Gett [2010]HCA 12 handed down on 21 April 2010 it appears that in Australia there is now very limited scope for recovery in negligence for the loss of a chance of a better medical outcome.

Loss of chance in medical negligence claims now a lost cause?

The question whether the loss of chance of a better medical outcome in cases of medical negligence should be recognised as actionable damage is ‘a question which has divided courts and commentators throughout the common law world.’ In April 2010, the High Court handed down its anticipated decision in the case of Tabet (by her Tutor Sheiban) v Gett (2010) 240 CLR 537. The issue considered by the court was whether the appellant could claim in negligence for the loss of a chance of a better medical outcome. This issue had not been considered by the High Court previously, the most relevant cases being Rufo v Hosking (2004) 61 NSWLR 678 and Gavalas v Singh (2001) 3 VLR 404. Claiming for a loss of chance in a personal injury action raises questions as to recognised damage and causation, and the members of the High Court considered both of these.

Theories of learning mathematics

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies – or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. So, for healthy theories on development to occur, four Darwinian functions should function: (a) variation – avoid orthodoxy and encourage divergent thinking, (b) selection – submit all assumptions and innovations to rigorous testing, (c) diffusion – encourage the shareability of new and/or viable ways of thinking, and (d) accumulation – encourage the reuseability of viable aspects of productive innovations.

Spatial SINR Games of Base Station Placement and Mobile Association

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.

[BSHM meetings] Topics in the history of financial mathematics: early commerce to chaos in modern stock markets

This account provides an overview of the study day, entitled 'Topics in the History of Financial Mathematics: Early commerce to chaos in modern stock markets,' held by the British Society for the History of Mathematics jointly with Gresham College, at Gresham College, London on 25th April 2008. The series of talks explored the development of mathematics and mathematical techniques in a commercial and financial context.