G. T. Vickers

A group of individuals resolve their disputes by a knockout tournament. In each round of the tournament, the remaining contestants form pairs which compete, the winners progressing to the next round and the losers being eliminated. The payoff received depends upon how far the player has progressed and a cost is incurred only when it is defeated. We only consider strategies in which individuals are constrained to adopt a fixed play throughout the successive rounds. The case where individuals can vary their choice of behaviour from round to round will be treated elsewhere. The complexity of the system is investigated and illustrated both by special cases and numerical examples.

The mobility of members of a species, which may be modelled by diffusion, plays an important role in biology, though much remains to be discovered concerning its effects. It is therefore relevant to ask how diffusion itself may evolve, in particular in a spatially homogeneous environment. The authors suggest that one mechanism driving the evolution of a higher diffusion rate is connected with the effect of a deleterious recessive gene which appears in the population. A reaction-diffusion model is proposed, and numerical and theoretical results are presented which support the above hypothesis.