In this paper we provide a $4$-GDD of type $2^2 5^5$, thereby solving the existence question for last remaining feasible with no more than $30$ points. We then show that $4$-GDDs $2^t 5^s$ exist all but finite specified set pairs $(t,s)$.

We study how group size a ects cooperation in an in nitely repeated n-player Prisoner's Dilemma (PD) game. In each repetition of the game, groups of size n ≤ M are randomly and anonymously matched from a xed population of size M to play the n-player PD stage game. We provide conditions for which the contagious strategy (Kandori, 1992) sustains a social norm of cooperation among allM players. Ou...

In the classical combinatorial (adaptive) group testing problem, one is given two integers d and n, where 0 ≤ d ≤ n, and a population of n items, exactly d of which are known to be defective. The question is to devise an optimal sequential algorithm that, at each step, tests a subset of the population and determines whether such subset is contaminated (i.e. contains defective items) or otherwis...

An elementary model of animal aggregation is presented. The group-size distributions resulting from this model are truncated power laws. The predictions of the model are found to be consistent with data that describe the group-size distributions of tuna fish, sardinellas, and African buffaloes.