This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the condition of separate exchangeability. We provide oracle inequalities with rate of convergence OP (n ) corresponding to profile likelihood maximization and mean-...

Separate selling of two independent goods is shown to yield at least 62% of the optimal revenue, and at least 73% when the goods satisfy the Myerson regularity condition. This improves the 50% result of Hart and Nisan (2017, originally circulated in 2012).

Generating action sequences to achieve a set of goals is a computationally di cult task. When multiple goals are present, the problem is even worse. Although many solutions to this problem have been discussed in the literature, practical solutions focus on the use of restricted mechanisms for planning or the application of domain dependent heuristics for providing rapid solutions (i.e. domain-d...

Furthermore, by using [2, p. 230, (1)] a computable representation for the G-function in (1) (and hence also for F,112(s)) may be given in terms of essentially a linear combination of four hypergeometric functions OF3[b2s2 /16] provided that no two of the parameters {1, 1 1+v-P1v-P) differ by an integer. This result for Fv-112(s) is given (correctly) in [3, p. 353, (9)] so that the proposed int...