10 problems

The $1/e$-strategy waits until time $1/e$ and then accepts the first candidate who is best so far. In certain two-person games, a decision maker faces an adversary trying to minimi…

In the two-sided secretary game, suppose there are $U$ men and $U$ women, each player meets $N$ partners over $N$ rounds, and preferences satisfy universal rank symmetry: if a man…

In the cooperative two-sided secretary game, let $N$ be the number of rounds and let $R_N(1)$ denote the expected $N$-rank of a player entering the game, under an optimal common st…

Let $T$ be the time horizon. In the finite-type multi-secretary problem, candidates have abilities drawn from a distribution with finitely many types, and regret measures the loss…

Consider the best-or-worst variant of the secretary problem, in which the objective is to select an object that is better or worse than all previously observed objects. Let the cla…

Let $n$ be the maximum possible number of objects under the uniform distribution on $[1,n]$. Define … where $W_{-1}$ is the lower real branch of the Lambert $W$ function, and let…

Asymptotic cutoff conjecture.

Let $\lambda$ be the parameter of the Poisson distribution for the unknown number of objects. Let $\mathfrak{m}(\lambda)$ denote the exact optimal cutoff and let…

Secretary problem conjecture. There is an algorithm for the secretary problem on $(P,\prec)$ that is successful with probability at least $p_k$.

Let a finite partially ordered set be presented to a selector in uniformly random order. A strategy observes the items online and may accept an item, with the objective of acceptin…