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We study a dynamic non-bipartite matching problem. There is a fixed set of agent types, and agents of a given type arrive and depart according to type-specific Poisson processes. Agent departures are not announced in advance. The value of a match is determined by the types of the matched agents. We present an online algorithm that is (1/6)-competitive with respect to the value of the optimal-in-hindsight policy, for arbitrary weighted graphs. Our algorithm treats agents heterogeneously, interpolating between immediate and delayed matching in order to thicken the market while still matching valuable agents opportunistically.

We study the problem of efficiently computing optimal strategies in asymmetric leader-follower games repeated a finite number of times, which presents a different set of technical challenges than the infinitehorizon setting. More precisely, we give efficient algorithms for finding approximate Stackelberg equilibria in finite-horizon repeated two-player games, along with rates of convergence depending on the horizon T . We give two algorithms, one computing strategies with an optimal 1 T rate at the expense of an exponential dependence on the number of actions, and another (randomized) approach computing strategies with no dependence on the number of actions but a worse dependence on T of 1 T 0.25 . Both algorithms build upon a linear program to produce simple automata leader strategies and induce corresponding automata bestresponses for the follower. We complement these results by showing that approximating the Stackelberg value in three-player finite-horizon repeated games is a computationally hard problem via a reduction from the balanced vertex cover problem.

We consider a revenue-maximizing single seller with m items for sale to a single buyer whose value (•) for the items is drawn from a known distribution D of support k. A series of works by Cai et al. establishes that when each (•) in the support of D is additive or unit-demand (or c-demand), the revenue-optimal auction can be found in poly(m, k) time. We show that going barely beyond this, even to matroid-based valuations (a proper subset of Gross Substitutes), results in strong hardness of approximation. Specifically, even on instances with m items and k ≤ m valuations in the support of D, it is not possible to achieve a 1/m 1−ε-approximation for any ε > 0 to the revenue-optimal mechanism for matroid-based valuations in (randomized) poly-time unless NP ⊆ RP (note that a 1/k-approximation is trivial). Cai et al. 's main technical contribution is a black-box reduction from revenue maximization for valuations in class V to optimizing the difference between two values in class V. Our main technical contribution is a black-box reduction in the other direction (for a wide class of valuation classes), establishing that their reduction is essentially tight. CCS Concepts: • Theory of computation → Algorithmic mechanism design.

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