online platform engineers

Abstract: We study the truthful and fair allocation of indivisible goods to $n$ strategic agents with additive valuations. Babaioff, Feige, and Manaker Morag [FOCS 2026] gave a randomized mechanism that uses only the agents' rankings of the goods, is truthful in expectation (TIE), and guarantees every agent $1/(H_{n-1}+2)=Θ(1/\log n)$ of her maximin share (MMS) in every realized allocation, where $H_{n-1}$ is the $(n-1)$th harmonic number; this is nearly the best possible with rankings alone. They conjectured that cardinal information allows TIE mechanisms to achieve a constant ex-post MMS guarantee. We confirm this conjecture: our TIE mechanism guarantees every agent at least $1/7$ of her MMS in every realized allocation; moreover, the mechanism is ex-ante envy-free and can be implemented in polynomial time. Our mechanism has two key technical ingredients, both of which may be of independent interest. The first is a truthful fractional allocation rule specifying each agent's probability of receiving each good: it favors each agent on her top $n-1$ goods and reduces her probability of receiving a good for each other agent who also ranks it among her top $n-1$ goods. The second is the balanced edge coloring: we decompose these probabilities into equally likely matchings from agents to high-value goods, those that alone meet an agent's guarantee, and balance these matchings in a fine-grained way without changing any marginal probability, so that every agent who receives no high-value good can obtain sufficient value from the remaining goods without over-allocating any good.

Abstract: We study gains from trade in matching markets with independent private values and costs, Bayesian incentive compatibility, interim individual rationality, and no expected budget deficit. A second-best guarantee for finite bilateral trade extends without loss to matching markets with independent Borel priors, arbitrary downward-closed feasibility, and finite expected first-best gains. For bounded buyers with monotone hazard rates and arbitrary bounded sellers, we determine the exact worst-case ratio of second-best to first-best gains, approximately $0.72490721$. For binary buyers and sellers with at most $m$ types, we determine the exact ratio for every $m$, including $8/9$ when $m=2$ and a limit of $4/5$ as $m$ grows. Both families of bounds are tight already in bilateral trade.

Abstract: Batched multi-armed bandits update on a service's own schedule, and the usual implementation carries each arm's absolute reward rate from one update to the next. When the shared level moves between batches, that memory goes stale even though the comparisons between arms may not have. Odds-Ratio Thompson Sampling (OR-TS) instead carries the joint posterior over log-odds contrasts and fits the common level afresh in every batch, marginalizing it out. This paper specifies that update, places it inside a Bayesian bandit agent with two controls, decay for how much past evidence survives an update and aggressiveness for how sharply belief becomes allocation, and evaluates it against absolute-rate memory. Across 86 public A/B series the level varies about twenty-five times more than the contrast. In prespecified synthetic environments a moving level costs absolute-rate memory five times the regret and leaves the best arm below a majority of traffic in 7 of 20 runs, against none for OR-TS. In a policy simulation built from 71 real experiments, where the contrasts are too small to resolve, expected-click differences stay within 0.1% for 58 of them, yet contrast memory still ends on the better arm more than twice as often. Where the contrasts themselves move, the bet fails, and that case is reported too.

Abstract: Can simple no-regret dynamics attain smaller regret in self-play than against arbitrary adversaries? In $n$-player general-sum games, Daskalakis et al. 2021 proved an $O(n\log d_i\log^4 T)$ individual regret bound for Optimistic Hedge, which improves upon the classical $O(\sqrt T)$ adversarial regret bound. In this work, we show that Optimistic Hedge with a constant step size can further achieve $O(\sqrt n\log d_i\log T)$ individual external regret under expected loss-vector feedback. The time-averaged play consequently enjoys a coarse correlated equilibrium gap $O(\sqrt n\log d\log T/T)$, where $d=\max_i d_i$. The improvement comes from a larger admissible step size $η=Θ(1/(\sqrt n\log T))$. Our analysis proves factorial bounds on high-order differences of probability-weighted pairwise loss gaps, then applies finite-difference interpolation in a fixed Euclidean norm. These estimates sharpen the analysis of Daskalakis et al. 2021 and yield a logarithmic regret bound.