digital advertising platforms

Abstract: We study the classical multi-item monopoly setting with a single additive buyer and $m$ heterogeneous items whose values are independent but not necessarily identically distributed. Optimal truthful auctions may be randomized and complicated. We analyze the approximation ratios of three simple deterministic auctions: selling all items separately, selling them as a single grand bundle, and choosing the better of the two. Our technical cornerstone is a nonlinear mathematical programming formulation of the worst-case approximation ratio of selling separately, in discrete auctions where values lie in the grid $\{0,1/K,2/K,\dots ,1\}$. For two iid items, we construct novel tight Lagrangian dual certificates that determine this ratio exactly for any discretization parameter $K$. Taking $K\to\infty$, we obtain the tight bound $1+W(1/e)\approx 1.278$ in the continuous-valued setting, where $W$ denotes the Lambert-W function, closing the $[1.278,1.368]$ gap from the work of Hart and Nisan [EC'12, JET 2017]. For $m\geq2$ independent items, a different dual construction gives an upper bound on the approximation ratio of selling separately in terms of basic statistics of the item values. Combining this bound with new inequalities relating optimal revenue (REV), separate-selling revenue (SREV), and grand-bundle revenue (BREV), we derive improved guarantees for all three auctions. Most notably, we prove \[REV\leq 3.5 \max\{SREV,BREV\},\] improving upon the $5.2$ factor of Ma and Simchi-Levi [AISTATS'21] and the $6$ factor of Babaioff, Immorlica, Lucier and Weinberg [FOCS'14, JACM 2020]. For iid items, we also prove $REV\leq 4.4534 BREV$.

Abstract: Moving ML-mediated decision making onto privacy-preserving clients decentralises the economic decision along with the inference. Shared budget constraints then depend on information that cannot be globally current, creating an information-structure failure that conventional pacing is not designed to solve. We study this information misalignment in an auction-logic-faithful on-device simulation with 36 campaigns and 50 devices. Accounting is in dimensionless integer score units; no currency semantics are claimed. Across 30 paired demand paths, proportional Even pacing overspends 17.77% after one tick of staleness and 1,669.31% after 50 ticks under the original 20-times budget pressure. The effect does not depend on that severe a budget: at two-times pressure, 50-tick overspend remains 106.95%. A visible-budget no-sale guard makes zero-lag compliance exact at this score-unit granularity, yet leaves 11.88% overspend at one tick because other devices' debits remain invisible. A declared bursty, heterogeneous-device sweep retains a strictly increasing mean lag curve. We derive a finite-window expected excess-debit bound under conditional charge caps and find positive paired slack in every bounded-value cell. A second, incentive misalignment arises when the ML/pacing score transformation is allowed to change payment units: 98.23% of rival auctions at one tick admit a profitable deviation. An executable implementation-level counterexample isolates the runner-up's multiplier in the winner's price. Critical-base-bid payment is per-auction DSIC conditional on current multipliers, but does not establish dynamic truthfulness and does not repair base-value ranking disagreement.

Abstract: Social simulation studies how individual behavior and social interaction produce collective outcomes. In social media marketing, campaign actions shape which consumers encounter the content and how they respond; these responses then spread through the population. We propose OranSim, a social simulation framework that connects creative, creator, targeting, and budget choices to this process. Heterogeneous consumers receive exposure according to content matching and platform allocation and generate initial responses, which propagate among 60 population segments. Candidate campaigns share the initial population and aligned random numbers, making their response trajectories comparable under action changes. In a controlled synthetic campaign, doubling the budget approximately doubles reach while lowering mean content match and engagement probability among the reached consumers; mean 14-day cumulative simulated response mass rises to 1.96 times the baseline. LightGBM predictors fitted to 39,000 historical RedNote notes estimate platform engagement with log-scale $R^2$ of 0.56--0.62 in five-fold cross-validation; a separate 12,154-note corpus supplies temporal, unseen-creator, and held-out-niche test splits. Public-data experiments evaluate policy value and audience ranking, and paired synthetic outcomes test counterfactual scoring. Together, scenario trajectories and engagement estimates support campaign selection according to a prespecified marketing objective. Code is available at https://github.com/OranAi-Ltd/oransim.