online platform managers

Abstract: The metric distortion framework asks voting rules to elect a candidate close to the voters using only their rankings. SimultaneousPluralityVeto elects from the plurality veto core and achieves the optimal worst-case distortion of 3, but it is not Pareto-efficient: it can declare a tie between two candidates even when every voter prefers one of them. Removing Pareto-dominated candidates afterward would break the convexity of tied winner sets. We instead introduce regularization, which adds a small $\varepsilon$ to every candidate's weight, restoring Pareto-efficiency. To study its effect on distortion, we introduce the rank score veto core, whose candidate weights come from a positional scoring vector $\mathbf{s}$, and prove that its distortion lies in $[1 + 2(||\mathbf{s}|| - s_m),\, 1 + 2||\mathbf{s}||]$; we conjecture that the lower bound is tight. A fixed $\varepsilon$ can increase distortion, but letting $\varepsilon$ depend on the number of voters preserves the distortion guarantee of the original veto core. Regularized SimultaneousPluralityVeto thus has optimal distortion, is Pareto-efficient, and has convex tied winner sets, resolving an open question of Kızılkaya and Kempe.

Abstract: Learning agents, whether humans or algorithms, adapt to one another rather than to a fixed environment. Selfish learning need not produce a good outcome for the group, especially when learners face a social dilemma. The iterated prisoner's dilemma (IPD) is the classical example, but it is usually studied in populations of agents who imitate successful strategies. Here, we instead study selfish gradient ascent learners on the two-dimensional space of reactive strategies. A reactive strategy is described by two continuous traits: reciprocity, the chance of cooperating after the co-player cooperates, and forgiveness, the chance of cooperating after the co-player defects. Each learner updates its strategy in the direction that most rapidly improves its payoff against all other learners, by an amount governed by its learning rate. We show that heterogeneity in learning rates can qualitatively change the long-term outcome: a population with uniform learning rates converges to always-defect (ALLD), whereas a population with variable learning rates approaches generous-tit-for-tat (GTFT), which produces nearly optimal collective payoffs. In simulations, every population passes through a transient state of minimal forgiveness, in which the distribution of reciprocity determines the outcome. Variable learning rates promote cooperation because slow learners preserve high reciprocity until the population reaches this state. We prove sufficient conditions on the distribution of reciprocity for convergence to ALLD or to tit-for-tat (TFT). Variable learning rates also allow cooperation to recover from perturbation, which is provably impossible under uniform learning. These results suggest that purely selfish and myopic learning can produce persistent cooperation provided the population has intrinsic variability in learning rates.

Abstract: Dashboards, feeds, and leaderboards determine whom agents believe they are playing against. We study how such information architectures shape strategic behavior, and how a designer who controls them can use visibility as a lever. We propose a behavioral model in which a transparency parameter governs how selectively agents are exposed to opponents of nearby reasoning depth, and embed it in a Cognitive Hierarchy environment, which provides a tractable language for tying agents' beliefs about the sophistication of others to what they see. We show that because the exposure operator is an exponential tilt of the type distribution, the effect of transparency on aggregate behavior has a closed form: the derivative of the aggregate action with respect to $p$ is proportional to the population-average variance of perceived sophistication. This identity signs the effect in games of strategic complements (opacity raises aggregate effort) and in coordination environments (opacity lowers the mean action), and an ordinal version holds for any response rule that is monotone in the belief. Notably, under a Poisson prior, opacity acts as a sophistication multiplier: every reasoner plays as if the population were $\mathrm{Poisson}(τ/p)$. We use this structure to characterize the disagreement-versus-level tradeoff faced by a coordination-minded designer, to identify the reasoning depths that respond most to visibility, and to show that opacity imposes a ``sophistication tax'' under which the deepest reasoners can lose to moderate ones. Simulations in which agents see only a noisy leaderboard of published actions reproduce both the reversal and the tax. Together, our findings highlight that who an agent sees, and not only how deeply it reasons, shapes strategic behavior, and point to visibility as a design lever.