multiagent system developers

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: We study deterministic strategyproof aggregation in finite-dimensional Euclidean spaces. For every odd number $n\ge3$ of agents and every finite dimension, we prove that the coordinate-wise median minimizes the worst-case approximation ratio for total Euclidean distance among all continuous, anonymous, deterministic strategyproof mechanisms. The same optimality result holds for every even $n\ge4$ when each coordinate uses a fixed choice of the lower or upper middle rank. The proof combines a rigidity theorem with a normalization that does not increase the approximation ratio: any hypothetical mechanism outperforming the median has a normalized representative that is a fixed coordinate-wise order-statistic rule in a single orthonormal frame. A reflection argument then shows that no such rule improves on the median.