AI benchmarks have well-documented limitations, with prior work examining contamination, saturation, and construct underspecification. Aggregation has received far less attention: benchmarks are typically summarized by uniformly averaging item-level scores, implicitly treating every test item as equally valuable. We model benchmarking as a multitask principal-agent game and show that the welfare loss from a benchmark is determined jointly by three item-level primitives: alignment with normative welfare priorities, marginal improvability, and performance variance. We translate the theory into an audit framework that ranks items along each of these three axes, and apply it to OLMES items using WORKBank for welfare, the EvoLM 4B suite for improvability, and the PolyPythias 410M panel for variance. The framework surfaces items that are Pareto-inferior within OLMES subject to a pro-worker welfare operationalization. All code is available at https://github.com/stair-lab/principal-agent-benchmarks.
We study how AI shopping interfaces affect price competition, platform profit, and consumer welfare. A platform hosts two of three products of different quality. Without AI, consumers compare the hosted pair under salience distortion and overweight whichever attribute, price or quality, stands out. Under assistance, an AI assistant recommends the two products with the highest true utility, leaving consumers to make the same distorted comparison. Under delegation, an AI agent selects the best product, subject to purchase approval. Both modes access all products and know consumers' preferences; firms price strategically. First, assistance can soften competition despite expanded product access. The middle-quality firm may forgo low-valuation consumers because attracting them requires cutting the price paid by higher-valuation consumers as well. Relative to no AI with the same assortment, assistance lowers both hosted prices under the high- and low-quality pair but can raise both under the high- and middle-quality pair. Second, we identify an alignment paradox: some consumers can become worse off than without AI even though their best option remains recommended and becomes cheaper. Salience can induce a switch to a lower-quality product whose quality loss exceeds the saving relative to the original purchase. The assistant ranks products accurately but does not optimize the shortlist for consumers' realized welfare. Third, assistance can raise both platform profit and aggregate consumer surplus with the high- and middle-quality pair; delegation can do so with the high- and low-quality pair. Fourth, among AI designs, the platform weakly prefers delegation with the high- and middle-quality pair wherever all compared pricing equilibria exist. Yet this preferred design can yield lower platform profit and aggregate consumer surplus than the no-AI optimum.
There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While counterfactual regret minimization and fictitious play are scalable to large games and have convergence guarantees in two-player zero-sum games, they do not guarantee convergence to Nash equilibrium in multiplayer games. Recently, an approach has been presented for exact computation of Nash equilibrium in multiplayer imperfect-information games that solves a quadratically constrained program based on a nonlinear complementarity problem formulation derived from the sequence-form game representation. This formulation was solved using Gurobi's nonconvex quadratic solver, which employs spatial branch-and-bound to iteratively refine variable bounds by solving convex relaxations of bilinear terms. During presolve, Gurobi introduces auxiliary variables and, in some cases, binary variables, leading to an internal mixed-integer quadratically constrained program. This approach was demonstrated to outperform prior algorithms from the Gambit software suite and quickly solve three-player Kuhn poker after removal of dominated actions; however, the algorithm was not able to solve the full version of the game within 24 hours. In this paper, we derive finite bounds on slack and multiplier variables in the nonlinear complementarity formulation. These bounds can strengthen the convex relaxations used within spatial branch-and-bound. We compare uniform corollary bounds with finer proposition-based bounds on full three-player Kuhn poker. All eight bounded configurations return numerically verified equilibria in under 17 seconds, while the unbounded formulation finds no feasible solution within 300 seconds. The finest bounds do not consistently yield the fastest computation.
Hopfield neural networks and noncooperative games provide seemingly different approaches to understanding how collective outcomes emerge from local interactions. In a neural network, individual units adjust their states according to local signals; in a game, players choose actions to maximise individual payoffs. I establish an exact equivalence between symmetric binary Hopfield networks and binary-action games that admit a quadratic potential. The equivalence identifies stable network configurations with pure-strategy Nash equilibria, and asynchronous neural updating with best-response dynamics. More broadly, the storage and retrieval of memories in neural networks correspond, respectively, to the design and selection of equilibria in games.
Automated markets increasingly route order flow from learning trading agents through automated market makers (AMMs). We model trader archetypes as AI agents defined by their reward functions and analyze the feedback they create on a constant-product AMM. Herd-dominated and arbitrage-dominated markets of equal size have identical return distributions and turnover, so no rule based on volatility, value-at-risk, stress frequency, or volume can tell them apart; yet their stress episodes differ in length by a factor unbounded in the feedback-to-noise ratio $\beta/s$. Serial statistics identify the feedback sign from $\Theta((s/\beta)^2\log(1/\delta))$ observations, and this rate is tight. When agents trade together, profit-seeking agents ride herds rather than lean against them, leading to all-or-nothing participation. Spread-earning market makers restore stability but make liquidity fragile, with discontinuous collapse and hysteresis; maker--taker pricing, not a uniform fee, is the effective instrument.