economic modelers

Abstract: Bergemann, Brooks, and Morris (2015) characterize the consumer and producer surplus pairs that segmentation can produce when the distribution of values is known. I fix only the set of possible values and characterize the pairs that some market and some segmentation can produce. They form a convex polygon. Its outer edge is the largest efficient surplus a market can have when its uniform-price profit is capped, net of that profit, and truncated equal-revenue markets attain it. At the values no segmentation is needed; strictly between two values, reaching the frontier requires splitting a market into two extremal markets. With a continuum of values up to $\bar{v}$, consumer surplus is at most $π\ln(\bar{v}/π)$ when producer surplus (the seller's profit) is $π$, this bound is reached without segmentation, and no market gives consumers more than $\bar{v}/e$.

Abstract: We study the best-response dynamics in games with random payoffs. We consider two-player bimatrix games, with $n$ strategies each. We assume that payoffs come from a continuous distribution, and study the best-response dynamics of these games, after imposing some structure on their payoff matrices. In particular, we focus on symmetric games, antisymmetric games, common-interest games, zero-sum games, and games with independent payoffs. When two players take turns in playing the best response to the opponent's action, they eventually end up cycling through the same sequence of actions. The main focus of the paper is the cycle structure of large random games. In particular, we study the number of cycles, the number of cycles of a certain length, the length of the longest cycle, and related quantities. We show that the structure of the game has an important impact on the typical cycle structure. Our arguments are based on a representation of the best-response dynamics of these games as directed bipartite graphs, and on the cycle structure that arises in them.

Abstract: Multi-agent reinforcement learning (MARL) offers a principled way of populating simulated economies with many heterogeneous decision makers. Its adoption, pioneered in finance, has nonetheless been slow in macroeconomics because of two main limitations: the lack of a shared frame of reference connecting MARL systems to dynamic stochastic general equilibrium (DSGE) models the profession already trusts, and the very long training times. The first limitation was recently addressed by the Multi-Agent Reinforcement Learning Business Cycle (MARL-BC), which places deep RL households in a real business cycle economy and reduces to classic DSGE models in specific limits. Here we address the second limitation. We present JaxMARL-BC, a JAX-accelerated simulator that trains MARL-BC economies in seconds (between 75x and 724x faster than the reference implementation), and scales to 200,000 independent learning households. We verify its correctness against the known DSGE limits, characterise its scaling through a simple cost law, and demonstrate its value by a proof-of-concept calibration of an extended model with heterogeneous returns on capital, in a two-hour experiment that would previously have taken over a month. We release JaxMARL-BC as open source.

Abstract: We show that computing an approximate correlated equilibrium of a polytope game is PPAD-complete, and thus polynomial-time equivalent to finding a Nash equilibrium. This challenges the conventional view in game theory that correlated equilibria are more tractable objects than Nash equilibria. From a conceptual standpoint, we connect correlated equilibria to a natural generalization of fixed points, which we call fixed sets. A fixed set of a continuous function $f$ is a nonempty finite set $S$ such that $S \subseteq \operatorname{conv} f(S)$. Our main technical contribution is to prove that computing a fixed set is PPAD-hard even at inverse polynomial precision.

Abstract: The minimum Birkhoff decomposition problem asks for a representation of a doubly stochastic matrix as a convex combination of as few permutation matrices as possible. This NP-hard problem arises in the scheduling of switches in data centers and satellite systems, in random assignments in economics and in the statistics of rankings. We consider doubly stochastic matrices whose entries are given with a fixed number of decimal digits and look for exact decompositions whose weights have the same precision. We propose a parallel method with three parts. For matrices built from few permutation matrices, the first part reads the weights from the frequencies of the entries and places them on the matrix positions by a rule that, given the correct weights, never fixes a position wrongly. The second part computes lower bounds from pairs of rows or columns, which remain valid for real weights, and from certificates of a satisfiability solver. For matrices built from many permutation matrices, the third part runs a beam search over steps that each make at least one entry zero. On 375 test instances with up to 100 rows, the method proves optimality for 208 instances, and 197 of these proofs also hold for real weights. Of the 190 instances built from few permutation matrices, 187 are solved to proven optimality, 180 of them within one second. Compared with the best exact decompositions known before, the new decompositions are shorter for 278 instances and never longer.

Abstract: We give the first unconditional family of polynomial-time algorithms that breaks the $1/3$ approximation barrier for symmetric bimatrix games. For every fixed $δ>0$, an algorithm in this family computes a symmetric $(1-1/\sqrt{2}+δ)$-approximate Nash equilibrium, improving on the previous best guarantee of $(1/3+δ)$ due to Kontogiannis and Spirakis [2011].

Abstract: The PPAD-completeness of computing Nash equilibria in bimatrix games has driven extensive research into polynomial-time algorithms for $ε$-approximate Nash equilibria. Determining the strongest approximation guarantee achievable in polynomial time is a fundamental question in the complexity of approximate Nash equilibria. Despite sustained efforts, breaking the $1/3$ barrier has long been regarded as a difficult open problem. In this paper, we give an affirmative answer by proposing a simple, symmetric deterministic polynomial-time algorithm that has no tunable hyperparameters and achieves an approximation guarantee of approximately $0.30954+δ$. The main idea is to enrich the optimization framework of Tsaknakis and Spirakis with building blocks drawn from our work on strategy mixing and automated approximation analysis, yielding a new algorithmic structure that provides a conceptual explanation for the improved guarantee.

Abstract: The investment acceleration principle is a heuristic for modelling investment time series out of consumption time series. The model presented herein develops a disaggregated accelerator equation whose coefficients are the weights of a Kohonen neural net that represents firms' decision-making. According to this model, investments take place when managers recognise emerging technological patterns. Furthermore, a technique borrowed from the theory of self-organising systems is used in order to disentangle innovation-driven investments from plant-replication investments.

Abstract: Zero-determinant (ZD) strategies are a class of strategies in repeated games, which unilaterally control payoffs. It has been shown that several ZD strategies promote cooperation in social dilemma games. It has been widely believed that the performance of ZD strategies is expressed as ``unilaterally enforce linear relations between payoffs''. However, in order to interpret properties of ZD strategies in repeated games without discounting, previous studies assumed that the limit of the Cesaro average of the probability distribution of the action profile exists. Here, we explain the performance of ZD strategies without this assumption, which leads to a stronger result than previous ones.

Abstract: Large language models can produce economic policy responses that sound reasonable, but this does not show that their actions are consistent with economic dynamics. We test this by placing an instruction-tuned language model inside six Snowdrop-backed dynamic stochastic general equilibrium (DSGE) simulators. At each turn, the model observes the economy and a change in economic discourse, selects a bounded policy action, and receives the next simulated state and an economic reward. We implement a common Python interface for repeated rollouts, persistent shocks, state cloning, and rolling-horizon simulation. This setting creates a long-horizon credit-assignment problem. Policy effects may appear several quarters after an action is taken. PPO has a learned value function that can propagate delayed reward to earlier tokens through generalized advantage estimation. GRPO has no learned value function and instead assigns a group-relative advantage from complete rollout returns. It therefore cannot distinguish which earlier turn caused the outcome; if every rollout receives the same return, the normalized advantage is zero. We use PPO as the primary method and GRPO as a matched critic-free baseline. The experiments also test directional semantic signals, reward horizon, trajectory warm starts, cross-simulator transfer, and historically anchored pandemic and monetary-policy shocks. The objective is to judge policy actions by their simulated economic consequences rather than by plausible language alone.

Abstract: Bimatrix games may have an exponential number of mixed Nash equilibria if both dimensions of the game are allowed to grow. Bounds on their maximal number give structural insights that have been used to construct hard-to-solve games. We show new sharp or asymptotically sharp bounds on the (polynomial) number of equilibria for generic games where one dimension of the game is fixed and the number of strategies of the other player grows. These results go beyond the hitherto studied square games. Our methods employ combinatorial properties of polytopes, and recent obstructions that relate to the graph of those polytopes. For $n\ge5$, we construct $3\times n$ games that have all $2n+1$ vertices of the best-response polytope as equilibrium strategies, proved using a simple case of the 4-color theorem for planar graphs. Generic $4\times 5$ games are shown to have at most 17 equilibria, using computer calculations with existing datasets for all combinatorial types of the relevant polytopes. For $d\times n$ games, we construct games where all but a fraction of $O(1/n)$ of the maximum number of vertices are equilibrium strategies.

Abstract: We study income taxation when an AI agent implements economically relevant choices through a rule hidden from the government. Alongside unobserved productive ability, this hidden preference-to-execution mapping creates \emph{double unobservability}: the same observable tax-base response can carry different welfare consequences. We call the resulting income \emph{welfare-opaque}. Our constructions show that tax-base statistics can coincide while reform welfare effects differ, even when mechanical welfare weights are identical. We derive an optimal-tax condition that adds a response-weighted execution wedge to the familiar sufficient statistics. A higher marginal rate gains a corrective benefit under local over-execution and an additional cost under local under-execution. Observing the wedge identifies the welfare effect of a marginal reform at the prevailing schedule; bounds on it deliver bounds on that effect. A controlled laboratory compares 4,500 model runs across five AI engines. Faithful delegation selects the score maximizer in essentially all runs. Conflicted objectives produce heterogeneous responses: Claude largely preserves the score maximizer, GLM moves predominantly downward, and GPT-mini and Qwen show concentrated lower-tail increases. Qwen also makes substantial downward adjustments. Different engines locate their departures at different points and in different directions of the designed distribution. Explicit scores align model rankings; formula-based objective instructions yield more uneven agreement. Qwen shows a clear positive tax-by-objective interaction, but its direction does not generalize across engines and the pooled sign depends on its inclusion. The analysis identifies execution information as a complement to conventional tax-base statistics.

Abstract: We study smooth strongly convex--strongly concave minimax optimization with general nonlinear coupling in the deterministic unconstrained setting. We propose a pure single-loop damped extragradient method with fixed parameters and two new full-gradient evaluations per iteration after one initialization query. The method uses an auxiliary feedback recursion and requires no inner solves, accuracy schedules, or staged restarts. We establish last-iterate linear convergence and show that reducing the squared Euclidean distance to the saddle point to an $\varepsilon$ fraction of its initial value requires $O(\sqrt{κ_xκ_y}\log(2κ_xκ_y/\varepsilon))$ full-gradient queries, where $κ_x=L/μ_x$ and $κ_y=L/μ_y$. This bound attains the optimal condition-number order up to logarithmic factors through fixed explicit updates. Numerical experiments demonstrate the effectiveness of the method.

Abstract: We placed 100 memory-equipped large language model (LLM) agents in charge of a closed, money-conserving spatial economy on real Pokhara Lakeside geography (earning wages, running businesses, setting prices) and ran this multi-agent simulation for up to 26 simulated weeks, well past the 1-2 weeks typical of agent-society studies. Across 91 validated runs (2.44M agent decisions, 21.5B tokens), the money stops moving, in a specific and measurable way. A 12x tourist demand shock raises business revenue 4.62x ($p<0.001$), which we decompose exactly into a 1.50x extensive margin (more businesses trading) and a 3.07x intensive margin (more revenue each). Monetary transmission stops there. Wages move 1.03x ($p=0.42$); 0.3% of 3,981 menu items are ever repriced ($p=0.47$). A randomized cash transfer (NPR 5,000 to 20 of 100 agents) shows the same pattern from the opposite direction: 96.7% is still held 311 pulses later, marginal propensity to consume 3-4% by two independent measures, indistinguishable from zero. The wealth distribution is consequently near-frozen at the horizon this literature uses ($ρ=0.964$ over 2 simulated weeks), but not frozen. $ρ$ falls to 0.832 at 12 weeks and 0.752 at 26, a horizon-dependence no short study can see. Matched ablations show which knob actually matters. Swapping the backing LLM moves every outcome we measure ($p=0.0039$); deleting agents' memory moves none of them detectably. A purely social tool fails 94-97% of the time across two model families, compared with ~96% success on economic tools, with no measurable shift away from it. Every headline number is verified twice, by a live validator and by an offline recomputation that reconciles each agent's wealth against its own signed transaction history, and we release the full run corpus for reanalysis.

Abstract: Current LLM-based multi-agent systems (MAS) periodically compress intermediate states to reduce inference-time token consumption, thereby attempting to incorporate more agents. However, naive scaling strategies face challenges. For example, in economic simulations, large-scale MAS typically discard semantically rich economic states, i.e., agent behavioral trajectories, which are key drivers of macroeconomic fluctuations. In this paper, we reveal a phenomenon in which agent heterogeneity gradually decreases during simulation, and propose Prospect-State Propagation for Multi-Agent Systems (PspMAS). Inspired by prospect theory, PspMAS decouples each agent's micro state into a compact Prospect State and an expressive Semantic State. The former records psychological traces through a lightweight, parallelizable propagator and continuously injects heterogeneity into the system. The latter leverages the strong perception, reasoning, planning, and decision-making abilities of LLMs. These two components work complementarily, providing a scalable LLM-based multi-agent simulation solution.