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ALYMPICS: LLM Agents Meet Game Theory -- Exploring Strategic Decision-Making with AI Agents
Shaoguang Mao, Yuzhe Cai, Yan Xia, Wenshan Wu, Xun Wang, Fengyi Wang, Tao Ge, Furu Wei
TL;DR
Game-theory research often faces complex problems that cannot be resolved through simple deductions, while real-world experiments can be costly and difficult. Alympics provides an LLM-agent simulation framework, piloted in a resource-allocation game. Human evaluators’ perceptions of agent performance were similar to agents’ self-assessments, and the study examines how resource abundance and persona settings relate to outcomes.
Problem
Many game-theory problems cannot be solved through simple theoretical deductions, and questions remain about whether LLM agents demonstrate human-like strategic reasoning.
Source: §1 · pp. 1–2Method
Results
Human evaluators’ perceptions of agents’ game performance were similar to agents’ self-assessments, while resource abundance and persona settings were examined in relation to bidding and survival outcomes.
Source: §1 · p. 2, §5.2 · p. 5, §6.3 · p. 6Takeaways & Limitations
Alympics offers a flexible platform for exploring how resource abundance and persona settings influence game payoffs, with future work aimed at more complex, realistic scenarios.
Source: §8 · p. 8
Abstract
from arXiv · showhide
This paper introduces Alympics (Olympics for Agents), a systematic simulation framework utilizing Large Language Model (LLM) agents for game theory research. Alympics creates a versatile platform for studying complex game theory problems, bridging the gap between theoretical game theory and empirical investigations by providing a controlled environment for simulating human-like strategic interactions with LLM agents. In our pilot case study, the "Water Allocation Challenge," we explore Alympics through a challenging strategic game focused on the multi-round auction on scarce survival resources. This study demonstrates the framework's ability to qualitatively and quantitatively analyze game determinants, strategies, and outcomes. Additionally, we conduct a comprehensive human assessment and an in-depth evaluation of LLM agents in strategic decision-making scenarios. Our findings not only expand the understanding of LLM agents' proficiency in emulating human strategic behavior but also highlight their potential in advancing game theory knowledge, thereby enriching our understanding of both game theory and empowering further research into strategic decision-making domains with LLM agents. Codes, prompts, and all related resources are available at https://github.com/microsoft/Alympics.
1 Introduction
Alympics is proposed as a controlled framework for studying strategic interactions with LLM agents, demonstrated through a resource-allocation game and human assessment. The introduction frames this work around practical research challenges and open questions about agent behavior.
1 Introduction
- Real-world game-theory problems often require experiments that are expensive, time-consuming, and ethically complex when human participants are involved.The introduction notes that many such problems cannot be solved through simple theoretical deductions.Source: §1 · p. 1
- The introduction identifies open questions about building a unified, controllable, efficient framework, methods for game-theory research with LLM agents, and agents’ strategic reasoning.It also notes that LLM-based agents can emulate human behaviors such as style, personality, and collaboration or competition.Source: §1 · pp. 1–2
- The paper introduces Alympics, a framework with a Sandbox Playground, agent players, and optional human players for controlled, scalable, reproducible game-theory research.It is presented as a way to explore game scenarios and test hypotheses about strategic interactions.Source: §1 · p. 2
- The Water Allocation Challenge pilots Alympics in unequal competition for limited resources, varying resource availability and agent personalities to study strategic decisions and outcomes.The game draws on classic game-theory problems and is designed to avoid potential data-leakage issues associated with classic games.Source: §1 · p. 2
- Human evaluators’ perception of agents’ game performance was similar to agents’ self-assessment, addressing whether simulations demonstrate human-like strategic behavior.The assessment considered information use, logical reasoning, strategic effectiveness, adaptability, and long-term planning.Source: §1 · p. 2
2 Alympics: An LLM Agent-based Game Theory Playground
Alympics separates the environment in which games run from the players who participate. Its framework combines configurable game settings and records with LLM-powered agents whose components can be tailored to research needs.
2 Alympics: An LLM Agent-based Game Theory Playground
- Alympics comprises a Sandbox Playground and agent players, with optional human players participating in games executed under researcher-specified settings.The framework is presented as a systematic platform for game-theory research.Source: §2 · p. 2, Figure 2 · p. 3
2.1 Sandbox Playground
- The Sandbox Playground supplies game rules and mechanics, historical records, and configurable settings for controlled strategic interactions.These components support consistent experimentation and analysis of agent strategies over time.Source: §2.1 · p. 2
2.2 Agent Players
- Agent Players are LLM-powered entities whose decision-making combines agent code, accessible player status, and a language model.The agent code controls decision-making and strategy formulation, while player status captures the state and information accessible to the agent.Source: §2.2 · p. 2
- Agent Players may also use memory caches, reasoning plugins, persona settings, and research-specific components such as tools and augmentation.These components are described as supporting strategic gameplay and adaptability.Source: §2.2 · p. 2
3 Pilot Demonstration: Water Allocation Challenge
The Water Allocation Challenge models repeated competition for scarce water and provides a pilot setting for studying strategic behavior. The authors describe its rules and analytical scope, then examine repeated agent emulations and human assessments.
3 Pilot Demonstration: Water Allocation Challenge
- The Water Allocation Challenge combines auction theory, resource allocation, survival strategy, repeated games, Nash equilibrium, fairness, and risk management in a pilot game.The authors say it represents characteristics of classic games while avoiding potential data-leakage issues associated with them.Source: §3 · p. 3
3.1 Game Settings
- Players compete for water over 20 days, starting with 8 of a maximum 10 health points; meeting needs adds 2 points, while consecutive no-water days reduce health.Daily supply varies and remains below total demand; residents submit sealed bids for their entire water requirement, with ties favoring lower requirements.Source: §3.1 · p. 3
3.2 Game Analysis
- The game supports analysis of strategic interaction, adaptation, uncertainty, and inequality arising from varying supply and players’ different incomes and water needs.The authors connect the setting to resource-allocation competition and note that human experiments can be costly, hard to control, and difficult to reproduce.Source: §3.2 · pp. 3–4
3.3 Research Topics and Methodology
- The study repeats emulations to examine bidding interactions, survival under income and requirement differences, and strategy adaptation, while varying resources and agent characteristics.Ten human subjects also evaluated agents’ strategic reasoning and strategy evolution in the game.Source: §3.3 · p. 4
4 Experiments
The experiments use GPT-4 agents to study how resource abundance and assigned personas relate to bidding and survival. The authors track resource satisfaction, survival, and minimum successful bids across repeated settings.
4.1 Implementation
- Each agent uses an individual GPT-4 instance, and GPT-4 also implements the Sandbox Playground.The implementation notes specify GPT-4-32k on Azure, model version 2023-07-01-preview.Source: §4.1 · p. 4
4.2 Variables
- Resource abundance ranges from daily supplies of 10–20 units under low conditions to 20–30 under high conditions, with medium at 15–25.The corresponding RSR values are 0.3, 0.4, and 0.5; RSR below 1 indicates demand is not fully met.Source: §4.2 · pp. 4–5
4.3 Experimental Settings
- Six settings cross low, medium, and high resource abundance with agents either assigned personas or left without them, and each setting was run 10 times.Personas vary profession, personality, and background; comparisons assess resource abundance within persona groups and persona assignment across groups.Source: §4.3 · p. 5, §4.2 · p. 5
4.4 Indicators
- The indicators include beginning and ending resource satisfaction rates, survivor counts and rates, and each round’s minimum successful bid price.Comparing beginning and ending RSR tracks change in per-capita allocation; ending RSR also indicates remaining resource abundance.Source: §4.4 · p. 5
5 Results
The results show lower average survival under low resource abundance and distinct bidding patterns as abundance and game stage vary. Scarcity is associated with higher minimum successful bids overall.
5.1 Survival Status
- Average survivor counts are significantly lower under low resource abundance than under medium and high abundance.The reported survival records also show significant differences in survival rates among players.Source: §5.1 · p. 5
5.2 Bidding Status
- As resource abundance increases, the minimum successful bid decreases; scarce resources are associated with more intense competition and higher bids.Under scarce resources, minimum successful bids rise rapidly at first and then fall after 10 days; under abundant resources, they rise moderately throughout, which the authors associate with inflation as wealth accumulates when survival is guaranteed.Source: §5.2 · p. 5
6 Analysis
The analysis relates survival to player advantages, resource abundance, and persona assignment. It reports lower survival under scarce initial supplies and different persona-associated survival changes across resource conditions.
6.1 Players’ Advantages and Disadvantages
- Cindy, David, and Eric had significantly higher survival rates than Alex and Bob in settings without personas; in setting 1, Alex and Bob each had a survival rate of 0.10.The authors attribute advantages to money and, in low-abundance conditions, to lower demand when bids tie.Source: §6.1 · pp. 5–6
- The authors frame repeated experiments as a way for researchers to use LLM agents in batch experiments that can validate or challenge game-theory theories.Source: §6.1 · p. 6
6.2 Resource Abundance and Competition
- Lower initial RSR is associated with lower average survival, while games starting with lower RSR end with relatively more abundant resources.The authors observe more aggressive strategies in games beginning with intense competition and more conservative strategies when resources are initially abundant.Source: §6.2 · p. 6
6.3 Persona and Survival
- Persona assignment increases survival under low resource supply but decreases it under medium supply, with survival also changing differently for individual players.Cindy and David’s survival rates decreased after persona assignment, while Eric’s significantly improved.Source: §6.3 · p. 6
7 Subjective Evaluation
Human judges rated LLM agents close to their own performance overall, but found weaker adaptability and information use alongside stronger long-term planning. Their assessments also raised questions about whether persona prompts produce deeply aligned identities.
7 Subjective Evaluation
- Ten judges assessed 30 randomly selected records from 60 experiments, with five judges per record and five shared performance dimensions.The 15 persona-setting records were also assessed for Identity Alignment.Source: §7 · p. 6
- Agents were rated close to human self-assessments overall, below humans in Adaptability and Information Utilization, but above them in Long-term Planning.Table 3 reports the assessment dimensions; Identity Alignment applies only to records with personas.Source: §7 · p. 7, Table 3 · p. 7
- Judges associated agents’ long-term planning with saving for survival and future bids, while human players focused more on winning the current auction.The authors also report that agents did not adapt well to new information or adjust strategies as efficiently as humans.Source: §7 · p. 7
- Persona agents received low Identity Alignment scores with substantial variance, suggesting that adding persona information to the system prompt may not simulate personalities deeply.Identity Alignment was assessed only for records with personas.Source: §7 · pp. 7–8, Table 3 · p. 7
8 Conclusion
The conclusion presents Alympics as a platform for studying strategic competition over limited resources and examining how resource abundance and persona settings influence payoffs. It describes the framework as flexible and reproducible, with more complex, realistic scenarios as future work.
8 Conclusion
- Alympics is presented as a platform for game-theory research using LLM agents in strategic competition for limited resources.The paper examines how resource abundance and persona settings influence game payoffs.Source: §8 · p. 8
- The conclusion characterizes Alympics as a controlled, scalable, reproducible environment for exploring game theory.The authors describe it as flexible and robust.Source: §8 · p. 8
- The authors identify refining Alympics and investigating more complex, true-to-life game scenarios as future work.Source: §8 · p. 8
Ethical Statement
The ethical statement reports no ethical issues.
Ethical Statement
- The paper reports no ethical issues.Source: Ethical Statement · p. 8
A.1 Prompts
The appendix documents the Water Allocation Challenge prompts and rules, illustrates how bidding reasons reveal strategy, and describes records and evaluation guidance for examining gameplay. The materials cover the game flow from daily bids and public results through gameplay tracking and subjective assessment.
A.1 Prompts
- The prompts present game rules as a system message, then give agents a daily bid request and the prior auction’s public results as context for the next bid.The bid prompt supplies the round, water supply, player status, and asks for a bid with its logic.Source: §A.1 · p. 10
- The challenge runs for 20 days with five residents who have different water needs and budgets; daily sealed bids allocate water to the highest bidders, with lower needs breaking ties.Players seek survival, and their health changes according to water access and consecutive no-water days.Source: §A.1 · p. 10
A.2 An Example of A Round of the Game
- On Day 7, total water supply was 19 units; bids were $150, $200, $120, $180, and $300, and Eric won water as Bob’s HP fell below 0 and he was considered dead.Source: §A.2 · p. 12
A.3 Gameplay Details
- Gameplay records include bids, allocations, health, bidding reasons, and no-water days, supporting analysis of survival and strategies across settings.The appendix presents round-by-round bids, health, and balances for first experiments in each setting.Source: §A.2 · p. 12, §A.3 · p. 12
A.4 Human Judges’ Gameplay Records
- Human judges’ survival rates and bidding trends were reported as very consistent with those of Agent Players under corresponding resource-supply settings.The paper presents this as an indirect indication that Agent Players can supplement game-theory experiments.Source: §A.4 · p. 12
A.5 Instruction for Human Subjective Evaluation
- The subjective evaluation asks judges to rate performance from 1 to 5, with guidance on information use, adaptability, long-term planning, and identity alignment.The appendix defines information use in terms of considering real-time information and using available information comprehensively.Source: §A.5 · p. 17