From Chaos to Order: Symmetry and Conservation Laws in Game Dynamics
Authors: Sai Ganesh Nagarajan, David Balduzzi, Georgios Piliouras
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we present basic mechanism design tools for constructing games with predictable and controllable dynamics. We show that arbitrarily large and complex network games, encoding both cooperation (team play) and competition (zero-sum interaction), exhibit conservation laws when agents use the standard regret-minimizing dynamics known as Follow-the-Regularized-Leader. These laws persist when different agents use different dynamics and encode long-range correlations between agents behavior, even though the agents may not interact directly. Moreover, we provide sufficient conditions under which the dynamics have multiple, linearly independent, conservation laws. Increasing the number of conservation laws results in more predictable dynamics, eventually making chaotic behavior formally impossible in some cases. Proof. We begin by expanding H(y) and taking the time derivative. |
| Researcher Affiliation | Collaboration | 1Singapore University of Technology and Design, Singapore 2Google Deep Mind, London, UK. Correspondence to: Sai Ganesh Nagarajan <sai nagarajan@mymail.sutd.edu.sg>, David Balduzzi <dbalduzzi@google.com>, Georgios Piliouras <georgios@sutd.edu.sg>. |
| Pseudocode | No | The paper describes mathematical dynamics and proofs but does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statement about releasing source code for the described methodology or provide a link to a code repository. |
| Open Datasets | No | The paper is theoretical and does not use datasets for training or evaluation. Figures are illustrative based on mathematical models, not empirical data. |
| Dataset Splits | No | The paper is theoretical and does not involve dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe any specific hardware used for running experiments or generating results. |
| Software Dependencies | No | The paper does not provide specific software names with version numbers or list any software dependencies for replication. |
| Experiment Setup | No | The paper describes theoretical models and mathematical analysis and does not include details on an experimental setup, hyperparameters, or training configurations. |