Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Certifying Concavity and Monotonicity in Games via Sum-of-Squares Hierarchies
Authors: Vincent Leon, Iosif Sakos, Ryann Sim, Antonios Varvitsiotis
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we apply our techniques to canonical examples of extensive-form games with imperfect recall. ...6 Application: Extensive-Form Games with Imperfect Recall 6.1 Experimental Methodology & Results |
| Researcher Affiliation | Academia | 1UIUC 2SUTD 3NUS CQT 4Archimedes/Athena RC EMAIL EMAIL All listed affiliations (UIUC, SUTD, NUS CQT, Archimedes/Athena RC) are universities or public research centers, and the email domains (.edu, .sutd.edu.sg) correspond to academic institutions. |
| Pseudocode | No | The paper describes mathematical formulations and hierarchies of optimization problems (e.g., SOSℓ(G) in Theorem 3.2), but these are not presented in a structured pseudocode block. It describes the approach algorithmically but not in pseudocode format. |
| Open Source Code | Yes | Our code1 is implemented using the Sum Of Squares package for Julia [36, 63] and run on a Mac Book Air with 16 GB RAM. 1Code used to generate the experiments in Section 6 can be found in our github repo. |
| Open Datasets | No | The paper constructs or refers to types of games and their mathematical representations (polynomials), rather than using pre-existing empirical datasets. For example: "Example 3: A degree-4 strictly monotone general-sum game. ... Using this method, we construct a two-player game..." and "Example 4: A degree-5 zero-sum game. We create a two-player zero-sum EFG..." No concrete access information for publicly available datasets is provided. |
| Dataset Splits | No | The paper does not use traditional empirical datasets with training, validation, and test splits. The experiments involve applying methods to constructed game examples, rather than analyzing data from predefined splits. |
| Hardware Specification | Yes | Our code1 is implemented using the Sum Of Squares package for Julia [36, 63] and run on a Mac Book Air with 16 GB RAM. |
| Software Dependencies | No | The paper mentions "Sum Of Squares package for Julia [36, 63]". While specific software is named, specific version numbers for Julia itself or the Sum Of Squares package are not provided. |
| Experiment Setup | Yes | Example 1: The absent-minded taxi driver in Figure 3. In the case of the game in Figure 3, we let x denote the probability of choosing C and 1 x be the probability of choosing E. We use the SDP hierarchy in Eq. (17) to certify SOS-monotonicity of the polynomial u(x) = 3x2 + 4x. We select ℓ= 2 and obtain SOS2(G ) 6 < 0. Then, by Statement 4 of Theorem 3.2, the game is strictly monotone. Example 4: ...Two additional constraints are imposed to retain the properties of the original EFG: The modified game has to be zero-sum, and the information structure of the original EFG has to be preserved. To preserve the information structure of the game, we select the monomial basis for the new payoff functions to be precisely the monomial basis that can appear in the original game. Example 5: ...randomly generate the payoff functions for P1 and P2 by independently sampling the coefficient of each monomial in the basis from a uniform distribution on [ 1, 1]. |