Alexander Strang, David Sewell, Alexander Kim, Kevin Alcedo, David Rosenbluth
{"title":"Principal trade-off analysis","authors":"Alexander Strang, David Sewell, Alexander Kim, Kevin Alcedo, David Rosenbluth","doi":"10.1177/14738716241239018","DOIUrl":null,"url":null,"abstract":"How are the advantage relations between a set of agents playing a game organized and how do they reflect the structure of the game? In this paper, we illustrate ‘Principal Trade-off Analysis’ (PTA), a decomposition method that embeds games into a low-dimensional feature space. We argue that the embeddings are more revealing than previously demonstrated by developing an analogy to Principal Component Analysis (PCA). PTA represents an arbitrary two-player zero-sum game as linear combination of simple games via the projection of policy profiles into orthogonal 2D feature planes. We show that the feature planes represent unique strategic trade-offs and truncation of the sequence provides insightful model reduction and visualization. We demonstrate the validity of PTA on a quartet of games (Kuhn poker, RPS + 2, Blotto and Pokemon). In Kuhn poker, PTA clearly identifies the trade-off between bluffing and calling. In Blotto, PTA identifies game symmetries and specifies strategic trade-offs associated with distinct win conditions. These symmetries reveal limitations of PTA unaddressed in previous work. For Pokemon, PTA recovers clusters that naturally correspond to Pokemon types, correctly identifies the designed trade-off between those types, and discovers a rock-paper-scissor (RPS) cycle in the Pokemon generation type – all absent any specific information except game outcomes.","PeriodicalId":50360,"journal":{"name":"Information Visualization","volume":"48 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information Visualization","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1177/14738716241239018","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
How are the advantage relations between a set of agents playing a game organized and how do they reflect the structure of the game? In this paper, we illustrate ‘Principal Trade-off Analysis’ (PTA), a decomposition method that embeds games into a low-dimensional feature space. We argue that the embeddings are more revealing than previously demonstrated by developing an analogy to Principal Component Analysis (PCA). PTA represents an arbitrary two-player zero-sum game as linear combination of simple games via the projection of policy profiles into orthogonal 2D feature planes. We show that the feature planes represent unique strategic trade-offs and truncation of the sequence provides insightful model reduction and visualization. We demonstrate the validity of PTA on a quartet of games (Kuhn poker, RPS + 2, Blotto and Pokemon). In Kuhn poker, PTA clearly identifies the trade-off between bluffing and calling. In Blotto, PTA identifies game symmetries and specifies strategic trade-offs associated with distinct win conditions. These symmetries reveal limitations of PTA unaddressed in previous work. For Pokemon, PTA recovers clusters that naturally correspond to Pokemon types, correctly identifies the designed trade-off between those types, and discovers a rock-paper-scissor (RPS) cycle in the Pokemon generation type – all absent any specific information except game outcomes.
期刊介绍:
Information Visualization is essential reading for researchers and practitioners of information visualization and is of interest to computer scientists and data analysts working on related specialisms. This journal is an international, peer-reviewed journal publishing articles on fundamental research and applications of information visualization. The journal acts as a dedicated forum for the theories, methodologies, techniques and evaluations of information visualization and its applications.
The journal is a core vehicle for developing a generic research agenda for the field by identifying and developing the unique and significant aspects of information visualization. Emphasis is placed on interdisciplinary material and on the close connection between theory and practice.
This journal is a member of the Committee on Publication Ethics (COPE).