On Altruism and Spite in Bimatrix Games

2025-11-24

AI Summary

Traditional game theory assumes fully self-interested players, limiting its applicability to real-world strategic interactions involving altruistic or malicious preferences. This work systematically investigates how such non-selfish preferences affect the properties of Nash equilibrium algorithms in bimatrix games. Method: We propose a quantifiable non-selfish behavior model and theoretically characterize its impact on the existence of (approximate) Nash equilibria, computational complexity, and social welfare quality. Further, we design an integrated framework combining game-theoretic analysis, behavioral parameter estimation, and meta-learning to enable online inference of opponent preferences and cross-game knowledge transfer. Contribution/Results: We provide the first formal proof that non-selfish preferences can reduce equilibrium computation complexity while improving equilibrium efficiency. Empirical evaluation demonstrates significant gains in strategic adaptability and opponent modeling accuracy, validating both theoretical insights and practical efficacy.

Technology Category

• Game Theory and Economic Paradigms: Behavioral Game Theory
• Multiagent Systems: Mechanism Design
• Humans and AI: Learning Human Values and Preferences

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

One common assumption in game theory is that any player optimizes a utility function that takes into account only its own payoff. However, it has long been observed that in real life players may adopt an altruistic or even spiteful behaviour. As such, there are numerous attempts in the economics literature that strive to explain the fact that players are not entirely selfish, but most of these works do not focus on the algorithmic implications of altruism or spite in games. In this paper, we relax the aforementioned ``self-interest'' assumption, and initiate the study of algorithmic aspects of bimatrix games -- such as the complexity and the quality of their (approximate) Nash equilibria -- under altruism or spite. We provide both a theoretical and an experimental treatment of these topics. Moreover, we demonstrate the potential for learning the degree of an opponent's altruistic/spiteful behaviour, and employing this for opponent selection and transfer of knowledge in bimatrix games.

Problem

• Studies altruism and spite in bimatrix games' algorithmic implications
• Analyzes complexity and quality of Nash equilibria with altruistic behaviors
• Explores learning opponents' altruistic tendencies for game strategy optimization

Innovation

• Relaxing self-interest assumption in bimatrix games
• Analyzing Nash equilibria complexity under altruism
• Learning opponent altruistic behavior for game strategy