Strategic evolution under varying dilemma strength and social efficiency deficit in asymmetric dyadic game

Understanding the emergence and stability of cooperation in asymmetric social interactions presents a central challenge in evolutionary game theory. In this study, we develop and analyze a two-population asymmetric dyadic game model that captures heterogeneity in behavioral traits, specifically, risk aversion and gambling tendencies alongside a payoff-sharing mechanism that induces structural asymmetry in reward distribution. By deriving analytical equilibrium conditions and exploring replicator dynamics, we identify key parameter regions where cooperation, mutual defection, and asymmetric strategy pairings become evolutionarily stable strategies (ESS). Our results reveal that strategic outcomes are susceptible to the interaction between behavioral predispositions, the asymmetry of payoff allocation, and the underlying dilemma strength. Importantly, we introduce the Social Efficiency Deficit (SED), a novel quantitative metric that measures the gap between the socially optimal outcome and the Nash equilibrium in the context of asymmetric dyadic games for the first time. Through analytical characterization and simulation, we show that SED effectively captures the intensity of the social dilemma and provides a meaningful assessment of how far strategic behavior deviates from collective efficiency. Positive SED values correspond to severe inefficiencies where individual rationality undermines group welfare, while zero SED regions mark conditions that align individual incentives with cooperative outcomes. Additionally, Multi Agent based Monte Carlo spatial simulations highlight how localized interactions and structural asymmetry give rise to dynamic spatial patterns, such as cooperative clusters and defective regions, depending on the alignment between strategic incentives and payoff structures. Our findings underscore the complex interplay between individual behavior, structural asymmetry, and systemic efficiency, offering both theoretical insights and practical implications for promoting cooperation in socio-economic systems marked by inequality and heterogeneous preferences.