Incentive mechanisms are critical for fostering active participation and ensuring honest behavior among system nodes in relay chains, particularly in the absence of centralized oversight. However, existing research on cross-chain incentives faces several limitations: the absence of a unified analytical framework, insufficient consideration of the bounded rationality of system nodes, and weak resilience against malicious behaviors. To overcome these issues, we propose IncentRelay, a comprehensive incentive mechanism that motivates bounded-rational nodes to participate and comply with system procedures. Specifically, we employ evolutionary game theory to model the behavioral dynamics of diverse nodes within a reward-penalty-based economic framework. By deriving replicator dynamic equations and analyzing the stability of local equilibrium points, we establish the conditions under which all participants adopt trusted strategies. Extensive experiments further demonstrate the existence of evolutionarily stable strategies (ESS) and validate the effectiveness of IncentRelay in mitigating collusion and free-riding behaviors, while maintaining strong scalability and adaptability in large-scale practical scenarios compared with baseline methods.