Federated learning (FL) enables social networks to utilize distributed user data without direct exposure. However, when FL updates are encrypted to prevent gradient inversion and privacy leakage, observability is significantly reduced and traditional anomaly detection is weakened. This creates opportunities for ciphertext poisoning while cryptographic audits incur prohibitive costs at scale. The key challenge is to design defenses that balance privacy protection, detection capability, and resource constraints. In this paper, we address this challenge by proposing an evolutionary game theoretic defense framework for encrypted FL in social networks. The framework models detection intensity of the server and poisoning propensity of clients as co-evolving strategies. It explicitly incorporates false positive penalties, external incentives for attackers, and practical constraints such as bandwidth and energy budgets. Through equilibrium analysis, we show how detection policies adapt to varying costs and incentives, and we identify stable strategy profiles under different deployment conditions. The framework yields actionable guidance for tuning server-side defenses, offering adaptive and cost-aware protection against ciphertext poisoning in large-scale social networks.