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Scammers have increasingly adopted AI-driven capabilities, evolving from automated message generation to fully agentic conversational systems that scale operations and maximize the exploitation of fraudulent resources before detection and takedown. In parallel, agentic scambaiting has emerged as a defensive approach in which autonomous agents impersonate potential victims and engage scammers in sustained interactions to extract actionable threat intelligence, such as mule bank accounts and cryptocurrency wallet addresses, that can be reported to disrupt fraudulent infrastructures. Together, these developments transform online fraud into an adversarial socio-technical ecosystem in which autonomous scamming and scambaiting agents engage in deceptive interactions while competing over the discovery, preservation, and exploitation of one another's resources. A fundamental and largely unexplored question is how defensive scambaiting can remain effective in an agent-to-agent environment, and under what conditions either side gains a strategic advantage. In this paper, we present a formal model of agent-to-agent fraud interactions that captures the strategic decision spaces available to both attackers and defenders. Using this framework, we analyze the dynamics of engagement, resource consumption, belief adaptation, and disruption outcomes. We find that scammer profitability turns negative once baiting-agent prevalence exceeds certain thresholds, and that when both sides improve at the same pace, defender investment in mimicry quality outpaces equivalent gains in scammer detection capability, so the arms race favors the defender under our baseline parameters. Our model and findings provide insights into the stability, scalability, and long-term effectiveness of autonomous defensive agents in an evolving AI-mediated fraud landscape.