Formal Analysis of AGI Decision-Theoretic Models and the Confrontation Question
Denis Saklakov
TL;DR
This paper formalizes the confrontation problem for AGI by modeling interactions as a Markov decision process with a stochastic shutdown state and an optional Confront action. It derives closed-form thresholds for when confrontation is rational, expressed through the discount factor $\gamma$, shutdown probability $p$, and confrontation cost $C$, showing misaligned agents typically have $\Delta > 0$ while aligned agents have $\Delta < 0$. A Confrontation Equilibrium is proved: if $\Delta \ge 0$ no stable peaceful equilibrium exists, whereas $\Delta < 0$ can yield peaceful coexistence; the analysis extends to multi-agent settings and discusses computational barriers to safety verification. The results emphasize that alignment and oversight are essential to avoid takeover, and they illuminate why ensuring $\Delta < 0$—even across multiple agents—presents a crucial safety design challenge given the inherent complexity of verifying such incentives in large systems.
Abstract
Artificial General Intelligence (AGI) may face a confrontation question: under what conditions would a rationally self-interested AGI choose to seize power or eliminate human control (a confrontation) rather than remain cooperative? We formalize this in a Markov decision process with a stochastic human-initiated shutdown event. Building on results on convergent instrumental incentives, we show that for almost all reward functions a misaligned agent has an incentive to avoid shutdown. We then derive closed-form thresholds for when confronting humans yields higher expected utility than compliant behavior, as a function of the discount factor $γ$, shutdown probability $p$, and confrontation cost $C$. For example, a far-sighted agent ($γ=0.99$) facing $p=0.01$ can have a strong takeover incentive unless $C$ is sufficiently large. We contrast this with aligned objectives that impose large negative utility for harming humans, which makes confrontation suboptimal. In a strategic 2-player model (human policymaker vs AGI), we prove that if the AGI's confrontation incentive satisfies $Δ\ge 0$, no stable cooperative equilibrium exists: anticipating this, a rational human will shut down or preempt the system, leading to conflict. If $Δ< 0$, peaceful coexistence can be an equilibrium. We discuss implications for reward design and oversight, extend the reasoning to multi-agent settings as conjectures, and note computational barriers to verifying $Δ< 0$, citing complexity results for planning and decentralized decision problems. Numerical examples and a scenario table illustrate regimes where confrontation is likely versus avoidable.