Conditions Under Which Paid AI Becomes Advantageous A Control-Theoretic Model of Success Index with Self-Expectation Error

We develop a phenomenological and control-theoretic model of social success under paid AI assistance. A success index Q is defined using invested resources, social expectations, and ability thresholds. Introducing paid AI effects, we show that the primary structural risk of payment is not cost itself but an internally generated self-expectation error. We derive explicit conditions under which paid AI is advantageous, neutral, or harmful, and present a control strategy for sustainable payment.