If the same thing sells for $100 in one market and $105 in another, you can buy in the first and sell in the second for a near-riskless $5 — arbitrage. But the very act of doing it pushes the low price up and the high price down, until the gap closes to nothing. That’s why textbook free lunches vanish the moment they appear. Slide the gap and watch the profit — and the closing.
Arbitrage is a riskless profit from the SAME asset priced differently in two places: buy at the low price p₁, sell at the high p₂, and pocket (p₂−p₁) minus transaction cost — profit only while the gap exceeds the cost. Crucially it is self-erasing: buying raises p₁ and selling lowers p₂, so the gap CLOSES, which is why efficient markets have (almost) none. The Law of One Price is arbitrage’s fixed point. A fail-loud self-check throws unless profit equals the gap minus cost when positive and is zero once the gap falls below cost. ◆ real finance, node-verified.
A single-round, frictionless-except-cost model (the exact gap−cost profit and the closing dynamic); real arbitrage carries execution risk, latency and capital limits — the self-erasing free-lunch is the exact core.