Cross-DEX Price Discrepancies

The same ETH can cost 1900 USDC on one exchange and 2100 USDC on another at the very same instant. That isn’t a glitch — it’s the default state of a world built from independent automated market makers. This lesson is about why that gap opens, exactly how much money sits inside it, and the deeply unintuitive reason you can’t just scoop up the whole thing.

Why two pools drift apart

Picture two lemonade stands on opposite ends of a beach. They don’t share a till, a menu, or a manager. If a thirsty crowd swarms the north stand, its prices creep up; the south stand, oblivious, keeps selling cheap. Nothing connects them except your willingness to walk between them.

An automated market maker (AMM) is exactly that lemonade stand. Each pool holds two reserves — say ETH and USDC — and prices every trade off the constant-product invariant:

$x \cdot y = k$

Here $x$ is the ETH reserve, $y$ is the USDC reserve, and $k$ is a constant the pool defends on every swap. The spot price of ETH (in USDC) is just the ratio of reserves:

$P = \frac{y}{x}$

Crucially, there is no shared order book across DEXes. Uniswap’s ETH/USDC pool and SushiSwap’s ETH/USDC pool are two separate piles of coins with two separate $k$ values. A swap on one pool changes only that pool’s reserves, and therefore only that pool’s price.

So when traders on different venues do their own thing — some buying on A, some selling on B — the two prices wander off in different directions. They diverge and stay diverged until someone deliberately trades the gap shut. That someone is an arbitrageur, and the gap is their paycheck.

When it matters

Every time you see “the price of ETH,” ask whose price. On-chain there is no single number — there’s a price per pool, and the spread between them is the raw material of cross-DEX MEV. The bigger and more fragmented the liquidity, the more often these gaps appear.

Buy cheap, sell dear — the constant-product math

Our two canonical pools:

The strategy writes itself: buy ETH where it’s cheap (A), sell it where it’s dear (B), pocket the difference. At the very first marginal unit, the math is gloriously simple — buy 1 ETH for $1900 on A, sell it for $2100 on B, and the gross spread is:

$2100 - 1900 = 200 \text{ (USDC per ETH)}$

That “200 USDC for moving one token between two pools” is the headline number that makes arbitrageurs salivate. It’s also a lie of omission, because it assumes the prices don’t budge while you trade. They do. The island below lets you slide the arbitrage size and watch the naive spread get devoured by reality.

Notice the left edge of the slider: at a tiny size, you really do capture roughly 200 USDC per ETH. The trouble starts the moment you get greedy.

When it matters

The naive spread tells you whether an opportunity exists; it never tells you how much you can extract. Confusing the two is how a bot “sees” a 200-USDC-per-ETH gap, fires a huge trade, and walks away with far less — or a loss. The real number always comes from the curve, never from the quote.

The trade moves the prices together

Here’s the twist that makes arbitrage self-extinguishing. When you buy ETH on A, you hand the pool USDC and take ETH out. A’s reserves shift: $x$ falls, $y$ rises, so its price $y/x$ climbs. When you sell that ETH on B, you do the reverse there: B’s $x$ rises, $y$ falls, so B’s price drops.

So the two prices march toward each other from both ends:

• Pool A (started at 1900): walks up as you buy.
• Pool B (started at 2100): walks down as you sell.

Keep going and they meet in the middle — at roughly 1999 USDC for the trade sizes around our optimum. The visual below shows a single pool climbing its own curve as you sell tokens into it; the spot price (the slope of the line from the origin) steepens with every unit.

The profound bit: the act that captures the spread is the act that closes it. You don’t arbitrage a gap and then watch it vanish — your own trade is the vanishing. Push enough volume through and the two pools quote the same price, the gap is gone, and there’s nothing left to capture. Arbitrage is a snake eating its own tail.

When it matters

This convergence is why no one stays rich off a single gap forever, and why the first bot to a discrepancy gets the cream. By the time the second arbitrageur arrives, the first one’s trade has already flattened most of the spread. Speed and ordering — the heart of MEV — exist precisely because the opportunity self-destructs on contact.

Why the optimal size is finite

Now the punchline. Naively you’d think: 200 USDC of gross edge per ETH, and the pools hold 100 ETH each — so just trade a huge amount and get rich. Wrong. Because every unit you trade closes the gap, your marginal profit per ETH falls as you go. Eventually it hits zero (the prices have met). Push past that and the prices cross — you’re now buying on the pool that’s become expensive and selling into the one that’s become cheap. You start handing the spread back.

That makes total profit hump-shaped in trade size: rising, peaking, then falling. For our canonical pools the peak sits at about 2.5 ETH, netting roughly 250 USDC:

Read the table top to bottom: profit climbs to its $250 peak at 2.5 ETH — exactly where the two prices kiss at ~1999 USDC — and then declines even though you’re trading more. By 6 ETH you’ve shoved A’s price clean above B’s and given most of the edge back.

What sets the cap is depth — how much liquidity each pool holds. Deeper pools (bigger reserves) move less per unit traded, so the gap closes slowly and the optimal trade is larger. Shallow pools impact-out almost immediately, so even a tiny arbitrage exhausts the edge. The optimum is wherever the marginal profit of one more ETH hits zero — not “as big as the reserves allow.”

When it matters

Sizing is the strategy. Two bots see the identical 200-USDC gap; the one that solves for the hump’s peak — and stops there — out-earns the one that fires the biggest possible trade. In the next lessons this exact “find the optimum, then race to land it first” problem is what the whole MEV supply chain is built around.

Recap