How is it possible that a token has the same price with five LPs in differents blockchains?

I’ve had this in my head for a long time and I’ve thought about asking the question in this wonderful space.
You always answer me.
They are very nice, thank you.
So I try my luck to see if the question seems interesting to you.
I also hope I didn’t make the wrong place to do it.

Ok, that is may question…

We have a token like Axies Infinity per example.
In which we verify that it have contracts deployed in several blockchains and ethereum too.

How is it possible that they have the same price if in each blockchain there will be different liquidity pools with different buying and selling markets in volume?

How do they do that?!!

I don’t know exactly how they do that, but if there is a way to do cross chain transfers for that token then the price will automatically sync between chains.

So the LPs are connected?

When someone buys in BSC, is the price updated in Ethereum and others blockchains?

It all seems so crazy to me.

not directly, but if you can transfer the token from one chain to another chain, with multiple intermediate transactions then the price will sync

thanks @cryptokid, then, the price is an estimate that “I don’t know what” with what exists in each PL?

I guess arbitrage trading is one way to balance prices between different exchanges.

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Arbitrage operates automated trades. But this cannot make it so that if there is a large sale in a PL, it distributes that volume to all the PLs. If I put 10 Ethereum against Axi for example… I have to do the equivalent in the other pools so that the price remains the same. This breaks my head.

Or maybe what moves are the PL tokens of each pool to balance?

if there is a big price difference between two places for the same token, and if the token can be transferred from one place to the other somehow, then someone will try to gain from that price difference and that is how the prices will get in sync

What you say is interesting. If the volume of the native token on a network increases, raising the price, holders who have tokens on a network with a lower price could pass their “tokens” with a bridge not?

The solution may be here:

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" user’s assets can only exist on one blockchain at any given point in time, liquidity within the application as a whole becomes fragmented across different on-chain environments. The result is reduced liquidity within each individual deployment, leading to higher slippage for users and a reduction in trading fees. Furthermore, each deployment of an AMM on another blockchain starts from scratch with zero liquidity, which can result in higher dilution of the protocol’s native token if liquidity mining programs are extended to the new deployment as a way to bootstrap liquidity."

text from here