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Does the lightning network have an inherent incentive to centralize? Routing payment requires locking large amounts of bitcoin. Only big players can do that. And furthermore the larger the player, the more payments he can route.
Has someone analyzed this?

(Please don't talk about the current situation because such processess take time.)

Almost 2 years ago I wrote (#486306) on SN about LN topology future and made this simple scheme:

Routing payment requires locking large amounts of bitcoin

Please stop saying that stupid thing. You are not "locking" but allocating liquidity to a payments market.
And LN is not formed only b y public routing nodes, but also with private nodes.

Only big players can do that

Wrong. Take advantage of them or LSPs... they are there to serve you and your private node. They are just liquidity providers.

Centralization comes only from Spark / Ark / Liquid that if they get too much use, and became main networks used for payments, than we are fucked.

You can have a total invisible private payment network with LN if you want, as I explained here: #843264. In fact is what Spark is trying to do, but it promote it as public... trying to fool gullible users.

So as long as the LN protocol is used properly, it could be several private networks used between small and large communities, for bitcoin payments. And you will not even see them.

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Locking is not a stupid thing to say. In fact, it's quite precise. A channel is money locked in a 2-of-2 multisig, where you do not have one of the keys. Your funds are only unlocked if your counter-party cooperates, or after the CSV delay.

Finance trends towards centralization generally, centralization is efficient

Economies of scale apply to larger lightning nodes like any other good or service

Edges have an incentive to connect to hubs in many cases because less hops = efficiency

That said, there is no real "moat" a pure Lightning node has. The network is about as flat as one could possibly be. The biggest nodes belong to services of other value-added things or external distribution, which in-turn attracts organic peering.

Routing payment requires locking large amounts of bitcoin.

This is the biggest misconception, and one of the reasons yield chasing is dumb. Nodes raking in high "yield" achieve that largely do to other peoples liquidity. CashApp famously boasts their 10% APY, but thats not 10% APY on their capital, by servicing an exchange they attract peers and are earning yield off other peoples capital.

A bank without depositors is just a bond holder, banks make money off other peoples cash.

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You are locking the bitcoin in a sense that if you deploy it (use it to buy something else), your node won't have any money to route anything. That's what I ment. Like... I don't know... Opportunity cost (and the fact that funds would be safer in non-hot wallet).

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I'm just saying that your node's capacity can be multiples of your own capital, so your yield isn't really correlated to how much you keep hot... but how much peering you attract for other reasons (CashApp example)

funds would be safer in non-hot wallet

This is also a good point as to why chasing yield is dumb

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I don't really care about yield itself. I more about care whether there is a possibility with time the routing nodes to become less in number.

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There's no such thing as a routing node, just nodes, some just route better than others.

The network is still small, so overall I expect they'll increase, but not relative to overall growth.

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LOL. There certainly are non-routing nodes. I have one running on my phone.

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That doesn't make one not on your phone a routing node, a node is a node, they are not distinct functions.

Yours is an edge node.

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Am I using a wrong word here? What is the correct term for a non-edge node that routes payments through it?

Read this: #1479081

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Yes, for two reasons.

  1. More payments will naturally flow through nodes with more channels and liquidity. For example, an LSP will route more traffic than a raspberry pi with two channels. This is inherent and good.
  2. The protocol does not give a node a reliable way to find a feasible path to the destination. Each channel a payment is routed through adds a risk of failing due to insufficient liquidity, which means longer payments routes are exponentially less likely to succeed than shorter routes. Generally speaking, there are two mitigation's to this: make bigger channels and prefer shorter routes during path finding. This is bad centralization.