Good morning Gregorio,
> We argue that in such scenario, in a network of n connected nodes, there is a
> tendency towards a state where exactly n-1 channels have perfectly balanced
> flows in the two directions ("self-balancing" channels), while all other
> channels are either unused, or have a permanent tendency towards imbalance:
> the channel balance accumulates at one end and the channel is only
> intermittently available in one direction ("stuttering" channels). We note
> that the "self-balancing" channels form a spanning tree of the network graph,
> which we call the "core spanning tree" of the payment network.
I have observed this as well in my armchair.
Indeed, the worst-case scenario for this would be a single central hub with n-1
channels to n-1 client nodes, with the hub itself as the nth node.
Fortunately, it seems to me that such a steady state will mildly shift and
additional channels will still be used intermittently.
(I have not read your paper in completeness yet, only the abstract above, so if
my ramblings have already been considered in your paper, do feel free to ignore
me).
For instance, consider a world where Lamborghini production experiences a
paradigm shift that massively reduces the cost of production while increase
quality.
Inevitably, Lambo prices in terms of Bitcoin will decline, as a consequence of
this improvement.
Thus, capacity in channels going Lamborghini producers becomes underutilized as
demand for the product saturates while supply increases.
However, "complementary goods" of such products are highly unlikely to
experience a commensurate increase in their own production.
For example, simply because Lamborghini production increases its efficiency,
does not mean that car insurance will experience the same increase in its
efficiency.
Thus, the supply of car insurance will remain largely the same, but demand
increases due to increased usage of Lamborghinis (a well-known phenomenon in
economics).
This implies that capacity in channels going to car insurance providers will be
overutilized and eventually saturate, leading to opportunistic reallocation of
funds from Lamborghini producers to car insurance providers (and concomitant
onchain activity to do this reallocation!).
Thus, I think that the minimum of n-1 channels would not remain stable for
long, given an actual real-world where change *is* the steady-state.
Assuming a continuously thriving and innovating global economy, we will expect
that there will be transient situations where demand and supply for various
products changes wildly.
In such situations, any "extra, unneeded" channels would end up catching the
additional capacity need as various innovations and improvements in the economy
occur and create change in demand and supply.
I believe the overall steady state will have c*n channels rather than merely
n-1, where c is some constant greater than 1, due to various local transient
demand/supply shocks.
Regards,
ZmnSCPxj
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