To spam, or not to spam, that is the question. The setup is as follows: in IOTA 2.0, the available bandwidth (for example, 1000tps), will be fairly divided between the actors according to their access mana. If the system is congested (the whole bandwidth is used), then, in the long run, no actor can exceed its quota; if the system is far from congestion, then exceeding one’s quota can be tolerated. See e.g. https://govern.iota.org/t/the-networking-layer-in-coordicide/369, https://govern.iota.org/t/buffer-management-for-the-icca-scheduler/1226, https://govern.iota.org/t/buffer-management-for-the-icca-scheduler/1226 for more details.
Since, as we all know, the token distribution (and hence the mana distribution too) is quite uneven, the large mana holders will have also proportionally large throughput quotas that they potentially won’t be wholly using for their own needs. They therefore would either sell the access mana directly (to those who want to operate their own nodes), or operate public nodes themselves to process other’s transactions. In some cases, they would be potentially giving some access to these nodes for free – if you are well invested into something, you naturally want it to grow-and-prosper, and so it’s in your interest to attract more users to the ecosystem. However, we of course cannot rely on (reasonable) altruism entirely; surely there will be many actors who will charge a fee for using their nodes.
Now, we finally come to the main topic of this note. It is clear that there will always be some demand for such node services – there will be people who do not want to deal with the costs of creating/maintaining own nodes, there will be businesses who want to guarantee their share in the bandwidth for the future in the case the system eventually becomes congested even if currently it is not, etc. However, it is also clear that the situation “the whole system is congested” is favorable for these big players: in such a case, all users which need more throughput would have to buy it, potentially at high prices. In view of that, some people argue that all big mana holders would be permanently spamming to occupy all their quota, and the system will be permanently congested. If there were only one big player (or all big players had some binding agreement on the common strategy, which is essentially the same), that would indeed be the case. On the other hand, we will now see that the situation is completely different when there are at least two big independent players (by the way, I didn’t rigorously define what I mean by “big player”, but hopefully you understand me anyway). Let us denote those by 1,\ldots,N, and let’s say that player k uses the “spamming strategy” if it decides to occupy its whole throughput quota by “completing” it with spam, and “non-spamming strategy” if it doesn’t do so. The strategy vector of the players is S=(s_1,\ldots,s_N), where s_k\in\{0,1\} is the k\rm{th} player’s strategy, 0 stands for spamming and 1 for non-spamming.
Claim. Assume N\geq 2. Then, the unique Nash equilibrium of the system is S=(1,\ldots,1) (that is, all players are not spamming).
Proof. In fact, this is really analogous to the Prisoner’s dilemma – a basic example in Game Theory which illustrates that the players’ behaviors will be not necessarily those that guarantee the “greatest common good” for them. Note that
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since malicious spamming of the sort “I’m spamming the hell out of the system to make you pay more” is not exactly a socially acceptable behavior (and IOTA is supposed to be a collaborative system, based on “you help me, I help you” principle), the spamming players will probably try to disguise their spamming to look like a legitimate activity; in any case, if someone clearly identifies some of his messages as spam, it would be reasonable for the honest actors to punish him (e.g., by reducing his bandwidth).
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now, if you are a customer who is looking for a node service provider for your transactions, which one would you choose, one who has spare bandwidth, or one who is completely occupied already? Clearly, you would choose the former one, because then you will be sure that your transactions will go through soon; it seems not likely that completely occupied nodes would get any new customers.
Therefore, we see that if s_k=0, then the k\rm{th} player would increase its expected payoff by adopting strategy 1 (i.e., non-spamming); this shows the claim. \Box