So, I did not forget about that particular case. In my particular brand of cryptoeconomic analysis, I try to decompose cooperation incentives into three types:
Incentives generated by the protocol
Altruism
Incentives arising from the desire to have the protocol succeed because one has a stake in it
I often group (2) and (3) into one category, “altruism-prime”, but here we can separate them.
The important point is that category 1 incentives are always present as long as the protocol specifies them, category 2 incentives are always present, but the size of category 3 incentives is proportional to the “probability of being pivotal” of each node—essentially, the probability that the node actually is in a situation where its activity will determine the outcome of the game.
Note that I do not consider 49⁄50 Nash equilibria realistic; in real massively multiplayer games, the level of confusion, asynchronicity, trembling hands/irrational players, bounded rationality, etc, is such that I think it’s impossible for such a finely targeted equilibrium to maintain itself (this is also the primary keystone of my case against standard and dominant assurance contracts). Hence why I prefer to think of the probability distribution on the number of players that will play a particular strategy and from there the probability of a single node being pivotal.
In the case of cryptoeconomic consensus protocols, I consider it desirable to achieve a hard bound of the form “the attacker must spend capital of at least C/k” where C is the amount of capital invested by all participants in the network and k is some constant. Since we cannot prove that the probability of being pivotal will be above any particular 1/k, I generally prefer to assume that it is simply zero (ie, the ideal environment of an infinite number of nodes of zero size). In this environment, my usage of “dominant strategy” is indeed fully correct. However, in cases where hostile parties are involved, I assume that the hostile parties are all colluding; this maximally hard double-standard is a sort of principle of charity that I believe we should hold to.
So, I did not forget about that particular case. In my particular brand of cryptoeconomic analysis, I try to decompose cooperation incentives into three types:
Incentives generated by the protocol
Altruism
Incentives arising from the desire to have the protocol succeed because one has a stake in it
I often group (2) and (3) into one category, “altruism-prime”, but here we can separate them.
The important point is that category 1 incentives are always present as long as the protocol specifies them, category 2 incentives are always present, but the size of category 3 incentives is proportional to the “probability of being pivotal” of each node—essentially, the probability that the node actually is in a situation where its activity will determine the outcome of the game.
Note that I do not consider 49⁄50 Nash equilibria realistic; in real massively multiplayer games, the level of confusion, asynchronicity, trembling hands/irrational players, bounded rationality, etc, is such that I think it’s impossible for such a finely targeted equilibrium to maintain itself (this is also the primary keystone of my case against standard and dominant assurance contracts). Hence why I prefer to think of the probability distribution on the number of players that will play a particular strategy and from there the probability of a single node being pivotal.
In the case of cryptoeconomic consensus protocols, I consider it desirable to achieve a hard bound of the form “the attacker must spend capital of at least C/k” where C is the amount of capital invested by all participants in the network and k is some constant. Since we cannot prove that the probability of being pivotal will be above any particular 1/k, I generally prefer to assume that it is simply zero (ie, the ideal environment of an infinite number of nodes of zero size). In this environment, my usage of “dominant strategy” is indeed fully correct. However, in cases where hostile parties are involved, I assume that the hostile parties are all colluding; this maximally hard double-standard is a sort of principle of charity that I believe we should hold to.