On the Security Budget Necessary and Available to Secure the Post-Mined Bitcoin Network

A Game Theoretical Floor and Ceiling for Post-mining Transaction Fees

In the future when all bitcoins have been mined we can consider the level of fees paid by transactors.

Game theoretically we can assume that every transactor or player won’t pay more than they have to (assumes a mature market etc.). We also assume that each player’s ‘willingness-to-pay’ function orders them (ie p1 is willing to the pay the most for inclusion, p2 the 2nd most…..plast the least).

Given a comparable game where only x amount of transactors will be able to have transactions included in a block, and thinking of blockspace as having (limited) slots for each transactor, we can think of the cutoff between the player that fills the last available blockspace slot and the ‘next-most-willing’ player who doesn’t make the cut.

We can think of this game such that the next-most-willing player sets the fee rate and understand that the players who are willing to pay enough to have their transactions included only need to pay more than the next-most-willing player’s highest fee consideration (rather than what they are most willing to pay).

On the Willingness to Pay to Use Bitcoin

From a certain view bitcoin can be thought to have 2 primary use cases: speculation and medium of exchange. The difference between the two seem to be time related and here we will simply only consider the latter use-case as the likely asymptotic future outcome and single primary use-case (ie loosely put bitcoin will become more stable over time as it gets further from its bootstrap stage).

We can distinguish between 2 game theoretically (ie assume players will only make transactions in which the benefit is greater than the cost) relevant reasons for a player to want to pay to be included in a block : 1) to make a beneficial transaction that is otherwise impossible and 2) using bitcoin to make a transaction is cheaper than any alternative means.

Here we can note (or re-solve with) the first consideration is as if the cost to use an alternative means is infinite (or more specifically is greater than the benefit).

Other cost benefit analysis can render different considerations as costs such as the liquidity which includes considerations on the size of the market cap of bitcoin and potential competitor mediums of exchange (ie if they must be exchanged for fiat).

On the Security of Other Chains

On this point we simply wish to axiomatically consider alt-coins as having intrinsically unviable cost-to-benefit if their market cap is significantly lower than bitcoin’s market cap.

This intrinsic unviability is true also for an alt-coin that has a significantly lower security budget (with respect to the benefit to an attacker attacking each chain).

Whether the above two observations hold true we want to suggest that an intrinsically unviable alt-coin option cannot contribute to bitcoin’s security budget dilemma.

On the Complexity of Avoiding Altruistic Security Payments

We can note there is no mechanism in place at the time to properly estimate the necessary security budget to defend versus a perpetual 51% attack nor is there a mechanism to determine which player(s) should contribute to what weight of the fees, if the “naturally determined” fees paid happen to otherwise fall short of securing the network.

In other words if the fee market doesn’t produce fees high enough thwart attack we consider the network to be lost in its current development state.

Who Might Be the Highest Paying Transactors?

Here we must consider those who would benefit (the most) from using bitcoin and what then they might be willing to pay to use it and what the implications of a fee market would set the fees at.

We also consider the most beneficial use-cases for transacting with bitcoin (where beneficial is the favorably weighted outcome of a cost-to-benefit observation).

If bitcoin suffers from a security dilemma in its current natural fee state it is destined to be secured, if to be secured at all, by at LEAST the highest value transactors and transactions of our global economy. Loosely put settlement between large institutions, corporations, governments etc.

Who are to be bitcoin’s Security Guarantors?

Who is to gain the most from turning off bitcoin’s network and what/how much is to gain? Is this gain enough to outweigh the ‘natural’ cost to transact with bitcoin? Is there a willingness from the transactors pool to pay a cost higher than what their greatest adversary would gain from destroying the network? Could there be a coordination mechanism to fundraise (feeraise)do so?

The cost of the security budget then is set as a function of the benefit of the most suitable attacker (aka The Great Excluder). And must not be above the net benefit of transacting for the transactors.

The Great Includer

Could there then be a global coordination to pay a necessary security budget through taxes to enshrine and secure bitcoin as a public good?

• Afterwards: That blockspace is secured with a temporal variable requires the considerations here to be extended to consider such a vector of time.*
• *it was meant to be implicit in this writing that an attacker must have reasonably tangible means to profit from attacking bitcoin or it isn’t very plausible they would waste so much value otherwise etc.*