Quote from: NewLiberty on August 05, 2014, 08:21:49 PM

Quote from: cypherdoc on August 05, 2014, 01:37:26 AM

Quote from: NewLiberty on August 05, 2014, 01:24:17 AM

Quote from: Trader Steve on August 05, 2014, 01:20:04 AM

Quote from: cypherdoc on August 04, 2014, 04:22:49 PM

it looks to me that mining would be best described as being in a Pure Strategy Nash Equilibrium - cypherdoc
Highlights are mine:

"A pure strategy Nash equilibrium is a profile of strategies such that each players (miner's) strategy is a best response ((results in the highest available payoff (block reward)) against the equilibrium strategies of the other players (miners).

A pure strategy Nash equilibrium only requires that the action taken by each agent (miner) be best against the actual equilibrium actions taken by the other players (miners), and not necessarily against all possible actions of the other players (miners). In other words, it's expected for some miners to be malicious.

A Nash equilibrium has the nice property that it is stable: if each player expects 'a' to be the profile of actions played, then no player (miner) has any incentive to change his or her action (no incentive to start cheating). In other words, no player (miner) regrets having played the action that he or she played in a Nash equilibrium."

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1968579

Nice. I hadn't looked at it that way but it makes perfect sense.

Nash equilibrium works well in theory, the real world is a little more messy.
Pre-mass adoption there are so many outside interests seeking bitcoin failure that there are other incentives at play.
Once there is more distribution and buy in, the full effects of the Nash Equilibrium will be much stronger than they are today.

the Nash equilibrium is a solution concept of a non-cooperative game; therefore, i think the Nash Equilibrium takes those hostile actors into account. the minimum # of participants required to apply the theory is 2 and doesn't depend on large #'s. what's also important for all actors to know and understand, and to know that the others know, is that the longest blockchain and the POW required to construct it is mathematically immutable. b/c we know that the hashrate of the Bitcoin Network is thousands of times larger than most of the supercomputers on Earth makes the strategical decision making of each individual actor clear; don't cheat.

Understood, I'm more referring to the folks that are the non-participants in the game. Lest we forget these currently vastly outnumber the participants with respect to potential game resources available to them. Game-ending scenarios are often dismissed as impossible when in fact they are merely unlikely, as are the application of non-monetary/computing power factors. Threats to date have generally been within the game players, and Nash applies well.

In general I not only agree but the also salute the application of the principle.

Consider however the implications if one were to throw something like stuxnet into the works or a fab level exploit into each of the main chip makers, say by coercion or covertly, and subsequently activated? There are defenses certainly, but it would be disruptive and could be timed with other types of interference. Unlikely but possible. Thankfully, we are not under serious attack or opposition, but I'd still give a BTC =~ 0 a >0 p value, and Nash holds the rest in place.

we're ALL part of a Nash Equilibrium. even the gubmints, banks, and skeptics.

when i decided to mine in 2011, i was fully aware that a non-economic attacker like a gubmint or bank could potentially screw my investment in BTC and mining equipment. but after reading thread after thread about the theoretical basis of a 51% attack, i decided it was worth the risk and that any such attempt would fail. that was my assessment. all the other miners are fully aware of that potential as well, yet we all plow forward. why?

the open source phenomenon that represents Bitcoin should shine enough light on any such potential attacker to prevent such an attack from happening. any such attack should be temporary and able to be dealt with. Gavin has already stated what could be done as a counter measure. i think the attacker could even be identified through various means.

corruption and dishonest behavior likes to be hidden. crooks don't want to be identified. i think a gubmint or bank will make the assessment that it's too politically risky an endeavor to take on which would cost them millions (billions?) in losses, not only in dollars but in trust. see this interesting study:

From 1961 to 1989, the Berlin Wall divided one nation into two distinct political regimes. We
exploited this natural experiment to investigate whether the socio-political context impacts
individual honesty. Using an abstract die-rolling task, we found evidence that East Germans
who were exposed to socialism cheat more than West Germans who were exposed to
capitalism. We also found that cheating was more likely to occur under circumstances of
plausible deniability. Subjects were more likely to cheat by mis-reporting the chosen side of
the die than by making up rolls altogether. These results indicate that most people are
motivated to hide their dishonesty either from others (Hao and Houser, 2011) or from
themselves (Mazar et al., 2008).

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2457000