Lets look at an example. Your mining pool controls some portion of the hashpower <50%. They have 2 binary decisions to make for how they participate in the protocol. Which makes 4 possibilities: True/True, True/False, False/True, False/False. Which we will write as 2 bits: 00 01 10 11. Lets assume that the default strategy programmed into the mining pool is 01.
A nash equilibrium can only exist on the diagonal of the matrix. All the other spots mean that you are incentivized to use a non-default strategy. When looking for a nash equilibrium, you want to find a row such that the intersection of that row and the diagonal is the highest payout strategy in that row.
3. voting where we will all be 50 tokens richer if we can decide on G, we get nothing if we decide on B, there are 100 voters, and there is an adversary who is willing to bribe 1 token per voter to pay them to vote on B.
m0t0k1ch1.icon G に決まれば全員 50 トークンの利得が得られ、B に決まったら何も得られない
m0t0k1ch1.icon 100 人の投票者が存在し、投票者 1 人あたり 1 トークンの賄賂を渡して B に投票させようとする悪者がいる
4. futarchy. You can bet in 2 directions. H = (Network makes decision H and the token value goes up OR we make decision L and the token value goes down), L = (we make decision H and the token value goes down OR we make decision L and the token value goes up). Lets assume that decision H is preferable, and it actually causes the token value to rise. If you bet correctly, you earn 100. if the network chooses decision H, then you earn 10 from the token value increase.