> By ensuring that no person could obtain an advantage over others, and by ensuring that anyone could join without exclusion, Satoshi created the Nash equilibrium to permit normally byzantine parties to enter and share safely in the definition of a shared network of contested assets.

This is roughly true, although Nakamoto's original paper only proves this for the case where no single entity controls > 50% of the mining power in the network (weak incentive compatibility). Nakamoto argued it was also true for the case where a single entity controls > 50% of the mining power (strong incentive compatibility) but failed to prove this, instead providing a vague argument based on some difficult-to-prove assumptions.

For more information, including an interesting theoretical attack based on this idea, see http://www.jbonneau.com/doc/BFGKN14-bitcoin_bribery.pdf.