The following post, Block School: Basic Blockchain Theory and Cryptoeconomics, touches upon the relationship of Cryptoeconomics and Game Theory.
One point:
In blockchains, tokens – or protocol defined cryptocurrencies, are used to incentivize the ‘players’ to act in a mutually beneficial way. The assumption is that the underlying objective for actors, such as miners, in a blockchain network is to maximize their profit, which equals their revenues minus their costs. The two primary methods of consensus methods currently used for most major cryptocurrencies is Proof of Work and Proof of Stake