When modeling token economics, it's important to consider Nash equilibrium as a potential means of demonstrating stability. Nash equilibrium is a concept from game theory that refers to a stable state in which every player has optimal strategy. Proving the existence of an equilibrium often involves writing out the "win" formulas for different strategies and using inequality. This involves specifying the formulas that determine a "win" for each player and showing that no player can improve their outcome by changing their strategy.
One method for proving Nash equilibrium is using the Viete tool, which allows you to specify the formulas that determine a "win" and provide a proof of the Nash equilibrium.
In addition of that A library of frameworks containing "win" formulas and proofs for various game mechanics and strategies is a valuable resource for web3 developers. It could help design stable token economics and ensure that systems are resistant to manipulation or exploitation.
Therefore, when modeling token economics, don't forget to consider Nash equilibrium as a potential means of demonstrating stability. It may take some effort to write out the "win" formulas and use inequality to prove the existence of an equilibrium, but it can pay off in the long run by helping to ensure the stability of your system.