Nobody upvoted my LW shortform relating inadequacy with PoA and PoS 💔
but it's really nice! if you have a upper bound on the PoA and a lower bound on the PoS, you can upper bound the PoI!
Same symmetrically for PoI lower bounds
and there's a bunch of results from routing games that e.g. say that the PoA is upper-bounded by the Pigou bound in arbitrary graphs, or the price of stability is upper-bounded 𝓗_k for cost-sharing games with k agents. (no lower bounds bc little interest sofar)
PoA: Price of Anarchy, an existing term from algorithmic game theory capturing how bad the worst Nash equilibrium is
PoS: Price of Stability, same except how bad the best Nash equilibrium is
PoI: Price of Inadequacy, a concept I made up in [can't give a link rn bc internet is barely enough for fedi] that tries to capture how much one can gain from moving to better Nash equilibria
LW: LessWrong, a website where I thought people might be interested in taht kind of thing
