Reducibility among Fractional Stability Problems

Abstract

We resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be ${\bf{PPAD}}$-complete, along with the domains of practical significance: fractional stable paths problem (FSPP)---Internet routing; core of balanced games---economics and game theory; Scarf's lemma---combinatorics; hypergraph matching---social choice and preference systems; fractional bounded budget connection games (FBBC)---social networks; and strong fractional kernel---graph theory. In fact, we show that no fully polynomial-time approximation schemes exist (unless ${\bf{PPAD}}$ is in ${\bf{FP}}$). This paper is entirely a series of reductions that build in nontrivial ways on the framework established in previous work. In the course of deriving these reductions, we created two new concepts---preference games and personalized equilibria. The entire set of new reductions can be presented as a lattice with the above problems sandwiched between preference ...