Equilibrium computation in games and strategic aspects of bitcoin mining

The focus of this thesis is twofold: on one hand we study the query complexity of equilibrium computation in games, and on the other hand, we use equilibrium concepts from game theory as a tool to understand miner incentives in Bitcoin. In terms of query complexity, we mostly focus on algorithms that have access to utility queries in large games and best response queries in bimatrix games. For the former, we demonstrate query-efficient completely uncoupled dynamics that achieve non-trivial approximate equilibria. For the latter, we reduce the problem of query-efficient approximate equilibrium computation to a natural geometric learning problem: approximately learning partitions of an n-dimensional simplex into disjoint convex polytopes via membership queries. Given this reduction we show query-efficient algorithms for the geometric problem, and ultimately provide an algorithm for computing ε-well-supported Nash equilibria in mxn bimatrix games with a query cost that is polynomial in log(1/ε) and max (m,n) provided that min (m,n) is constant. This leads to a polynomial query complexity algorithm for 2-player games,provided that one of the players has a constant number of strategies. As for incentives in Bitcoin, we shed some light into how robust honest mining protocols are to the presence of strategic agents. Our focus is on the strategic aspects of both solo mining and pool mining in Bitcoin. For the former, we take a multiplayer approach and exhibit specific strategy profiles of multiple strategic miners that outperform honest mining, even if said miners would not be incentivised to be dishonest individually. This effectively renders the Bitcoin protocol less secure than previously thought. As for the latter, we propose a new mining pool protocol that is a randomised variant of the already-ubiquitous pay-per-last-N-shares (PPLNS) mining pool scheme in Bitcoin. Our pool protocol, randomised pay-per-last-N-shares (RPPLNS),enjoys the same desirable properties of PPLNS, but with the added benefit of an exponentially reduced state space required to maintain the protocol. More importantly, this reduced state space also allows us to prove robust guarantees against a richer class of strategic pool mining than before.