Jasper de Jong

The sequential price of anarchy for atomic congestion games

In situations without central coordination, the price of anarchy relates the quality of any Nash equilibrium to the quality of a global optimum. Instead of assuming that all players choose their actions simultaneously, we consider games where players choose their actions sequentially. The sequential price of anarchy, recently introduced by Paes Leme, Syrgkanis, and Tardos, relates the quality of any subgame perfect equilibrium to the quality of a global optimum. The effect of sequential decision making on the quality of equilibria, depends on the specific game under consideration. We analyze the sequential price of anarchy for atomic congestion games with affine cost functions. We derive several lower and upper bounds, showing that sequential decisions mitigate the worst case outcomes known for the classical price of anarchy. Next to tight bounds on the sequential price of anarchy, a methodological contribution of our work is, among other things, a “factor revealing” linear programming approach we use to solve the case of three players.

Decentralized Throughput Scheduling

Motivated by the organization of online service systems, we study models for throughput scheduling in a decentralized setting. In throughput scheduling, we have a set of jobs j with values w(j), processing times p(j), and release dates r(j) and deadlines and d(j), to be processed non-preemptively on a set of unrelated machines. The goal is to maximize the total value of jobs scheduled within their time window [r(j),d(j)]. While several approximation algorithms with different performance guarantees exist for this and related models, we are interested in the situation where subsets of servers are governed by selfish players. We give a universal result that bounds the price of decentralization, in the sense that any local a-approximation algorithms yield equilibria that are at most a factor (a+1) away from the global optimum, and this bound is tight. For models with identical machines, we improve this bound to approximately (a+1/2). We also address some variations of the problem.

Quality of equilibria in resource allocation games

In situations where multiple parties are involved, local or selfish decisions result in outcomes that rarely align with what is best for society. In order to evaluate the quality of the resulting outcomes, we first need to predict which outcomes can occur. Game theory offers answers to this question, the Nash equilibrium being the most prominent example: it is an outcome where no party can improve by unilateral deviations. In that sense Nash equilibria are a good description of a stable outcome, but do not ask how that outcome was actually obtained. Implicitly, Nash equilibria make the assumption that parties choose their actions simultaneously. However, sequential decisions, where parties anticipate each other’s actions, are often more natural, and may lead to different equilibria. We consider multiple equilibrium concepts for a variety of games, including Nash and subgame perfect equilibria, and analyze the quality of these equilibria. The results include several lower and upper bounds on what is known as the price of anarchy, or variations thereof. The main class of games we consider is the class of congestion games. Congestion games model the allocation of scarce resources to a set of players. The model includes as special case the celebrated network routing games, a classical showcase problem in algorithmic game theory. Applications include the design of street networks in order to mitigate delays due to traffic jams, or the design of internet protocols that result in more efficient use of available bandwidth.