LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

Trustworthiness and Motivations

Trust can be thought of as a three place relation: A trusts B to do X. Trustworthiness has two components: competence (does the trustee have the relevant skills, knowledge and abilities to do X?) and willingness (is the trustee intending or aiming to do X?). This chapter is about the willingness component, and the different motivations that a trustee may have for fulfilling trust. The standard assumption in economics is that agents are self-regarding, maximizing their own consumption of goods and services. This is too restrictive. In particular, people may be concerned with the outcomes of others, and they may be concerned to follow ethical principles. I distinguish weak trustworthiness, which places no restrictions on B’s motivation for doing X, from strong trustworthiness, where the behaviour must have a particular non-selfish motivation, in finance the fiduciary commitment to promote the interests of the truster. I discuss why strong trustworthiness may be more efficient and also normatively preferable to weak. In finance, there is asymmetric information between buyer and seller, which creates a need for trustworthy assessment of products. It also creates an ambiguity about whether the relationship is one of buyer and seller, governed by caveat emptor, or a fiduciary relationship of advisor and client. This means that there are two possible reasons why trust may be breached: because the trustee didn’t realise that the truster framed the relationship as a fiduciary one, or because the trustee did realise but actively sought to take advantage of the trust. Correspondingly, there are two possible types of agent: normal people who are not always self-regarding and who are trust responsive (if they believe that they are being trusted then they are likely to fulfill that trust), and knaves, after Hume’s character who is always motivated by his own private interest. We can increase the trustworthiness of normal people by getting them to re-frame the situation as one of trust, so they will be strongly trustworthy (i.e. change of institutional culture), and by providing non-monetary incentives (the correct choice of incentive will depend on exactly what their non-selfish motivation is). Knaves need sanctions, which can make them weakly trustworthy. However, this is a delicate balance because sanctions can crowd out normative frames. We can also increase the trustworthiness of financiers by making finance less attractive to knaves; changing the mix of types in finance could help support the necessary cultural change

Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round

Many algorithms that are originally designed without explicitly considering incentive properties are later combined with simple pricing rules and used as mechanisms. The resulting mechanisms are often natural and simple to understand. But how good are these algorithms as mechanisms? Truthful reporting of valuations is typically not a dominant strategy (certainly not with a pay-your-bid, first-price rule, but it is likely not a good strategy even with a critical value, or second-price style rule either). Our goal is to show that a wide class of approximation algorithms yields this way mechanisms with low Price of Anarchy. The seminal result of Lucier and Borodin [SODA 2010] shows that combining a greedy algorithm that is an $\alpha$-approximation algorithm with a pay-your-bid payment rule yields a mechanism whose Price of Anarchy is $O(\alpha)$. In this paper we significantly extend the class of algorithms for which such a result is available by showing that this close connection between approximation ratio on the one hand and Price of Anarchy on the other also holds for the design principle of relaxation and rounding provided that the relaxation is smooth and the rounding is oblivious. We demonstrate the far-reaching consequences of our result by showing its implications for sparse packing integer programs, such as multi-unit auctions and generalized matching, for the maximum traveling salesman problem, for combinatorial auctions, and for single source unsplittable flow problems. In all these problems our approach leads to novel simple, near-optimal mechanisms whose Price of Anarchy either matches or beats the performance guarantees of known mechanisms.Comment: Extended abstract appeared in Proc. of 16th ACM Conference on Economics and Computation (EC'15

Coverage and Vacuity in Network Formation Games

The frameworks of coverage and vacuity in formal verification analyze the effect of mutations applied to systems or their specifications. We adopt these notions to network formation games, analyzing the effect of a change in the cost of a resource. We consider two measures to be affected: the cost of the Social Optimum and extremums of costs of Nash Equilibria. Our results offer a formal framework to the effect of mutations in network formation games and include a complexity analysis of related decision problems. They also tighten the relation between algorithmic game theory and formal verification, suggesting refined definitions of coverage and vacuity for the latter