Computer Science and Game Theory: A Brief Survey

There has been a remarkable increase in work at the interface of computer science and game theory in the past decade. In this article I survey some of the main themes of work in the area, with a focus on the work in computer science. Given the length constraints, I make no attempt at being comprehensive, especially since other surveys are also available, and a comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic

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Resilient Mechanisms For Truly Combinatorial Auctions

Dominant-strategy truthfulness is traditionally considered the best possible solution concept in mechanism design, as it enables one to predict with confidence which strategies INDEPENDENT players will actually choose. Yet, as with any other form of equilibrium, it too can be extremely vulnerable to COLLUSION. The problem of collusion is particularly evident for UNRESTRICTED combinatorial auctions}, arguably the hardest type of auctions.We thus investigate how much revenue can be guaranteed, in unrestricted combinatorial auctions, by dominant-strategy-truthful mechanisms that are COLLUSION-RESILIENT in a very strong sense; and obtain almost matching upper- and lower-bounds

Building Political Collusion: Evidence from Procurement Auctions

We investigate the relationship between the time politicians stay in office and the functioning of public procurement. To this purpose, we collect a data set on the Italian municipal governments and all the procurement auctions they administered between 2000 and 2005. Identification is achieved through the introduction of a two-term limit for the mayor in March 1993: since elections were not coordinated across cities, and previous terms were not counted in the limit, mayors appointed right before the reform could be reelected for two additional terms, while the others for one only. Our primary finding is that one extra term in office deteriorates public spending. In fact, it decreases the number of bidders and, most importantly, the winning rebate. Interestingly, we also find that the probability that the same firm is awarded more auctions, or that the winning firm is local, increases with time in office. These results are compatible with the predictions of a model of favoritism in repeated procurement auctions, where time reveals collusive types, thus increasing the value of illegal connections at the expense of higher procurement costs.procurement auction, collusion, public works, time in office

Core-competitive Auctions

One of the major drawbacks of the celebrated VCG auction is its low (or zero) revenue even when the agents have high value for the goods and a {\em competitive} outcome could have generated a significant revenue. A competitive outcome is one for which it is impossible for the seller and a subset of buyers to `block' the auction by defecting and negotiating an outcome with higher payoffs for themselves. This corresponds to the well-known concept of {\em core} in cooperative game theory. In particular, VCG revenue is known to be not competitive when the goods being sold have complementarities. A bottleneck here is an impossibility result showing that there is no auction that simultaneously achieves competitive prices (a core outcome) and incentive-compatibility. In this paper we try to overcome the above impossibility result by asking the following natural question: is it possible to design an incentive-compatible auction whose revenue is comparable (even if less) to a competitive outcome? Towards this, we define a notion of {\em core-competitive} auctions. We say that an incentive-compatible auction is $\alpha$-core-competitive if its revenue is at least $1/\alpha$ fraction of the minimum revenue of a core-outcome. We study the Text-and-Image setting. In this setting, there is an ad slot which can be filled with either a single image ad or $k$ text ads. We design an $O(\ln \ln k)$ core-competitive randomized auction and an $O(\sqrt{\ln(k)})$ competitive deterministic auction for the Text-and-Image setting. We also show that both factors are tight

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Consider a setting where selfish agents are to be assigned to coalitions or projects from a fixed set P. Each project k is characterized by a valuation function; v_k(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.Comment: Under Revie

New Resiliency in Truly Combinatorial Auctions (and Implementation in Surviving Strategies)

Following Micali and Valiant [MV07.a], a mechanism is resilient if it achieves its objective without any problem of (1) equilibrium selection and (2) player collusion. To advance resilient mechanism design,We put forward a new meaningful benchmark for the COMBINED social welfare-revenue performance of any mechanism in truly combinatorial auctions.We put forward a NEW notion of implementation, much more general than the ones used so far, which we believe to be of independent interest.We put forward a new RESILIENT mechanism that, by leveraging the knowledge that the players have about each other, guarantees at least one half of our benchmark under a very general collusion model

Adaptive and Resilient Revenue Maximizing Dynamic Resource Allocation and Pricing for Cloud-Enabled IoT Systems

Cloud computing is becoming an essential component of modern computer and communication systems. The available resources at the cloud such as computing nodes, storage, databases, etc. are often packaged in the form of virtual machines (VMs) to be used by remotely located client applications for computational tasks. However, the cloud has a limited number of VMs available, which have to be efficiently utilized to generate higher productivity and subsequently generate maximum revenue. Client applications generate requests with computational tasks at random times with random complexity to be processed by the cloud. The cloud service provider (CSP) has to decide whether to allocate a VM to a task at hand or to wait for a higher complexity task in the future. We propose a threshold-based mechanism to optimally decide the allocation and pricing of VMs to sequentially arriving requests in order to maximize the revenue of the CSP over a finite time horizon. Moreover, we develop an adaptive and resilient framework based that can counter the effect of realtime changes in the number of available VMs at the cloud server, the frequency and nature of arriving tasks on the revenue of the CSP.Comment: American Control Conference (ACC 2018

Robustly Leveraging Collusion in Combinatorial Auctions

Because of its devastating effects in auctions and other mechanisms, collusion is prohibited and legally prosecuted. Yet, colluders have always existed, and may continue to exist. We thus raise the following question for mechanism design: What desiderata are achievable, and by what type of mechanisms, when any set of players who wish to collude are free to do so without any restrictions on the way in which they cooperate and coordinate their actions? In response to this question we put forward and exemplify the notion of a collusion-leveraging mechanism. In essence, this is a mechanism aligning its desiderata with the incentives of all its players, including colluders, to a significant and mutually beneficial extent. Of course such mechanisms may exist only for suitable desiderata. In unrestricted combinatorial auctions, where classical mechanisms essentially guarantee 0 social welfare and 0 revenue in the presence of just two colluders, we prove that it is possible for collusion-leveraging mechanisms to guarantee that the sum of social welfare and revenue is always high, even when all players are collusive. To guarantee better performance, collusion-leveraging mechanisms in essence “welcome" collusive players, rather than pretending they do not exist, raising a host of new questions at the intersection of cooperative and noncooperative game theory