Algorithms for Game-Theoretic Environments

Game Theory constitutes an appropriate way for approaching the Internet and modelling situations where participants interact with each other, such as networking, online auctions and search engine’s page ranking. Mechanism Design deals with the design of private-information games and attempts implementing desired social choices in a strategic setting. This thesis studies how the efficiency of a system degrades due to the selfish behaviour of its agents, expressed in terms of the Price of Anarchy (PoA). Our objective is to design mechanisms with improved PoA, or to determine the exact value of the PoA for existing mechanisms for two well-known problems, Auctions and Network Cost-Sharing Design. We study three different settings of auctions, combinatorial auction, multi- unit auction and bandwidth allocation. The combinatorial auction constitutes a fundamental resource allocation problem that involves the interaction of selfish agents in competition for indivisible goods. Although it is well-known that by using the VCG mechanism the selfishness of the agents does not affect the efficiency of the system, i.e. the social welfare is maximised, this mechanism cannot generally be applied in computationally tractable time. In practice, several simple auctions (lacking some nice properties of the VCG) are used, such as the generalised second price auction on AdWords, the simultaneous ascending price auction for spectrum allocation, and the independent second-price auction on eBay. The latter auction is of particular interest in this thesis. Precisely, we give tight bounds on the PoA when the goods are sold in independent and simultaneous first-price auctions, where the highest bidder gets the item and pays her own bid. Then, we generalise our results to a class of auctions that we call bid-dependent auctions, where the goods are also sold in independent and simultaneous auctions and further the payment of each bidder is a function of her bid, even if she doesn’t get the item. Overall, we show that the first-price auction is optimal among all bid-dependent auctions. The multi-unit auction is a special case of combinatorial auction where all items are identical. There are many variations: the discriminatory auction, the uniform price auction and the Vickrey multi-unit auction. In all those auctions, the goods are allocated to the highest marginal bids, and their difference lies on the pricing scheme. Our focus is on the discriminatory auction, which can be seen as the variant of the first-price auction adjusted to multi-unit auctions. The bandwidth allocation is equivalent to auctioning divisible resources. Allocating network resources, like bandwidth, among agents is a canonical problem in the network optimisation literature. A traditional model for this problem was proposed by Kelly [1997], where each agent receives a fraction of the resource proportional to her bid and pays her own bid. We complement the PoA bounds known in the literature and give tight bounds for a more general case. We further show that this mechanism is optimal among a wider class of mechanisms. We further study design issues for network games: given a rooted undirected graph with nonnegative edge costs, a set of players with terminal vertices need to establish connectivity with the root. Each player selects a path and the global objective is to minimise the cost of the used edges. The cost of an edge may represent infrastructure cost for establishing connectivity or renting expense, and needs to be covered by the users. There are several ways to split the edge cost among its users and this is dictated by a cost-sharing protocol. Naturally, it is in the players best interest to choose paths that charge them with small cost. The seminal work of Chen et al. [2010] was the first to address design questions for this game. They thoroughly studied the PoA for the following informational assumptions. i) The designer has full knowledge of the instance, that is, she knows both the network topology and the players’ terminals. ii) The designer has no knowledge of the underlying graph. Arguably, there are situations where the former assumption is too optimistic while the latter is too pessimistic. We propose a model that lies in the middle-ground; the designer has prior knowledge of the underlying metric, but knows nothing about the positions of the terminals. Her goal is to process the graph and choose a universal cost-sharing protocol that has low PoA against all possible requested subsets. The main question is to what extent prior knowledge of the underlying metric can help in the design. We first demonstrate that there exist graph metrics where knowledge of the underlying metric can dramatically improve the performance of good network cost-sharing design. However, in our main technical result, we show that there exist graph metrics for which knowing the underlying metric does not help and any universal protocol matches the bound of Chen et al. [2010] which ignores the graph metric. We further study the stochastic and Bayesian games where the players choose their terminals according to a probability distribution. We showed that in the stochastic setting there exists a priority protocol that achieves constant PoA, whereas the PoA under the the Bayesian setting can be very high for any cost- sharing protocol satisfying some natural properties

Cost-Sharing Methods for Scheduling Games under Uncertainty

We study the performance of cost-sharing protocols in a selfish scheduling setting with load-dependent cost functions. Previous work on selfish scheduling protocols has focused on two extreme models: omnipotent protocols that are aware of every machine and every job that is active at any given time, and oblivious protocols that are aware of nothing beyond the machine they control. The main focus of this paper is on a well-motivated middle-ground model of resource-aware protocols, which are aware of the set of machines that the system comprises, but unaware of what jobs are active at any given time. Apart from considering budget-balanced protocols, to which previous work was restricted, we augment the design space by also studying the extent to which overcharging can lead to improved performance. We first show that, in the omnipotent model, overcharging enables us to enforce the optimal outcome as the unique equilibrium, which largely improves over the Θ(log n)-approximation of social welfare that can be obtained by budget-balanced protocols, even in their best equilibrium. We then transition to the resource-aware model and provide price of anarchy (PoA) upper and lower bounds for different classes of cost functions. For concave cost functions, we provide a protocol with PoA of 1+ε for arbitrarily small ε0. When the cost functions can be both convex and concave we construct an overcharging protocol that yields PoA ≤ 2; a spectacular improvement over the bounds obtained for budget-balanced protocols, even in the omnipotent model. We complement our positive results with impossibility results for general increasing cost functions. We show that any resource-aware budget-balanced cost-sharing protocol has PoA of Θ(n) in this setting and, even if we use overcharging, no resource-aware protocol can achieve a PoA of o(√n)

A general framework for energy-efficient cloud computing mechanisms

We present a general model for the operation of a cloud computing server comprised of one or more speed-scalable processors. Typically, tasks are submitted to such a cloud computing server in an online fashion, and the server operator has to schedule the tasks and decides on payments without knowledge about the tasks arriving in the future. Although very natural, this cloud computing problem on speed-scalable processors has not been studied from a mechanism design perspective in the online setting. We provide a mechanism for this setting, both for a single and multiprocessor environment, that has several desirable properties: (1) the induced game admits a subgame perfect equilibrium in pure strategies and therefore a pure Nash equilibrium, (2) the Price of Anarchy is constant, (3) the mechanism is budget balanced, i.e., the sum of the payments of the agents is equal to the total energy costs, (4) the communication complexity is low, (5) the mechanism is computationally tractable for both the service operator and the agents, and (6) the agents' payment is also intuitive and easy to communicate to them. We also provide a second mechanism with a better Price of Anarchy, which in turn is more involved to implement. We are able to extend our mechanisms and results to the Bayesian setting, where the type of each agent is drawn independently from some underlying distribution and agents are minimizing their expected costs. In this setting we also show the same approximation factor of our mechanism as in the basic online setting in both the single and the multiprocessor environment

Ancient DNA reveals admixture history and endogamy in the prehistoric Aegean (advance online)

The Neolithic and Bronze Ages were highly transformative periods forthe genetic history of Europe but for the Aegean—a region fundamentalto Europe’s prehistory—the biological dimensions of cultural transitionshave been elucidated only to a limited extent so far. We have analysed newlygenerated genome-wide data from 102 ancient individuals from Crete, theGreek mainland and the Aegean Islands, spanning from the Neolithic tothe Iron Age. We found that the early farmers from Crete shared the sameancestry as other contemporaneous Neolithic Aegeans. In contrast, the endof the Neolithic period and the following Early Bronze Age were marked by‘eastern’ gene flow, which was predominantly of Anatolian origin in Crete.Confirming previous findings for additional Central/Eastern Europeanancestry in the Greek mainland by the Middle Bronze Age, we additionallyshow that such genetic signatures appeared in Crete gradually from theseventeenth to twelfth centuries bc, a period when the influence of themainland over the island intensified. Biological and cultural connectednesswithin the Aegean is also supported by the finding of consanguineousendogamy practiced at high frequencies, unprecedented in the globalancient DNA record. Our results highlight the potential of archaeogenomicapproaches in the Aegean for unravelling the interplay of genetic admixture,marital and other cultural practice

RA-PI-NE-U

This volume, in honour of one of the Odysseuses in Aegean archaeology, Professor Robert Laffineur, comprises a combination of papers presented during a seminar series on recent developments in Mycenaean archaeology at the Université de Louvain during the academic year 2015-2016. These were organised within the frame of the ARC13/18-049 (concerted research action) ’A World in Crisis?’To these are added a series of papers by friends of Robert Laffineur who were keen to offer a contribution to honour him foremost as a friend and scholar in his own right but also as editor of a respected international series founded by him - Aegaeum - and as the driving force and inspiration behind the biannual Aegean meetings that have travelled the world. Several papers within touch scientific domains close to Robert’s heart while others present new excavations or new interpretations of known data