DOCSLIB.ORG

Selfish Routing and the Price of Anarchy

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Selfish Routing and the Price of Anarchy The Price of Anarchy Tim Roughgarden UC Berkeley + Stanford University also featuring some slides contributed by Christos Papadimitriou (UC Berkeley) The Price of Anarchy OR, a rendezvouz of computer science and game theory Tim Roughgarden UC Berkeley + Stanford University also featuring some slides contributed by Christos Papadimitriou (UC Berkeley) The Price of Anarchy OR, a rendezvouz of computer science and game theory OR, how free food can lead to a thesis topic Tim Roughgarden UC Berkeley + Stanford University also featuring some slides contributed by Christos Papadimitriou (UC Berkeley) (Very) Brief Overview • basic object of study: noncooperative games • widespread phenomenon: selfish (or “rational”) behavior is inefficient – could improve natural objective functions by dictating behavior •price of anarchy-- “competitive analysis for noncooperative games” – when does noncooperative behavior lead to an approximately optimal outcome? Example: Load-Balancing • setup: 4 jobs self-schedule on 2 machines – each wants a lightly loaded machine • with coordination, can achieve the following “good” outcome (makespan = 5) 1 2 4 3 m1 m2 Example: Load-Balancing • if they cannot be centrally scheduled? Example: Load-Balancing • if they cannot be centrally scheduled? • e.g., the following outcome is “stable” – no job has incentive to switch machines 2 1 4 3 m1 m2 Example: Braess’s Paradox • setup: traffic (e.g., many cars or packets) pick s-t paths to minimize travel time • travel time increases with congestion c(x)=x c(x)=1 s t c(x)=1 c(x)=x Example: Braess’s Paradox • setup: traffic (e.g., many cars or packets) pick s-t paths to minimize travel time • travel time increases with congestion c(x)=x c(x)=1 ½ of traffic s t c(x)=1 c(x)=x ½ of traffic • at “equilibrium”: travel time = 3/2 for all Braess’s Paradox Initial Network: ½ ½ x1 s ½ ½ t 1 x Travel time = 1.5 Braess’s Paradox Initial Network: Augmented Network: ½ ½ ½ ½ x1x1 0 s ½ ½ t s ½ ½ t 1 x 1 x Travel time = 1.5 Now what? Braess’s Paradox Initial Network: Augmented Network: ½ ½ x1 x 1 s 0 t s ½ ½ t 1 x 1 x Travel time = 1.5 Travel time = 2 Braess’s Paradox Initial Network: Augmented Network: ½ ½ x1 x 1 s 0 t s ½ ½ t 1 x 1 x Travel time = 1.5 Travel time = 2 All traffic worse off! [Braess 68] • (with thanks to Leonard Schulman) The Price of Anarchy • both examples: selfish behavior inefficient – e.g., equilibria need not minimize avg/max cost vs. vs. The Price of Anarchy • both examples: selfish behavior inefficient – e.g., equilibria need not minimize avg/max cost vs. vs. • price of anarchy: worst-case ratio between “social cost” of equilibrium and of optimum – w.r.t. a game + a definition of social cost Agenda of Tutorial • small price of anarchy: – selfish behavior benign; little benefit of centralized control over “laissez-faire” • our focus: bounding the price of anarchy--- when, what, how, why? – want techniques that cut across applications Caveats • price of anarchy = active subfield bordering theoretical CS, game theory – we will only scratch the surface – will focus on the two most well-studied models – even for these models, will only discuss results that I can describe simply – see also bibliography to appear on my Web page • will not have many proofs or all the details – 3 hours only seems long to audience! Road Map: First Half • Part I: Basic Notions – games, strategies, Nash equilibria, the price of anarchy, examples next • Part II: The KP Model (load-balancing) – upper and lower bounds on the price of anarchy – extensions and open questions Road Map: Second Half • Part III: Selfish Routing – the potential function technique – tight bounds on the price of anarchy – extensions and open questions • Part IV: Other cool models: a brief tour – resource allocation, submodular, facility location, and network design games Part I: Basic Notions • finite (normal-form) games • strategies • Nash equilibria • nonatomic games + their equilibria – models large population of players •price of anarchy – pessimistic vs. optimistic Games In a (finite, normal-form) game there is: • a finite set of players • for each player, a finite set of strategies • for each strategy profile (each player picks a strategy), a payoff to each player Games In a (finite, normal-form) game there is: • a finite set of players • for each player, a finite set of strategies • for each strategy profile (each player picks a strategy), a payoff to each player Row 12 Column 12 player: 1 -2 -1 player: 1 -2 -1 2 -1 -2 2 -1 -2 Pure vs. Mixed Strategies Pure strategy: player picks single strategy Mixed strategy: player picks probability distribution over its strategies Pure vs. Mixed Strategies Pure strategy: player picks single strategy Mixed strategy: player picks probability distribution over its strategies • allowing randomization has pros and cons – permits universal existence of equilibria – seems to model some real behavior • e.g., bluffing in poker – still, conceptually problematic • how often to people really randomize? Example: Load-Balancing Example: 2 jobs scheduled on 2 machines • players = jobs; strategies = machines • payoff to job = -1 × #jobs on its machine j2 j1 j2 vs. j1 Example: Load-Balancing Example: 2 jobs scheduled on 2 machines • players = jobs; strategies = machines • payoff to job = -1 × #jobs on its machine j2 j1 j2 vs. j1 m1 m2 m1 m2 m1 -2 -1 m1 -2 -1 Job 1: Job 2: m2 -1 -2 m2 -1 -2 Nash Equilibria Defn: a set of mixed strategies (one per player) is a Nash equilibrium if no player has a unilateral incentive to change its strategy. – no player can increase expected payoff w/some other strategy, if strategies of others are fixed Nash Equilibria Defn: a set of mixed strategies (one per player) is a Nash equilibrium if no player has a unilateral incentive to change its strategy. – no player can increase expected payoff w/some other strategy, if strategies of others are fixed Fact 1: pure-strategy Nash eq need not exist. – “matching pennies” Fact 2: mixed-strategy Nash eq always exist. – Nash’s theorem (1950) Example: Load-Balancing Back to: two-machine, two-job example. Two pure-strategy Nash eq, with jobs on different machines. j1 j2 j2 j1 m1 m2 m1 m2 Example: Load-Balancing Back to: two-machine, two-job example. Two pure-strategy Nash eq, with jobs on different machines. j1 j2 j2 j1 m1 m2 m1 m2 One mixed-strategy Nash eq: j1 50% 50% j2 50% 50% m1 m2 Nonatomic Games • nonatomic game = model large population with infinitely many players • sounds scary, but can increase analytical tractability – (continuous math a good thing) • could define a payoff per strategy profile – but we will only care what fraction of population picks each strategy; we will only model this Nonatomic Games (con'd) Ingredients (abstract and in selfish routing): • finite # of player types [(si,ti) pairs] • population sizes [amt of traffic per pair] • finite strategy sets [(si,ti) paths] • for each distribution (fraction of population using each strategy), payoffs corresponding to each strategy – given traffic pattern, cost of each path Equilibria in Nonatomic Games • like Nash eq, though note that individual deviations do not affect payoffs – strategies used by a player type have equal cost x 1 x 1 s 0 t vs. s 0 t 1 x 1 x – cf., load-balancing: Equilibria in Nonatomic Games • like Nash eq, though note that individual deviations do not affect payoffs – strategies used by a player type have equal cost x 1 x 1 s 0 t vs. s 0 t 1 x 1 x – cf., load-balancing: • existence in general: [Schmeidler 73], etc. • WLOG, can focus on pure-strategy eq The Price of Anarchy Defn: price of obj fn value of a Nash eq = sup anarchy optimal obj fn value ⇒ with respect to a game + an objective fn ⇒ supremum is over the set of equilibria ⇒ price of anarchy of a collection C of games = take supremum over games in C Comparison to Other Notions • approximation ratio = quantifies cost of not having exponential computing time • competitive ratio = quantifies cost of not knowing the future •price of anarchy= quantifies cost of not being able to dictate behavior – also called coordination ratio [Koutsoupias/Papadimitriou 99] Optimistic Price of Anarchy • optimistic price of anarchy: compare best Nash equilibrium with the social optimum • interpretation: what is achievable with “single-shot” centralized control – e.g., for network design (later) • can often upper bound the optimistic p.o.a. but not the pessimistic p.o.a. Road Map: First Half • Part I: Basic Notions – games, strategies, Nash equilibria, the price of anarchy, examples next • Part II: The KP Model (load-balancing) – upper and lower bounds on the price of anarchy – extensions and open questions The KP Model: Overview • formal definition of model • special case: uniform machine speeds • non-uniform speeds • extensions + open problems The KP Model •nplayers/jobs, each with weight wj •mstrategies/machines, each with speed si • outcomes: assignment of jobs to machines The KP Model •nplayers/jobs, each with weight wj •mstrategies/machines, each with speed si • outcomes: assignment of jobs to machines • J(i) = jobs on machine i 2 • L(i) = load of i = 1 Σ 1/si j in J(i) wj 4 • [Koutsoupias/ 3 Papadimitriou 99] m1 m2 Costs with Mixed Strategies i • mixed strategy pj = Pr[job j on machine i] • expected load of machine i: i EL(i) = 1/si Σj wj pj • Cost of i from job j’s perspective: i Cj(i) = 1/si [(Σk not j wk pk ) + wj] j1 50% 50% j2 50% 50% m1 m2 What is a Nash equilibrium? i • no job j has incentive to change its pj ‘s • equivalently: for each job j, i pj > 0 ⇒ Cj(i) = min all machines
Load more

Recommended publications
  • Potential Games. Congestion Games. Price of Anarchy and Price of Stability
    8803 Connections between Learning, Game Theory, and Optimization Maria-Florina Balcan Lecture 13: October 5, 2010 Reading: Algorithmic Game Theory book, Chapters 17, 18 and 19. Price of Anarchy and Price of Staility We assume a (finite) game with n players, where player i's set of possible strategies is Si. We let s = (s1; : : : ; sn) denote the (joint) vector of strategies selected by players in the space S = S1 × · · · × Sn of joint actions. The game assigns utilities ui : S ! R or costs ui : S ! R to any player i at any joint action s 2 S: any player maximizes his utility ui(s) or minimizes his cost ci(s). As we recall from the introductory lectures, any finite game has a mixed Nash equilibrium (NE), but a finite game may or may not have pure Nash equilibria. Today we focus on games with pure NE. Some NE are \better" than others, which we formalize via a social objective function f : S ! R. Two classic social objectives are: P sum social welfare f(s) = i ui(s) measures social welfare { we make sure that the av- erage satisfaction of the population is high maxmin social utility f(s) = mini ui(s) measures the satisfaction of the most unsatisfied player A social objective function quantifies the efficiency of each strategy profile. We can now measure how efficient a Nash equilibrium is in a specific game. Since a game may have many NE we have at least two natural measures, corresponding to the best and the worst NE. We first define the best possible solution in a game Definition 1.
    [Show full text]
  • Price of Competition and Dueling Games
    Price of Competition and Dueling Games Sina Dehghani ∗† MohammadTaghi HajiAghayi ∗† Hamid Mahini ∗† Saeed Seddighin ∗† Abstract We study competition in a general framework introduced by Immorlica, Kalai, Lucier, Moitra, Postlewaite, and Tennenholtz [19] and answer their main open question. Immorlica et al. [19] considered classic optimization problems in terms of competition and introduced a general class of games called dueling games. They model this competition as a zero-sum game, where two players are competing for a user’s satisfaction. In their main and most natural game, the ranking duel, a user requests a webpage by submitting a query and players output an or- dering over all possible webpages based on the submitted query. The user tends to choose the ordering which displays her requested webpage in a higher rank. The goal of both players is to maximize the probability that her ordering beats that of her opponent and gets the user’s at- tention. Immorlica et al. [19] show this game directs both players to provide suboptimal search results. However, they leave the following as their main open question: “does competition be- tween algorithms improve or degrade expected performance?” (see the introduction for more quotes) In this paper, we resolve this question for the ranking duel and a more general class of dueling games. More precisely, we study the quality of orderings in a competition between two players. This game is a zero-sum game, and thus any Nash equilibrium of the game can be described by minimax strategies. Let the value of the user for an ordering be a function of the position of her requested item in the corresponding ordering, and the social welfare for an ordering be the expected value of the corresponding ordering for the user.
    [Show full text]
  • Prophylaxy Copie.Pdf
    Social interactions and the prophylaxis of SI epidemics on networks Géraldine Bouveret, Antoine Mandel To cite this version: Géraldine Bouveret, Antoine Mandel. Social interactions and the prophylaxis of SI epi- demics on networks. Journal of Mathematical Economics, Elsevier, 2021, 93, pp.102486. 10.1016/j.jmateco.2021.102486. halshs-03165772 HAL Id: halshs-03165772 https://halshs.archives-ouvertes.fr/halshs-03165772 Submitted on 17 Mar 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Social interactions and the prophylaxis of SI epidemics on networkssa G´eraldineBouveretb Antoine Mandel c March 17, 2021 Abstract We investigate the containment of epidemic spreading in networks from a nor- mative point of view. We consider a susceptible/infected model in which agents can invest in order to reduce the contagiousness of network links. In this setting, we study the relationships between social efficiency, individual behaviours and network structure. First, we characterise individual and socially efficient behaviour using the notions of communicability and exponential centrality. Second, we show, by computing the Price of Anarchy, that the level of inefficiency can scale up to lin- early with the number of agents.
    [Show full text]
  • Strategic Behavior in Queues
    Strategic behavior in queues Lecturer: Moshe Haviv1 Dates: 31 January – 4 February 2011 Abstract: The course will first introduce some concepts borrowed from non-cooperative game theory to the analysis of strategic behavior in queues. Among them: Nash equilibrium, socially optimal strategies, price of anarchy, evolutionarily stable strategies, avoid the crowd and follow the crowd. Various decision models will be considered. Among them: to join or not to join an M/M/1 or an M/G/1 queue, when to abandon the queue, when to arrive to a queue, and from which server to seek service (if at all). We will also look at the application of cooperative game theory concepts to queues. Among them: how to split the cost of waiting among customers and how to split the reward gained when servers pooled their resources. Program: 1. Basic concepts in strategic behavior in queues: Unobservable and observable queueing models, strategy profiles, to avoid or to follow the crowd, Nash equilibrium, evolutionarily stable strategy, social optimization, the price of anarchy. 2. Examples: to queue or not to queue, priority purchasing, retrials and abandonment, server selection. 3. Competition between servers. Examples: price war, capacity competition, discipline competition. 4. When to arrive to a queue so as to minimize waiting and tardiness costs? Examples: Poisson number of arrivals, fluid approximation. 5. Basic concepts in cooperative game theory: The Shapley value, the core, the Aumann-Shapley prices. Ex- amples: Cooperation among servers, charging customers based on the externalities they inflict on others. Bibliography: [1] M. Armony and M. Haviv, Price and delay competition between two service providers, European Journal of Operational Research 147 (2003) 32–50.
    [Show full text]
  • Pure and Bayes-Nash Price of Anarchy for Generalized Second Price Auction
    Pure and Bayes-Nash Price of Anarchy for Generalized Second Price Auction Renato Paes Leme Eva´ Tardos Department of Computer Science Department of Computer Science Cornell University, Ithaca, NY Cornell University, Ithaca, NY [email protected] [email protected] Abstract—The Generalized Second Price Auction has for advertisements and slots higher on the page are been the main mechanism used by search companies more valuable (clicked on by more users). The bids to auction positions for advertisements on search pages. are used to determine both the assignment of bidders In this paper we study the social welfare of the Nash equilibria of this game in various models. In the full to slots, and the fees charged. In the simplest model, information setting, socially optimal Nash equilibria are the bidders are assigned to slots in order of bids, and known to exist (i.e., the Price of Stability is 1). This paper the fee for each click is the bid occupying the next is the first to prove bounds on the price of anarchy, and slot. This auction is called the Generalized Second Price to give any bounds in the Bayesian setting. Auction (GSP). More generally, positions and payments Our main result is to show that the price of anarchy is small assuming that all bidders play un-dominated in the Generalized Second Price Auction depend also on strategies. In the full information setting we prove a bound the click-through rates associated with the bidders, the of 1.618 for the price of anarchy for pure Nash equilibria, probability that the advertisement will get clicked on by and a bound of 4 for mixed Nash equilibria.
    [Show full text]
  • Efficiency of Mechanisms in Complex Markets
    EFFICIENCY OF MECHANISMS IN COMPLEX MARKETS A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Vasileios Syrgkanis August 2014 ⃝c 2014 Vasileios Syrgkanis ALL RIGHTS RESERVED EFFICIENCY OF MECHANISMS IN COMPLEX MARKETS Vasileios Syrgkanis, Ph.D. Cornell University 2014 We provide a unifying theory for the analysis and design of efficient simple mechanisms for allocating resources to strategic players, with guaranteed good properties even when players participate in many mechanisms simultaneously or sequentially and even when they use learning algorithms to identify how to play and have incomplete information about the parameters of the game. These properties are essential in large scale markets, such as electronic marketplaces, where mechanisms rarely run in isolation and the environment is too complex to assume that the market will always converge to the classic economic equilib- rium or that the participants will have full knowledge of the competition. We propose the notion of a smooth mechanism, and show that smooth mech- anisms possess all the aforementioned desiderata in large scale markets. We fur- ther give guarantees for smooth mechanisms even when players have budget constraints on their payments. We provide several examples of smooth mech- anisms and show that many simple mechanisms used in practice are smooth (such as formats of position auctions, uniform price auctions, proportional bandwidth allocation mechanisms, greedy combinatorial auctions). We give algorithmic characterizations of which resource allocation algorithms lead to smooth mechanisms when accompanied by appropriate payment schemes and show a strong connection with greedy algorithms on matroids.
    [Show full text]
  • Intrinsic Robustness of the Price of Anarchy
    Intrinsic Robustness of the Price of Anarchy Tim Roughgarden Department of Computer Science Stanford University 353 Serra Mall, Stanford, CA 94305 [email protected] ABSTRACT ble to eliminate in many situations, with large networks be- The price of anarchy, defined as the ratio of the worst-case ing one obvious example. The past ten years have provided objective function value of a Nash equilibrium of a game and an encouraging counterpoint to this widespread equilibrium that of an optimal outcome, quantifies the inefficiency of self- inefficiency: in a number of interesting application domains, ish behavior. Remarkably good bounds on this measure have decentralized optimization by competing individuals prov- been proved in a wide range of application domains. How- ably approximates the optimal outcome. ever, such bounds are meaningful only if a game’s partici- A rigorous guarantee of this type requires a formal behav- pants successfully reach a Nash equilibrium. This drawback ioral model, in order to define“the outcome of self-interested motivates inefficiency bounds that apply more generally to behavior”. The majority of previous research studies pure- weaker notions of equilibria, such as mixed Nash equilibria, strategy Nash equilibria, defined as follows. Each player i correlated equilibria, or to sequences of outcomes generated selects a strategy si from a set Si (like a path in a network). by natural experimentation strategies, such as simultaneous The cost Ci(s) incurred by a player i in a game is a function regret-minimization. of the entire vector s of players’ chosen strategies, which We prove a general and fundamental connection between is called a strategy profile or an outcome.
    [Show full text]
  • A Game-Theoretic Model of Attention in Social Networks
    A Game-theoretic Model of Attention in Social Networks Ashish Goel ⇤ Farnaz Ronaghi † March 25, 2012 Abstract We model the economics of producing content in online social networks such as Facebook and Twitter. We propose a game-theoretic model within which we quantify inefficiencies from contributions by strategic users in online environments. Attention and information are assumed to be the main motivation for user contributions. We treat attention as a mechanism for sharing the profit from consuming information and introduce a general framework for analyzing dynamics of contributions in online environments. We analyze the proposed model and identify conditions for existence and efficient computation of pure-strategy Nash equilibrium. We prove a bicriteria bound on the price of anarchy; in particular we show that the social welfare from central control over level of contribution by users is no larger than the social welfare from strategic agents with twice as large consumption utilities. We then construct and analyze a family of production games that have an arbitrarily large price of anarchy. We also prove non- robustness of the price of anarchy for a particular instance of the introduced family, establishing a distinction between the games studied here and network congestion games. 1 Introduction Social networking websites allow users to sign up and keep in touch with others by friending them. Users are allowed to post short status updates, photos, videos and links depending on the social network. Despite the di↵erences between these networks, one feature is common to many of them: Users see a linear news feed reflecting a chronologically sorted ordering of posts from friends whenever she logs into each of these sites [BCK+10].
    [Show full text]
  • Congestion Games with Multisets of Resources and Applications in Synthesis
    Congestion Games with Multisets of Resources and Applications in Synthesis Guy Avni1, Orna Kupferman1, and Tami Tamir2 1 School of Computer Science and Engineering, The Hebrew University, Jerusalem, Israel 2 School of Computer Science, The Interdisciplinary Center, Israel Abstract In classical congestion games, players’ strategies are subsets of resources. We introduce and study multiset congestion games, where players’ strategies are multisets of resources. Thus, in each strategy a player may need to use each resource a different number of times, and his cost for using the resource depends on the load that he and the other players generate on the resource. Beyond the theoretical interest in examining the effect of a repeated use of resources, our study enables better understanding of non-cooperative systems and environments whose behavior is not covered by previously studied models. Indeed, congestion games with multiset-strategies arise, for example, in production planing and network formation with tasks that are more involved than reachability. We study in detail the application of synthesis from component libraries: different users synthesize systems by gluing together components from a component library. A component may be used in several systems and may be used several times in a system. The performance of a component and hence the system’s quality depends on the load on it. Our results reveal how the richer setting of multisets congestion games affects the stability and equilibrium efficiency compared to standard congestion games. In particular, while we present very simple instances with no pure Nash equilibrium and prove tighter and simpler lower bounds for equilibrium inefficiency, we are also able to show that some of the positive results known for affine and weighted congestion games apply to the richer setting of multisets.
    [Show full text]
  • Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions
    Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions Asish Ghoshal Jean Honorio [email protected] [email protected] Department of Computer Science, Purdue University, West Lafayette, IN, U.S.A. - 47907. Abstract identified, from congressional voting records, the most influential senators in the U.S. congress — a small In this paper we obtain sufficient and neces- set of senators whose collective behavior forces every sary conditions on the number of samples re- other senator to a unique choice of vote. Irfan and quired for exact recovery of the pure-strategy Ortiz [4] also observed that the most influential sena- Nash equilibria (PSNE) set of a graphical tors were strikingly similar to the gang-of-six senators, game from noisy observations of joint actions. formed during the national debt ceiling negotiations of We consider sparse linear influence games — 2011. Further, using graphical games, Honorio and Or- a parametric class of graphical games with tiz [6] showed that Obama’s influence on Republicans linear payoffs, and represented by directed increased in the last sessions before candidacy, while graphs of n nodes (players) and in-degree of McCain’s influence on Republicans decreased. at most k.Weshowthatonecanefficiently The problems in algorithmic game theory described recover the PSNE set of a linear influence above, i.e., computing the Nash equilibria, comput- game with k2 log n samples, under very O ing the price of anarchy or finding the most influ- general observation models. On the other ential agents, require a known graphical game which hand, we show that ⌦(k log n) samples are is not available apriori in real-world settings.
    [Show full text]
  • Closing the Price of Anarchy Gap in the Interdependent Security Game
    Closing the Price of Anarchy Gap in the Interdependent Security Game Parinaz Naghizadeh and Mingyan Liu Department of Electrical Engineering and Computer Science University of Michigan, Ann Arbor, Michigan, 48109-2122 Email: {naghizad, mingyan}@umich.edu Abstract—The reliability and security of a user in an intercon- these papers, under-investment in security is verified by finding nected system depends on all users’ collective effort in security. the levels of effort exerted in a Nash equilibrium of the IDS Consequently, investments in security technologies by strategic game, and comparing them with the socially optimal levels of users is typically modeled as a public good problem, known as the Interdependent Security (IDS) game. The equilibria for such investment. games are often inefficient, as selfish users free-ride on positive The increasing number of unprotected devices connected to externalities of others’ contributions. In this paper, we present a the Internet, the constant emergence of new security threats, mechanism that implements the socially optimal equilibrium in and the insufficiency of improved security technologies in an IDS game through a message exchange process, in which users compensating for the under-investment problem [7], motivates submit proposals about the security investment and tax/price profiles of one another. This mechanism is different from existing the study of mechanisms for improving network security. solutions in that (1) it results in socially optimal levels of Several methods for increasing users’ investments, and thus the investment, closing the Price of Anarchy gap in the IDS game, (2) reliability of the interconnected system, have been proposed in it is applicable to a general model of user interdependencies.
    [Show full text]
  • Design and Analysis of Sponsored Search Mechanisms
    DESIGN AND ANALYSIS OF SPONSORED SEARCH MECHANISMS A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Renato Paes Leme December 2012 c 2012 Renato Paes Leme ALL RIGHTS RESERVED DESIGN AND ANALYSIS OF SPONSORED SEARCH MECHANISMS Renato Paes Leme, Ph.D. Cornell University 2012 Auctions have become the standard way of allocating resources in electronic markets. Two main reasons why designing auctions is hard are the need to cope with strategic behavior of the agents, who will constantly adjust their bids seeking more items at lower prices, and the fact that the environment is highly dynamic and uncertain. Many market designs which became de-facto industrial standards allow strategic manipulation by the agents, but nevertheless display good behavior in practice. In this thesis, we analyze why such designs turned out to be so successful despite strategic behavior and environment uncertainty. Our goal is to learn from this analysis and to use the lessons learned to design new auction mechanisms; as well as fine-tune the existing ones. We illustrate this research line through the analysis and design of Ad Auc- tions mechanisms. We do so by studying the equilibrium behavior of a game induced by Ad Auctions, and show that all equilibria have good welfare and revenue properties. Next, we present new Ad Auction designs that take into ac- count richer features such as budgets, multiple keywords, heterogeneous slots and online supply. BIOGRAPHICAL SKETCH Renato Paes Leme was born in December 1st, 1984 in Rio de Janeiro, where he spent most of his life.
    [Show full text]