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... : O # # represents his valuations of each of the system states, and p i is his payment. For such problems, there is a class of strategyproof mechanisms, called Vickrey-Clarke-Groves (VCG) mechanisms =-=[13, 29, 64]-=-, that result in the system state that optimizes P i v i (o). Direct strategyproof mechanisms provide a conceptually simple, if not always ideal (see Section 7), way to achieve strategyproof SCFs. How...

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...ponses to rational beliefs about the other agents' strategy choices [10, 57]), evolutionarily stable strategies (agents imitate the successful strategies used by others in previous rounds of the game =-=[62]-=-), and dominant strategies (agents only choose strategies that, regardless of how other agents play, never result in lower payo#s than any other strategy). To date, most of the AMD and DAMD literature...

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...s, each node has a set of neighbors to whom it forwards queries. There have also been many proposals for application-layer networks to perform unicast routing (e.g., [4]) and multicast routing (e.g., =-=[12]-=-). These overlay networks are formed by algorithms that assume nodes are obedient and ignore their own incentives. Clearly, obedience may not be in a node's best interest. In the case of P2P file shar...

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...ugh this is theoretically appealing, it is contradicted by preliminary measurement studies suggesting that there is a very wide range of node capabilities (in bandwidth, CPU, and disk) in P2P systems =-=[59]-=-. Wide heterogeneities may lead to significantly increased efficiency in P2P systems; that is, the highly capable nodes can act as semi-centralized repositories. Open Problem 19. How does the performa...

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...e, in many P2P file-sharing systems, each node has a set of neighbors to whom it forwards queries. There have also been many proposals for application-layer networks to perform unicast routing (e.g., =-=[4]-=-) and multicast routing (e.g., [12]). These overlay networks are formed by algorithms that assume nodes are obedient and ignore their own incentives. Clearly, obedience may not be in a node's best int...

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... : O # # represents his valuations of each of the system states, and p i is his payment. For such problems, there is a class of strategyproof mechanisms, called Vickrey-Clarke-Groves (VCG) mechanisms =-=[13, 29, 64]-=-, that result in the system state that optimizes P i v i (o). Direct strategyproof mechanisms provide a conceptually simple, if not always ideal (see Section 7), way to achieve strategyproof SCFs. How...

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...annot "compose" a direct distributed algorithmic mechanism with a standard SMFE protocol, for several fundamental reasons: . The strategic models may be di#erent. Some standard SMFE techniqu=-=es (e.g., [9, 11]-=-) apply to networks in which at least a constant fraction of the agents are obedient; the other agents are often assumed to be Byzantine adversaries. Although one usually does not have to design distr...

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... and lying to the mechanism, then at least one agent in the group suffers. An important class of problems are those in which the utilities are quasilinear, and the outcome space O factors into a set of system states O and a set of payment states P ⊆ n that represent a vector of payoffs (or charges). At a particular outcome o = (o, p), agent i’s utility factors into ui(o) = vi(o) + pi, where vi : O → represents his valuations of each of the system states, and pi is his payment. For such problems, there is a class of strategyproof mechanisms, called Vickrey-Clarke-Groves (VCG) mechanisms [13, 29, 64], that result in the system state that optimizes P i vi(o). Direct strategyproof mechanisms provide a conceptually simple, if not always ideal (see Section 7), way to achieve strategyproof SCFs. However, there are many cases in which the desired result, i.e., the desired social choice function F , is not strategyproof. To describe how to realize such nonstrategyproof SCFs, we now introduce indirect mechanisms. Here, one designs a mechanism < M,S >, where S is a strategy space, and M : Sn → O maps vectors of strategies into outcomes.2 These are called indirect mechanisms, because the agents no...

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...intelligence (e.g., [55, 61]), and marketbased computation (e.g., [65]) --- the first work in TCS to address incentives and computational complexity simultaneously was Nisan and Ronen's seminal paper =-=[52] on algori-=-thmic mechanism design (AMD). This paper put forth a formal model of centralized computation that combined incentive compatibility (the &quot;mechanism design&quot; part) with computational tractabili...

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... strategies at different rates. New definitions of learning and new solution concepts that attempt to capture these aspects of Internetbased, repeated games have been proposed by, e.g., Erev and Roth =-=[17]-=- and Friedman and Shenker [24]. Which, if any, of these solution concepts and game-theoretic definitions of learning will play a central role in the emerging theory of DAMD is a wide open question. Mo...

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...,&quot; in which individual users o#er up their resources -- content, access bandwidth, storage, and CPU -- for the greater good. However, initial studies show that there is a serious &quot;free rider=-= problem&quot; [2]-=-. It may be that, without some systematic way of providing incentives for users to share their files, these P2P systems will become increasingly centralized, with only a few commercially supported nod...

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...annot &quot;compose&quot; a direct distributed algorithmic mechanism with a standard SMFE protocol, for several fundamental reasons: . The strategic models may be di#erent. Some standard SMFE techniqu=-=es (e.g., [9, 11]-=-) apply to networks in which at least a constant fraction of the agents are obedient; the other agents are often assumed to be Byzantine adversaries. Although one usually does not have to design distr...

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...nilaterally increase his utility. Other solution concepts include rationalizable strategies (agents use strategies that are best responses to rational beliefs about the other agents' strategy choices =-=[10, 57]-=-), evolutionarily stable strategies (agents imitate the successful strategies used by others in previous rounds of the game [62]), and dominant strategies (agents only choose strategies that, regardle...

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...incentive compatibility and computational tractability -- be jointly addressed. Although many subdisciplines of computer science have a long history of using game theory --- such as networking (e.g., =-=[21, 25, 35]-=-), distributed artificial intelligence (e.g., [55, 61]), and marketbased computation (e.g., [65]) --- the first work in TCS to address incentives and computational complexity simultaneously was Nisan ...

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...ous open problems, some very specific and others quite general, concerning the foundations and applications of DAMD. Additional material about the AMD and DAMD research agendas can be found in, e.g., =-=[50, 51, 54]-=-. 2. MD TO AMD TO DAMD In essence, game theory is the study of what happens when independent agents act selfishly. Mechanism design asks how one can design systems so that agents' selfish behavior res...

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...l model of centralized computation that combined incentive compatibility (the &quot;mechanism design&quot; part) with computational tractability (the &quot;algorithmic&quot; part). Feigenbaum, Papadim=-=itriou, and Shenker [20]-=- extended this to distributed algorithmic mechanism design (DAMD), in which the same goals of incentive compatibility and computational tractability are present, but, in addition, the agents, the rele...

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... in control of those nodes). However, the situation is significantly more complicated when the computational and strategic aspects become intertwined. For instance, an important issue not resolved in =-=[19]-=- is the need to reconcile the strategic model with the computational model. On the one hand, the problem formulation in [19] captures the fact that ASs may have incentives to lie about costs in order ...

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...GP-compatible distributed algorithm is given that computes these prices. This algorithm requires only minor and straightforward modifications of the BGP computational model given by Gri#n and Wilfong =-=[28]-=-. Specifically, the algorithm in [19] requires a small constant-factor increase in both the table sizes and the message sizes of BGP, but it does not require any new messages or any new infrastructura...

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...nt solution concepts; see Jackson [32] for an overview. With the Nash-equilibrium solution concept, one can design mechanisms to achieve a very wide range of non-strategyproof social choice functions =-=[38]-=-. When M = F and S = U , we reduce to the direct2 Our assumption that all agents are equivalent, made for notational simplicity, renders all strategy spaces the same; in general, we could have di#eren...

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...nsider the virtual implementation literature [39, 1], in which mechanisms produce lotteries over outcomes, to be a form of approximation. We don't discuss virtual implementation here. Nisan and Ronen =-=[53]-=- were the first to address the question of approximate computation in AMD. They considered VCG mechanisms in which optimal outcomes are NP-hard to compute (as they are in combinatorial auctions). They...

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...e, straightforward extensions of existing protocols are easier to deploy than de novo designs. cast transmission (the sum of the valuations minus the total transmission cost). Economic considerations =-=[47]-=- point to two strategyproof mechanisms that are worthy of algorithmic consideration: marginal-cost (MC) and Shapley-value (SH). The MC mechanism is e#cient, which means that it chooses the receiver se...

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...e nonstrategyproof SCFs with direct mechanisms by invoking different solution concepts. For example, one can achieve e#- ciency and budget balance using the Bayesian-Nash-equilibrium solution concept =-=[7, 14]-=- -- something that is impossible using the dominant-strategy solution concept [27, 58]. It is important to note that, although the mechanism is chosen by the system designer, the solution concept is s...

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...echnical foundations of DAMD; we discuss the notion of hardness in DAMD problems (Section 4), the role of approximations (Section 5), aspects of strategic models (Section 6), the use of indirect mechanisms (Section 7), and alternative solution concepts (Section 8). We then end the paper in Section 9 with a discussion of several promising applications of DAMD. Throughout Sections 4-9, we pose numerous open problems, some very specific and others quite general, concerning the foundations and applications of DAMD. Additional material about the AMD and DAMD research agendas can be found in, e.g., [50, 51, 54]. 2. MD TO AMD TO DAMD In essence, game theory is the study of what happens when independent agents act selfishly. Mechanism design asks how one can design systems so that agents’ selfish behavior results in the desired system-wide goals. The “mechanisms” in this field are output specifications and payments to agents that incentivize them to behave in ways that lead to the desired system-wide result. For example, consider the problem of routing. Agents may be individual routers within a network or entire autonomous domains. Each agent incurs a cost when it transports a packet, and this cost is...

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...be jointly addressed. Although many subdisciplines of computer science have a long history of using game theory --- such as networking (e.g., [21, 25, 35]), distributed artificial intelligence (e.g., =-=[55, 61]-=-), and marketbased computation (e.g., [65]) --- the first work in TCS to address incentives and computational complexity simultaneously was Nisan and Ronen's seminal paper [52] on algorithmic mechanis...

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...incentive compatibility and computational tractability -- be jointly addressed. Although many subdisciplines of computer science have a long history of using game theory --- such as networking (e.g., =-=[21, 25, 35]-=-), distributed artificial intelligence (e.g., [55, 61]), and marketbased computation (e.g., [65]) --- the first work in TCS to address incentives and computational complexity simultaneously was Nisan ...

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...d lead to indirect mechanisms, because agents would not be revealing their utilities but instead would be using strategies drawn from some other strategy space. For an overview of SMFE, see Goldreich =-=[26]. One cannot always -=-apply SMFE techniques &quot;o# the shelf &quot; to DAMD. In particular, one often cannot &quot;compose&quot; a direct distributed algorithmic mechanism with a standard SMFE protocol, for several funda...

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...ill be incentive-compatible. There is a large game-theory literature on which SCFs can be achieved for di#erent notions of &quot;incentive compatibility,&quot; e.g., for di#erent solution concepts; se=-=e Jackson [32]-=- for an overview. With the Nash-equilibrium solution concept, one can design mechanisms to achieve a very wide range of non-strategyproof social choice functions [38]. When M = F and S = U , we reduce...

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...s. For example, one can achieve e#- ciency and budget balance using the Bayesian-Nash-equilibrium solution concept [7, 14] -- something that is impossible using the dominant-strategy solution concept =-=[27, 58]-=-. It is important to note that, although the mechanism is chosen by the system designer, the solution concept is supposed to reflect reality. The solution concept thus depends greatly on the context (...

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...s, according to the MilgromRoberts definition [42], then the play asymptotically heads towards the serially undominated set. If the learning algorithms are calibrated in the sense of Foster and Vohra =-=[23]-=-, then the solution concept is the set of correlated equilibria. Internet-based agents typically have very little information even about their own payo# functions and know still less about those of ot...

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...efly review three of them here. Approximation of equilibria is considered in the gametheory literature independent of distributed-algorithmic concerns. 13 For example, Schummer [60] and Parkes et al. =-=[56]-=- consider #-dominance. A strategy vector (s1 , . . . , sn) is an #- dominant equilibrium if, for every agent i, every strategy t i , and every set of other players' strategies (t1 , . . . , t i-1 , t ...

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...ategic design goals need only be approximated? Characterization results that should be considered include the Moulin-Sprumont characterization of strategyproof mechanisms with single-peaked utilities =-=[45, 63]-=- and the BarberaJackson characterization of strategyproof exchange markets [8]. 6. STRATEGIC MODELS In this section, we look more carefully at an aspect of DAMD that we have thus far oversimplified. I...

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...ra#c at all. In the model of Feigenbaum et al. [19], which is an extension of an earlier (centralized) LCP-mechanism model proposed by Nisan and Ronen [52] and studied further by Hershberger and Suri =-=[30]-=-, each AS incurs a per-packet cost for carrying tra#c, where the cost represents the additional load imposed on the internal AS network by this tra#c. Furthermore, the model also assumes that, to comp...

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...strategies, and reach an equilibrium through repeated play. The resulting solution concept depends on how the agents learn. If agents are adaptive learners, according to the MilgromRoberts definition =-=[42]-=-, then the play asymptotically heads towards the serially undominated set. If the learning algorithms are calibrated in the sense of Foster and Vohra [23], then the solution concept is the set of corr...

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...ects of multicast cost sharing. By contrast, in the scenario in which the multicast delivery is done by a monopoly content owner, profit maximization is the natural mechanism-design goal. Fiat et al. =-=[22]-=- provide several novel cost-sharing mechanisms for this scenario. Finally, we note that, in the problem as we have stated it here, the potential receivers are strategic, but the networks(i.e., the uni...

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... reasons discussed at length by Moulin and Shenker [47], but it is only one of several group-strategyproof, budget-balanced mechanisms in the literature that have properties NPT, VP, CS, and SYM; see =-=[16, 33]-=- for more examples. It is shown in [18] that no group-strategyproof, budget-balanced multicast cost-sharing mechanism that satisfies conditions NPT, VP, CS, and SYM can have low absolute network compl...

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...ines of computer science have a long history of using game theory --- such as networking (e.g., [21, 25, 35]), distributed artificial intelligence (e.g., [55, 61]), and marketbased computation (e.g., =-=[65]-=-) --- the first work in TCS to address incentives and computational complexity simultaneously was Nisan and Ronen's seminal paper [52] on algorithmic mechanism design (AMD). This paper put forth a for...

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...ard SMFE literature [26], work that might be relevant to Open Problem 12 includes but is not limited to the papers of Naor and Nissim [48], Naor, Pinkas, and Sumner [49], and Dodis, Halevi, and Rabin =-=[15]-=-. Thus far, our motivation for considering indirect mechanisms has been the desire to preserve agents' privacy, and we have observed that low network complexity and agent privacy may be hard to achiev...

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...is the “right” solution concept for interdomain routing? The game-theory literature contains a very rich set of solution concepts to which we cannot possibly do justice here. For example, one can consider “repeated-play” settings in which each agent knows its own payoff function but not those of others; as the game continues, agents learn more about the payoff functions of others, adapt their own strategies, and reach an equilibrium through repeated play. The resulting solution concept depends on how the agents learn. If agents are adaptive learners, according to the MilgromRoberts definition [42], then the play asymptotically heads towards the serially undominated set. If the learning algorithms are calibrated in the sense of Foster and Vohra [23], then the solution concept is the set of correlated equilibria. Internet-based agents typically have very little information even about their own payoff functions and know still less about those of other agents. All they know is which strategy they played and what the resulting payoff was. In addition, the payoff functions change over time in unpredictable and sudden ways, reflecting the dynamic nature of the Internet infrastructure. Further...

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...he TCS literature traditionally did the opposite. The emergence of the Internet as a standard platform for distributed computation has radically changed this state of affairs: Ownership, operation, and use by many selfinterested, independent parties give the Internet the characteristics of an economy as well as those of a computer. This development requires that these previously separable concerns – incentive compatibility and computational tractability – be jointly addressed. Although many subdisciplines of computer science have a long history of using game theory — such as networking (e.g., [21, 25, 35]), distributed artificial intelligence (e.g., [55, 61]), and marketbased computation (e.g., [65]) — the first work in TCS to address incentives and computational complexity simultaneously was Nisan and Ronen’s seminal paper [52] on algorithmic mechanism design (AMD). This paper put forth a formal model of centralized computation that combined incentive compatibility (the “mechanism design” part) with computational tractability (the “algorithmic” part). Feigenbaum, Papadimitriou, and Shenker [20] extended this to distributed algorithmic mechanism design (DAMD), in which the same goals of incent...

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...ategic design goals need only be approximated? Characterization results that should be considered include the Moulin-Sprumont characterization of strategyproof mechanisms with single-peaked utilities =-=[45, 63]-=- and the BarberaJackson characterization of strategyproof exchange markets [8]. 6. STRATEGIC MODELS In this section, we look more carefully at an aspect of DAMD that we have thus far oversimplified. I...

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...ctable, given the information available to agent i, and that the computation of M() is tractable, given a strategy vector (s1 , . . . , sn ). 13 One can consider the virtual implementation literature =-=[39, 1]-=-, in which mechanisms produce lotteries over outcomes, to be a form of approximation. We don't discuss virtual implementation here. Nisan and Ronen [53] were the first to address the question of appro...

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...me important pages uncached, and yielding sub-optimal performance. Thus, the system needs to provide incentives designed to have the caches report their true operating costs. 10 Open Problem 16. Develop distributed algorithmic mechanisms for caching in which clients are induced to reveal their true preferences, and caches are induced to implement the optimal resource allocation. Demonstrate that these caching mechanisms can be built as scalable extensions to existing distributed caching protocols and provide provable performance guarantees. Some aspects of this problem are addressed in, e.g., [34]. 9.2 Peer-to-Peer File Sharing Peer-to-peer (P2P) file-sharing networks, e.g., Gnutella, KaZaA, and Freenet, are the ne plus ultra of autonomous distributed systems; each machine belongs to a different user, and there is no central administrative authority. Thus, incentive issues are likely to be very important to the future of P2P technology; this provides a great opportunity for DAMD research. P2P file-sharing represents a shift from purely commercial content-distribution systems (e.g., content providers paying CDNs to distribute their content) to a “gift economy,” in which individual users...

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...ous open problems, some very specific and others quite general, concerning the foundations and applications of DAMD. Additional material about the AMD and DAMD research agendas can be found in, e.g., =-=[50, 51, 54]-=-. 2. MD TO AMD TO DAMD In essence, game theory is the study of what happens when independent agents act selfishly. Mechanism design asks how one can design systems so that agents' selfish behavior res...

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...gorithm designed to compute this mechanism; even if the ASs input their true costs, what is to stop them from running a di#erent algorithm that computes prices more favorable to them? Mitchell et al. =-=[43]-=- have observed that, if ASs are required to sign all of the messages that they send and to verify all of the messages that they receive from their neighbors, then the protocol in [19] can be modified ...

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...be jointly addressed. Although many subdisciplines of computer science have a long history of using game theory --- such as networking (e.g., [21, 25, 35]), distributed artificial intelligence (e.g., =-=[55, 61]-=-), and marketbased computation (e.g., [65]) --- the first work in TCS to address incentives and computational complexity simultaneously was Nisan and Ronen's seminal paper [52] on algorithmic mechanis...

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...r set and cost shares by sending just two modest-sized messages over each l # L and doing two very simple calculations at each node. On the other hand, the SH mechanism has bad network complexity: In =-=[18]-=-, it is shown that any algorithm, deterministic or randomized, that computes SH must, in the worst case, send# |P |) bits over linearly many links. Before turning to our next representative DAMD probl...

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...S = U , we reduce to the direct2Our assumption that all agents are equivalent, made for notational simplicity, renders all strategy spaces the same; in general, we could have different strategy spaces Si. 2 mechanism case, and so our preceding discussion applies to direct mechanisms as well. That is, one can achieve nonstrategyproof SCFs with direct mechanisms by invoking different solution concepts. For example, one can achieve efficiency and budget balance using the Bayesian-Nash-equilibrium solution concept [7, 14] – something that is impossible using the dominant-strategy solution concept [27, 58]. It is important to note that, although the mechanism is chosen by the system designer, the solution concept is supposed to reflect reality. The solution concept thus depends greatly on the context (e.g., is it a repeated game or a single-shot game, do agents collude, do they know about the other agents, do they know about the other agents’ strategic choices, etc.). Because the Internet is somewhat different from traditional game-theoretic contexts, the traditional solution concepts may not be sufficient; we shall return to this issue in Section 8. The game-theory literature on mechanism desi...

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... be considered include the Moulin-Sprumont characterization of strategyproof mechanisms with single-peaked utilities [45, 63] and the BarberaJackson characterization of strategyproof exchange markets =-=[8]-=-. 6. STRATEGIC MODELS In this section, we look more carefully at an aspect of DAMD that we have thus far oversimplified. It need not be the case that all parties in a distributed, algorithmic mechanis...

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...ctable, given the information available to agent i, and that the computation of M() is tractable, given a strategy vector (s1 , . . . , sn ). 13 One can consider the virtual implementation literature =-=[39, 1]-=-, in which mechanisms produce lotteries over outcomes, to be a form of approximation. We don't discuss virtual implementation here. Nisan and Ronen [53] were the first to address the question of appro...

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...edient, centralized computational device that is distinct from the strategic agents who supply the inputs; similarly, it is the case for previous work on distributed multicast cost-sharing mechanisms =-=[5, 3, 18, 20, 22, 33, 41]-=-, where the mechanism is executed on an obedient, distributed computational device (i.e., the multicast tree) that is distinct from the strategic agents (who are resident at various nodes of the tree ...

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...S = U , we reduce to the direct2Our assumption that all agents are equivalent, made for notational simplicity, renders all strategy spaces the same; in general, we could have different strategy spaces Si. 2 mechanism case, and so our preceding discussion applies to direct mechanisms as well. That is, one can achieve nonstrategyproof SCFs with direct mechanisms by invoking different solution concepts. For example, one can achieve efficiency and budget balance using the Bayesian-Nash-equilibrium solution concept [7, 14] – something that is impossible using the dominant-strategy solution concept [27, 58]. It is important to note that, although the mechanism is chosen by the system designer, the solution concept is supposed to reflect reality. The solution concept thus depends greatly on the context (e.g., is it a repeated game or a single-shot game, do agents collude, do they know about the other agents, do they know about the other agents’ strategic choices, etc.). Because the Internet is somewhat different from traditional game-theoretic contexts, the traditional solution concepts may not be sufficient; we shall return to this issue in Section 8. The game-theory literature on mechanism desi...

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... reasons discussed at length by Moulin and Shenker [47], but it is only one of several group-strategyproof, budget-balanced mechanisms in the literature that have properties NPT, VP, CS, and SYM; see =-=[16, 33]-=- for more examples. It is shown in [18] that no group-strategyproof, budget-balanced multicast cost-sharing mechanism that satisfies conditions NPT, VP, CS, and SYM can have low absolute network compl...

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...ery set of other players’ strategies (t1, . . . , ti−1, ti+1, . . . , tn), the inequality ui(M(t1, . . . , ti−1, si, ti+1, . . . , tn)) + # ≥ ui(M(t1, . . . , ti−1, ti, ti+1, . . . , tn)) holds – so, si may not be a best possible strategy, but it is always within # of best possible, regardless of what other agents do. In the AMD context, one also insists that, for all i, the computation of si is tractable, given the information available to agent i, and that the computation of M(·) is tractable, given a strategy vector (s1, . . . , sn). 13One can consider the virtual implementation literature [39, 1], in which mechanisms produce lotteries over outcomes, to be a form of approximation. We don’t discuss virtual implementation here. Nisan and Ronen [53] were the first to address the question of approximate computation in AMD. They considered VCG mechanisms in which optimal outcomes are NP-hard to compute (as they are in combinatorial auctions). They pointed out that, if an optimal outcome is replaced by a computationally tractable, approximately optimal outcome, the resulting mechanism may no longer be strategyproof. The above discussion of how we should define “approximating the SH mechanism...

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...nilaterally increase his utility. Other solution concepts include rationalizable strategies (agents use strategies that are best responses to rational beliefs about the other agents' strategy choices =-=[10, 57]-=-), evolutionarily stable strategies (agents imitate the successful strategies used by others in previous rounds of the game [62]), and dominant strategies (agents only choose strategies that, regardle...

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...edient, centralized computational device that is distinct from the strategic agents who supply the inputs; similarly, it is the case for previous work on distributed multicast cost-sharing mechanisms =-=[5, 3, 18, 20, 22, 33, 41]-=-, where the mechanism is executed on an obedient, distributed computational device (i.e., the multicast tree) that is distinct from the strategic agents (who are resident at various nodes of the tree ...

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...e nonstrategyproof SCFs with direct mechanisms by invoking different solution concepts. For example, one can achieve e#- ciency and budget balance using the Bayesian-Nash-equilibrium solution concept =-=[7, 14]-=- -- something that is impossible using the dominant-strategy solution concept [27, 58]. It is important to note that, although the mechanism is chosen by the system designer, the solution concept is s...

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...hese caching mechanisms can be built as scalable extensions to existing distributed caching protocols and provide provable performance guarantees. Some aspects of this problem are addressed in, e.g., =-=[34]-=-. 9.2 Peer-to-Peer File Sharing Peer-to-peer (P2P) file-sharing networks, e.g., Gnutella, KaZaA, and Freenet, are the ne plus ultra of autonomous distributed systems; each machine belongs to a di#eren...

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... : O # # represents his valuations of each of the system states, and p i is his payment. For such problems, there is a class of strategyproof mechanisms, called Vickrey-Clarke-Groves (VCG) mechanisms =-=[13, 29, 64]-=-, that result in the system state that optimizes P i v i (o). Direct strategyproof mechanisms provide a conceptually simple, if not always ideal (see Section 7), way to achieve strategyproof SCFs. How...

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...ents is unknown to each individual agent. In addition to the standard SMFE literature [26], work that might be relevant to Open Problem 12 includes but is not limited to the papers of Naor and Nissim =-=[48]-=-, Naor, Pinkas, and Sumner [49], and Dodis, Halevi, and Rabin [15]. Thus far, our motivation for considering indirect mechanisms has been the desire to preserve agents' privacy, and we have observed t...

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...ual agent. In addition to the standard SMFE literature [26], work that might be relevant to Open Problem 12 includes but is not limited to the papers of Naor and Nissim [48], Naor, Pinkas, and Sumner =-=[49]-=-, and Dodis, Halevi, and Rabin [15]. Thus far, our motivation for considering indirect mechanisms has been the desire to preserve agents' privacy, and we have observed that low network complexity and ...

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...he TCS literature traditionally did the opposite. The emergence of the Internet as a standard platform for distributed computation has radically changed this state of affairs: Ownership, operation, and use by many selfinterested, independent parties give the Internet the characteristics of an economy as well as those of a computer. This development requires that these previously separable concerns – incentive compatibility and computational tractability – be jointly addressed. Although many subdisciplines of computer science have a long history of using game theory — such as networking (e.g., [21, 25, 35]), distributed artificial intelligence (e.g., [55, 61]), and marketbased computation (e.g., [65]) — the first work in TCS to address incentives and computational complexity simultaneously was Nisan and Ronen’s seminal paper [52] on algorithmic mechanism design (AMD). This paper put forth a formal model of centralized computation that combined incentive compatibility (the “mechanism design” part) with computational tractability (the “algorithmic” part). Feigenbaum, Papadimitriou, and Shenker [20] extended this to distributed algorithmic mechanism design (DAMD), in which the same goals of incent...

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.... New definitions of learning and new solution concepts that attempt to capture these aspects of Internetbased, repeated games have been proposed by, e.g., Erev and Roth [17] and Friedman and Shenker =-=[24]-=-. Which, if any, of these solution concepts and game-theoretic definitions of learning will play a central role in the emerging theory of DAMD is a wide open question. Moreover, we have yet to underst...

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...s. For example, one can achieve e#- ciency and budget balance using the Bayesian-Nash-equilibrium solution concept [7, 14] -- something that is impossible using the dominant-strategy solution concept =-=[27, 58]-=-. It is important to note that, although the mechanism is chosen by the system designer, the solution concept is supposed to reflect reality. The solution concept thus depends greatly on the context (...

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...retain the strategic properties of the original mechanism exactly and approximate one or more of its other properties. This type of approximation is studied in the economics literature as well (e.g., =-=[37]-=-), but not for the purpose of reducing computational or communication costs. An important and open research issue is to explore alternative notions of approximation, as well as to design computational...

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...ous open problems, some very specific and others quite general, concerning the foundations and applications of DAMD. Additional material about the AMD and DAMD research agendas can be found in, e.g., =-=[50, 51, 54]-=-. 2. MD TO AMD TO DAMD In essence, game theory is the study of what happens when independent agents act selfishly. Mechanism design asks how one can design systems so that agents' selfish behavior res...

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...n put forth, and we briefly review three of them here. Approximation of equilibria is considered in the gametheory literature independent of distributed-algorithmic concerns. 13 For example, Schummer =-=[60]-=- and Parkes et al. [56] consider #-dominance. A strategy vector (s1 , . . . , sn) is an #- dominant equilibrium if, for every agent i, every strategy t i , and every set of other players' strategies (...