Abstract. We consider the Offline Ad Slot Scheduling problem, where advertisers must be scheduled to sponsored search slots during a given period of time. Advertisers specify a budget constraint, as well as a maximum cost per click, and may not be assigned to more than one slot for a particular search. We give a truthful mechanism under the utility model where bidders try to maximize their clicks, subject to their personal constraints. In addition, we show that the revenue-maximizing mechanism is not truthful, but has a Nash equilibrium whose outcome is identical to our mechanism. As far as we can tell, this is the first treatment of sponsored search that directly incorporates both multiple slots and budget constraints into an analysis of incentives. Our mechanism employs a descending-price auction that maintains a solution to a certain machine scheduling problem whose job lengths depend on the price, and hence is variable over the auction. The price stops when the set of bidders that can afford that price pack exactly into a block of ad slots, at which point the mechanism allocates that block and continues on the remaining slots. To prove our result on the equilibrium of the revenue-maximizing mechanism, we first show that a greedy algorithm suffices to solve the revenue-maximizing linear program; we then use this insight to prove that bidders allocated in the same block of our mechanism have no incentive to deviate from bidding the fixed price of that block. ⋆ This work was done while the author was visiting Google, Inc., New York, NY. 1

We develop a novel auction-based algorithm to allow users to fairly compete for a wireless fading channel. We use the second-price auction mechanism whereby user bids for the channel, during each time slot, based on the fade state of the channel, and the user that makes the highest bid wins use of the channel by paying the second highest bid. Under the assumption that each user has a limited budget for bidding, we show the existence of a Nash equilibrium strategy, and the Nash equilibrium leads to a unique allocation for certain channel state distribution, such as the exponential distribution and the uniform distribution over [0, 1]. For uniformly distributed channel state, we establish that the aggregate throughput received by the users using the Nash equilibrium strategy is at least 3/4 of what can be obtained using an optimal centralized allocation that does not take fairness into account. We also show that the Nash equilibrium strategy leads to an allocation that is Pareto optimal (i.e., it is impossible to make some users better off without making some other users worse off). Based on the Nash equilibrium strategies of the second-price auction with money constraint, we further propose a centralized opportunistic scheduler that does not suffer the shortcomings associated with the proportional fair scheduler.

The single-source min-cost multicast problem, which can be framed as a convex optimization problem with the use of network codes and convex increasing edge costs is considered. A decentralized approach to this problem is presented by Lun, Ratnakar et. al. for the case where all users cooperate to reach the global minimum. Further, the cost for the scenario where each of the multicast receivers greedily routes its flows is analyzed and the existence of a Nash equilibrium is proved. An allocation rule by which edge cost at each edge is allocated to flows through that edge is presented. We prove that under our pricing rule, the flow cost at user equilibrium is the same as the min-cost. This leads to the construction of a selfish flow-steering algorithm for each receiver, which is also globally optimal. Further, the algorithm is extended for completely distributed flow adaptation at nodes in the network to achieve globally minimal cost in steady state. Analogous results are also presented for the case of multiple multicast sessions.

We initiate the study of the price of anarchy of selfish routing with variable traffic rates and when the path cost is a non-additive function of the edge costs. The latter arises, for example, in networking applications, where a key performance metric is the achievable throughput along a path, which is controlled by its bottleneck (most congested) edge. We prove the following results. • In multicommodity networks, the price of anarchy under the ℓp path cost with 1 < p ≤ ∞ can be dramatically larger than under the standard ℓ1 path cost. • In single-commodity networks, the price of anarchy under the ℓp path cost with 1 < p < ∞ is no more than with the standard ℓ1 path norm. This upper bound also applies to the ℓ∞ path cost if and only if attention is restricted to the natural subclass of equilibria generated by distributed shortest-path routing protocols. • For a natural cost-minimization objective function, the price of anarchy with endogenous traffic rates (and under any ℓp path cost) is no larger than that in fixed-demand networks. Intuitively, the worst-case inefficiency arising from the “tragedy of the commons ” is no more severe than that from routing inefficiencies.

In this work we study the relationship between a WLAN owner acting as a wireless access provider and a paying client. We model the interaction as a dynamic game in which the players have asymmetric information – the client knows more about her utility function than the access provider knows. In earlier work [1], we found that if a client has a “web browser ” utility function (a temporal utility function that grows linearly), it

We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communication networks; in particular, we restrict attention to mechanisms where users are restricted to one-dimensional strategy spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differentiate. We study the worst-case efficiency loss (ratio of the utility associated with a Nash equilibrium to the maximum possible utility), and show that the proportional allocation mechanism of Kelly (1997) minimizes the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price differentiation is permitted; using an adaptation of the Vickrey-Clarke-Groves class of mechanisms, we construct a class of mechanisms with one-dimensional strategy spaces where Nash equilibria are fully efficient. These mechanisms are shown to be fully efficient even in general convex environments, under reasonable assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually improve the efficiency guarantee.

Users share an increasing marginal cost technology. A cost sharing method charges non negative cost shares covering costs. We look at the worst surplus (relative to the efficient surplus) in a Nash equilibrium of the demand game, where the minimum is taken over all convex preferences quasi-linear in cost shares. We compare average cost pricing and serial cost sharing, two budget-balanced methods, and incremental cost sharing, a method collecting a budget surplus, that we count as a welfare loss. For any convex cost function, the average cost and serial methods guarantee a (relative) surplus no less than 1,wherenis the number of n users. For some cost functions incremental cost sharing guarantees no positive gain. With quadratic costs, the surplus guaranteed by serial cost sharing is θ ( 1

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We study the interaction among users of unstructured file sharing applications, who compete for available network resources (link bandwidth or capacity) by opening multiple connections on multiple paths so as to accelerate data transfer. We model this interaction with an unstructured file sharing game. Users are players and their strategies are the numbers of sessions on available paths. We consider a general bandwidth sharing framework proposed by Kelly [1] and Mo and Walrand [2], with TCP as a special case. Furthermore, we incorporate the Tit-for-Tat strategy (adopted by BitTorrent [3] networks) into the unstructured file sharing game to model the competition in which a connection can be set up only when both users find this connection beneficial. We refer to this as an overlay formation game. We prove the existence of Nash equilibrium in several variants of both games, and quantify the losses of efficiency of Nash equilibria. We find that the loss of efficiency due to selfish behavior is still unbounded even when the Tit-for-Tat strategy is believed to prevent selfish behavior. I.

Abstract — The VCG-Kelly mechanism is proposed, which is obtained by composing the communication efficient, onedimensional signaling idea of Kelly with the VCG mechanism, providing efficient allocation for strategic buyers at Nash equilibrium points. It is shown that the revenue to the seller can be maximized or minimized using a particular one-dimensional family of surrogate valuation functions. Index Terms— I.