Kshipra Bhawalkar

Weighted Congestion Games: The Price of Anarchy, Universal Worst-Case Examples, and Tightness

We characterize the Price of Anarchy (POA) in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost function-independent) worst-case examples. One noteworthy by-product of our proofs is the fact that weighted congestion games are “tight,” which implies that the worst-case price of anarchy with respect to pure Nash equilibria, mixed Nash equilibria, correlated equilibria, and coarse correlated equilibria are always equal (under mild conditions on the allowable cost functions). Another is the fact that, like nonatomic but unlike atomic (unweighted) congestion games, weighted congestion games with trivial structure already realize the worst-case POA, at least for polynomial cost functions. We also prove a new result about unweighted congestion games: the worst-case price of anarchy in symmetric games is as large as in their more general asymmetric counterparts.

Coevolutionary opinion formation games

We present game-theoretic models of opinion formation in social networks where opinions themselves co-evolve with friendships. In these models, nodes form their opinions by maximizing agreements with friends weighted by the strength of the relationships, which in turn depend on difference in opinion with the respective friends. We define a social cost of this process by generalizing recent work of Bindel et al., FOCS 2011. We tightly bound the price of anarchy of the resulting dynamics via local smoothness arguments, and characterize it as a function of how much nodes value their own (intrinsic) opinion, as well as how strongly they weigh links to friends with whom they agree more.

Simultaneous single-item auctions

In a combinatorial auction (CA) with item bidding, several goods are sold simultaneously via single-item auctions. We study how the equilibrium performance of such an auction depends on the choice of the underlying single-item auction. We provide a thorough understanding of the price of anarchy, as a function of the single-item auction payment rule. When the payment rule depends on the winners bid, as in a first-price auction, we characterize the worst-case price of anarchy in the corresponding CAs with item bidding in terms of a sensitivity measure of the payment rule. As a corollary, we show that equilibrium existence guarantees broader than that of the first-price rule can only be achieved by sacrificing its property of having only fully efficient (pure) Nash equilibria. For payment rules that are independent of the winners bid, we prove a strong optimality result for the canonical second-price auction. First, its set of pure Nash equilibria is always a superset of that of every other payment rule. Despite this, its worst-case POA is no worse than that of any other payment rule that is independent of the winners bid.

Value of Targeting

We undertake a formal study of the value of targeting data to an advertiser. As expected, this value is increasing in the utility difference between realizations of the targeting data and the accuracy of the data, and depends on the distribution of competing bids. However, this value may vary non-monotonically with an advertiser’s budget. Similarly, modeling the values as either private or correlated, or allowing other advertisers to also make use of the data, leads to unpredictable changes in the value of data. We address questions related to multiple data sources, show that utility of additional data may be non-monotonic, and provide tradeoffs between the quality and the price of data sources. In a game-theoretic setting, we show that advertisers may be worse off than if the data had not been available at all. We also ask whether a publisher can infer the value an advertiser would place on targeting data from the advertiser’s bidding behavior and illustrate that this is impossible.

Online Set Cover with Set Requests

We consider a generic online allocation problem that generalizes the classical online set cover framework by considering requests comprising a set of elements rather than a single element. This problem has multiple applications in cloud computing, crowd sourcing, facility planning, etc. Formally, it is an online covering problem where each online step comprises an offline covering problem. In addition, the covering sets are capacitated, leading to packing constraints. We give a randomized algorithm for this problem that has a nearly tight competitive ratio in both objectives: overall cost and maximum capacity violation. Our main technical tool is an online algorithm for packing/covering LPs with nested constraints, which may be of interest in other applications as well.

Concise Bid Optimization Strategies with Multiple Budget Constraints

A major challenge faced by the marketers attempting to optimize their advertising campaigns is to deal with budget constraints. The problem is even harder in the face of multidimensional budget constraints, particularly in the presence of many decision variables involved, and the interplay among the decision variables through these such constraints. Concise bidding strategies help advertisers deal with this challenge by introducing fewer variables to act on.