Riccardo Colini-Baldeschi

On Multiple Keyword Sponsored Search Auctions with Budgets

We study multiple keyword sponsored search auctions with budgets. Each keyword has multiple ad slots with a click-through rate. The bidders have additive valuations, which are linear in the click-through rates, and budgets, which are restricting their overall payments. Additionally, the number of slots per keyword assigned to a bidder is bounded. We show the following results: (1) We give the first mechanism for multiple keywords, where click-through rates differ among slots. Our mechanism is incentive compatible in expectation, individually rational in expectation, and Pareto optimal. (2) We study the combinatorial setting, where each bidder is only interested in a subset of the keywords. We give an incentive compatible, individually rational, Pareto-optimal, and deterministic mechanism for identical click-through rates. (3) We give an impossibility result for incentive compatible, individually rational, Pareto-optimal, and deterministic mechanisms for bidders with diminishing marginal valuations.

On the Price of Anarchy of Highly Congested Nonatomic Network Games

We consider nonatomic network games with one source and one destination. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we show that, under suitable conditions, the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case. The counterexamples occur in very simple parallel graphs.

Variance Allocation and Shapley Value

Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of n possibly dependent random variables. This criterion, the Shapley value, requires to translate the problem into a cooperative game. The Shapley value has nice properties, but, in general, is computationally demanding. The main result of this paper shows that in our particular case the Shapley value has a very simple form that can be easily computed. The same criterion is used also to allocate the standard deviation of the sum of n random variables and a conjecture about the relation of the values in the two games is formulated.

Fixed Price Approximability of the Optimal Gain from Trade

Bilateral trade is a fundamental economic scenario comprising a strategically acting buyer and seller (holding an item), each holding valuations for the item, drawn from publicly known distributions. It was recently shown that the only mechanisms that are simultaneously dominant strategy incentive compatible, strongly budget balanced, and ex-post individually rational, are fixed price mechanisms, i.e., mechanisms that are parametrised by a price p, and trade occurs if and only if the valuation of the buyer is at least p and the valuation of the seller is at most p. The gain from trade (GFT) is the increase in welfare that results from applying a mechanism. We study the GFT achievable by fixed price mechanisms. We explore this question for both the bilateral trade setting and a double auction setting where there are multiple i.i.d. unit demand buyers and sellers. We first identify a fixed price mechanism that achieves a GFT of at least 2 / r times the optimum, where r is the probability that the seller’s valuation does not exceed that of the buyer’s valuation. This extends a previous result by McAfee. Subsequently, we improve this approximation factor in an asymptotic sense, by showing that a more sophisticated rule for setting the fixed price results in a GFT within a factor \(O(\log (1/r))\) of the optimum. This is asymptotically the best approximation factor possible. For the double auction setting, we present a fixed price mechanism that achieves for all \(\epsilon > 0\) a gain from trade of at least \((1-\epsilon )\) times the optimum with probability \(1 - 2/e^{\#T \epsilon ^2 /2}\), where \(\#T\) is the expected number of trades of the mechanism. This can be interpreted as a “large market” result: Full efficiency is achieved in the limit, as the market gets thicker.

Price of Anarchy for Highly Congested Routing Games in Parallel Networks

We consider nonatomic routing games with one source and one destination connected by multiple parallel edges. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we prove that under suitable conditions on the costs the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case, and that these counterexamples already occur in simple networks with only 2 parallel links.

The asymptotic behavior of the price of anarchy

This paper examines the behavior of the price of anarchy as a function of the traffic inflow in nonatomic congestion games with multiple origin-destination (O/D) pairs. Empirical studies in real-world networks show that the price of anarchy is close to 1 in both light and heavy traffic, thus raising the question: can these observations be justified theoretically? We first show that this is not always the case: the price of anarchy may remain bounded away from 1 for all values of the traffic inflow, even in simple three-link networks with a single O/D pair and smooth, convex costs. On the other hand, for a large class of cost functions (including all polynomials), the price of anarchy does converge to 1 in both heavy and light traffic conditions, and irrespective of the network topology and the number of O/D pairs in the network.

Revenue Maximizing Envy-Free Pricing in Matching Markets with Budgets

We study envy-free pricing mechanisms in matching markets with m items and n budget constrained buyers. Each buyer is interested in a subset of the items on sale, and she appraises at some single-value every item in her preference-set. Moreover, each buyer has a budget that constraints the maximum affordable payment, while she aims to obtain as many items as possible of her preference-set. Our goal is to compute an envy-free pricing allocation that maximizes the revenue. This pricing problem is hard to approximate better than

Approximately efficient double auctions with strong budget balance

\varOmega \mathrm{min} \{n,m\}^{1/2-\epsilon }