Finding Fair and Efficient Allocations for Matroid Rank Valuations

In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions . This is a versatile valuation class with several desirable properties (such as monotonicity and submodularity), which naturally lends itself to a number of real-world domains. We use these properties to our advantage; first, we show that when agent valuations are matroid rank functions, a socially optimal (i.e., utilitarian social welfare-maximizing) allocation that achieves envy-freeness up to one item (EF1) exists and is computationally tractable. We also prove that the Nash welfare-maximizing and the leximin allocations both exhibit this fairness/efficiency combination by showing that they can be achieved by minimizing any symmetric strictly convex function over utilitarian optimal outcomes. To the best of our knowledge, this is the first valuation function class not subsumed by additive valuations for which it has been established that an allocation maximizing Nash welfare is EF1. Moreover, for a subclass of these valuation functions based on maximum (unweighted) bipartite matching, we show that a leximin allocation can be computed in polynomial time. Additionally, we explore possible extensions of our results to fairness criteria other than EF1 as well as to generalizations of the above valuation classes.

The randomized communication complexity of revenue maximization

We study the communication complexity of incentive compatible auction-protocols between a monopolist seller and a single buyer with a combinatorial valuation function over n items [Rubinstein and Zhao 2021]. Motivated by the fact that revenue-optimal auctions are randomized [Thanassoulis 2004; Manelli and Vincent 2010; Briest et al. 2010; Pavlov 2011; Hart and Reny 2015] (as well as by an open problem of Babaioff, Gonczarowski, and Nisan [Babaioff et al. 2017]), we focus on the randomized communication complexity of this problem (in contrast to most prior work on deterministic communication). We design simple, incentive compatible, and revenue-optimal auction-protocols whose expected communication complexity is much (in fact infinitely) more efficient than their deterministic counterparts. We also give nearly matching lower bounds on the expected communication complexity of approximately-revenue-optimal auctions. These results follow from a simple characterization of incentive compatible auction-protocols that allows us to prove lower bounds against randomized auction-protocols. In particular, our lower bounds give the first approximation-resistant, exponential separation between communication complexity of incentivizing vs implementing a Bayesian incentive compatible social choice rule, settling an open question of Fadel and Segal [Fadel and Segal 2009].

Combinatorial Assortment Optimization

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a choice model in which each consumer selects a utility-maximizing bundle subject to a private valuation function, and study the complexity of the resulting optimization problem. Our main result is an exact algorithm for additive k -demand valuations, under a model of vertical differentiation in which customers agree on the relative value of each pair of items but differ in their absolute willingness to pay. For valuations that are vertically differentiated but not necessarily additive k -demand, we show how to obtain constant approximations under a “well-priced” condition, where each product’s price is sufficiently high. We further show that even for a single customer with known valuation, any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS and that no FPTAS exists even when the valuation is succinctly representable.

LOSS AVERSION IS CONSISTENT WITH STOCK MARKET BEHAVIOR

The purpose of this paper is to verify that discrete statistical distributions of the US stock market are consistent with loss aversion. Loss aversion has the following tenets: an S-shaped valuation function, characterized by diminishing sensitivity, a loss aversion coefficient higher than +1, probability weighting, and reference-dependence. Diminishing sensitivity implies that the exponent of the valuation function is between 0 and +1. It is expected that this exponent be higher for losses. Probability weighting replaces objective with subjective probabilities. Loss aversion is indicated by a coefficient higher than +1 for the valuation of losses. There are three parameters: the two exponents of the valuation function, and the loss aversion coefficient. There is one non-linear equation: the certainty equivalence relation. The procedure is to fix two parameters and find the third parameter by solving the non-linear certainty equivalence equation, using the EXCEL spreadsheet. The program is repeated for more than one case about the fixed parameters, and by enriching the analysis with probability weighting. The calibrations executed point strongly to the conclusion that loss aversion is consistent with six discrete distributions of the first two moments of returns of the US stock markets. The calibration process provides for reasonable estimates of the key parameters of loss aversion. These estimates suggest a more pronounced diminishing sensitivity, and a higher than expected coefficient of loss aversion, especially when probability weighting is imposed.

A Multi-Unit Profit Competitive Mechanism for Cellular Traffic Offloading

Cellular traffic offloading is nowadays an important problem in mobile networking. We model it as a procurement problem where each agent sells multi-units of a homogeneous item with privately known capacity and unit cost, and the auctioneer's demand valuation function is symmetric submodular. Based on the framework of random sampling and profit extraction, we aim to design a prior-free mechanism which guarantees a profit competitive to the omniscient single-price auction. However, the symmetric submodular demand valuation function and 2-parameter setting present new challenges. By adopting the highest feasible clear price, we successfully design a truthful profit extractor, and then we propose a mechanism which is proved to be truthful, individually rational and constant-factor competitive in a fixed market.

Approximately Maximizing the Broker's Profit in a Two-sided Market

We study how to maximize the broker's (expected) profit in a two-sided market, where she buys items from a set of sellers and resells them to a set of buyers. Each seller has a single item to sell and holds a private value on her item, and each buyer has a valuation function over the bundles of the sellers' items. We consider the Bayesian setting where the agents' values/valuations are independently drawn from prior distributions, and aim at designing dominant-strategy incentive-compatible (DSIC) mechanisms that are approximately optimal. Production-cost markets, where each item has a publicly-known cost to be produced, provide a platform for us to study two-sided markets. Briefly, we show how to covert a mechanism for production-cost markets into a mechanism for the broker, whenever the former satisfies cost-monotonicity. This reduction holds even when buyers have general combinatorial valuation functions. When the buyers' valuations are additive, we generalize an existing mechanism to production-cost markets in an approximation-preserving way. We then show that the resulting mechanism is cost-monotone and thus can be converted into an 8-approximation mechanism for two-sided markets.

Can Existing Estimates for Ecosystem Service Values Inform Forest Management?

: This paper aims at analyzing whether existing economic value estimates for forest ecosystem services (ES) might be transferred and used for valuation purposes elsewhere, and whether these data are appropriate for application in forest management. Many forest ES are public goods or positive externalities, and as a consequence they do not have a market price. The valuation of forest ES can provide important information for decision making in forest management and planning as well as in political processes, especially by allowing the comparison of different alternatives and helping set priorities for practical actions, as well as developing financial incentives or support mechanisms. We analyze whether an integrated economic valuation model for forest ES can be developed based on existing published data. To achieve this, we assess to which extent a benefit transfer could be expedient, and which challenges must be addressed. Based on a literature search, we compiled an extensive database of forest ES values. Given that these values vary substantially for the same ES, such a database alone does not seem useful to serve as a decision and management support tool. In addition, the available information mainly focuses on forests as such, and does not include desirable forest composition and management targets. If existing estimates should be transferred and used for forest management decisions, both the background conditions of the primary studies and the indicators used for valuation need to be specified in detail. The most expedient approach in this context seemed to be a valuation function transfer based on a broad set of indicators, offering the possibility to adapt the valuation function to changing background conditions.

Valuing the historical heritage: the case of the Venetian Villas in Italy

Purpose The historic assets are heterogeneous and different to each other, and for this reason, consolidated valuation methodologies do not exist in practice or in the literature. It is, therefore, necessary to dwell on the study of a particular historic building type or category. The assessment process of the valuers of Venetian Villas was explored, focusing on the study of the valuation function construction. The paper investigated if a possible value function, based on the partition of the characteristics, which significantly influence the value, exists and it is generalizable to the whole set of Venetian Villas. The purpose of this paper is to contribute knowledge on the economic valuation of Venetian Villas. Design/methodology/approach An application of Hedonic Pricing study to a database of 71 Venetian Villas has been tested. This statistical procedure allowed the authors to discover which results in a percentage of property values can be attributed to the historical characteristics of a building. Using a multiple linear regression and its variables an analysis of residuals and data relating to the variance has been performed. Findings This research identifies and proposes, therefore, a valuation approach that can be generalizable to the whole set of Venetian Villas (over 4,000 properties). The models show that the most important variables which influence the value of the villas are: age, internal and external area, maintenance conditions, and author. This model could be used for future valuations of the same type of asset. Originality/value The model enables valuers to address better to the property valuation of the Venetian Villas through the valuation functions, which suggest which are the main features which focus in the case of a Venetian Villa valuation and what impact they have on the value asset. The model can be specifically used for valuation reports in the enhancement project of such properties.