A Double-Track Auction for Substitutes and Complements

We propose a new t^atonnement process called a double-track auction for efficiently allocating multiple heterogeneous indivisible items in two distinct sets S1 and S2 to many buyers who view items in the same set as substitutes but items across the two sets as complements. The auctioneer initially announces sufficiently low prices for items in one set, say S1, but sufficiently high prices for items in the other set S2. In each round, the buyers respond by reporting their demands at the current prices and the auctioneer adjusts prices upwards for items in S1 but downwards for items in S2 based on buyers' reported demands until the market is clear. Unlike any existing auction, this auction is a blend of a multi-item ascending auction and a multi-item descending auction. We prove that the auction finds an efficient allocation and its market-clearing prices in finitely many rounds. Based on the auction we also establish a dynamic, efficient and strategy-proof mechanism.Market design, dynamic auction, t^atonnement process, gross substitutes and complements, Walrasian equilibrium, incentives.

Monotonicity and Nash implementation in matching markets with contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005) and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.matching with contracts, (Maskin) monotonicity, Nash implementation, stability.

Matrix bids in combinatorial auctions: expressiveness and micro-economic properties

A combinatorial auction is an auction where multiple items are for sale simultaneously to a set of buyers. Furthermore, buyers are allowed to place bids on subsets of the available items. This paper focuses on a combinatorial auction where a bidder can express his preferences by means of a so-called ordered matrix bid. Ordered matrix bids are a bidding language that allows a compact representation of a bidder''s preferences, and was developed by Day (2004). We give an overview of how a combinatorial auction with matrix bids works. We elaborate on the relevance of the matrix bid auction and we develop methods to verify whether a given matrix bid satisfies properties related to micro-economic theory as free disposal, subadditivity, submodularity and the gross substitutes property. Finally, we investigate how a collection of arbitrary bids can be represented as a matrix bid.microeconomics ;

Competitive equilibrium with indivisible objects

We study exchange economies in which objects are heterogeneous and indivisible, and may not be substitutes for each other. We give new equilibrium existence results with the $p$-substitutability condition, under which a certain degree of complementarity among objects is permitted according to the parameter vector $p$. Moreover, we introduce conditions under which the contributions of objects to the social welfare are equilibrium prices

An Efficient and Strategy-Proof Double-Track Auction for Substitutes and Complements

Sun N, Yang Z. An Efficient and Strategy-Proof Double-Track Auction for Substitutes and Complements. Center for Mathematical Economics Working Papers. Vol 523. Bielefeld: Center for Mathematical Economics; 2014.We propose a dynamic auction mechanism for efficiently allocating multiple heterogeneous indivisible goods. These goods can be split into two distinct sets so that items in each set are substitutes but complementary to items in the other set. The seller has a reserve value for each bundle of goods and is assumed to report her values truthfully. In each round of the auction, the auctioneer announces the current prices for all items, bidders respond by reporting their demands at these prices, and then the auctioneer adjusts simultaneously the prices of items in one set upwards but those of items in the other downwards. We prove that although bidders are not assumed to be price-takers and thus can strategically exercise their market power, this dynamic auction always induces the bidders to bid truthfully as price-takers, yields an efficient outcome and also has the merit of being a detail-free, transparent and privacy preserving mechanism

Designing Matching Mechanisms under Constraints: An Approach from Discrete Convex Analysis

We consider two-sided matching problems where agents on one side of the market (hospitals) are required to satisfy certain distributional constraints. We show that when the preferences and constraints of the hospitals can be represented by an M-natural-concave function, (i) the generalized Deferred Acceptance mechanism is strategyproof for doctors, (ii) it produces the doctor-optimal stable matching, and (iii) its time complexity is proportional to the square of the number of possible contracts. Furthermore, we provide sufficient conditions for representation by an M-natural-concave function. These conditions are applicable to various existing works and enable new applications as well, thereby providing a recipe for developing desirable mechanisms in practice

Designing Matching Mechanisms under Constraints: An Approach from Discrete Convex Analysis

We consider two-sided matching problems where agents on one side of the market (hospitals) are required to satisfy certain distributional constraints. We show that when the preferences and constraints of the hospitals can be represented by an M-natural-concave function, (i) the generalized Deferred Acceptance (DA) mechanism is strategyproof for doctors, (ii) it produces the doctor-optimal stable matching, and (iii) its time complexity is proportional to the square of the number of possible contracts. Furthermore, we provide sufficient conditions under which the generalized DA mechanism satisfies these desirable properties. These conditions are applicable to various existing works and enable new applications as well, thereby providing a recipe for developing desirable mechanisms in practice

Designing Matching Mechanisms under Constraints: An Approach from Discrete Convex Analysis

We consider two-sided matching problems where agents on one side of the market (hospitals) are required to satisfy certain distributional constraints. We show that when the preferences and constraints of the hospitals can be represented by an \Mnatural-concave function, (i) the generalized Deferred Acceptance (DA) mechanism is strategyproof for doctors, (ii) it produces the doctor-optimal stable matching, and (iii) its time complexity is proportional to the square of the number of possible contracts. Furthermore, we provide sufficient conditions under which the generalized DA mechanism satisfies these desirable properties. These conditions are applicable to various existing works and enable new applications as well, thereby providing a recipe for developing desirable mechanisms in practice

Models of Pentecostal healing and practice in light of early twentieth century Pentecostalism

This thesis offers an examination of healing theology and practice as found in early North American Pentecostalism. The thesis begins with a brief survey of recent scholarship and research on the subject of healing in America, establishing that little attention has been given to the theology and practice of the early Pentecostal movement. The first major section of the thesis is devoted to an examination of the Divine Healing Movement of the nineteenth century, providing the historical and theological background of the Pentecostal Movement's healing theology and practice. By examining the writings of five major practitioners of the movement (including A.B. Simpson, Andrew Murray and Carrie Judd Montgomery), a nineteenth-century theology of 'divine healing provided in the atonement' is articulated. A major portion of the thesis is devoted to an analysis of healing theology and practice in early North American Pentecostalism. An inductive approach is employed, examining the earliest (1906 to 1923) periodical literature of the movement, and where that is not available examining other extant materials, such as sermons, songs and tracts. This portion of the study consists of two major parts: Wesleyan-Pentecostalism and Finished Work Pentecostalism. The result of this examination is the identification of two distinct healing theologies and the attendant practices, which are consistent with each group's distinct soteriological characteristics. A models approach is then employed by which, out of the materials previously examined, these two distinct theologies of healing are constructed. A case study of Pentecostal responses to the 1918 Influenza Epidemic serves both to illustrate and test the two models of healing. A final chapter summarizes conclusions including contributions, clarifications, and implications of the research for further Pentecostal studies as well as a theological reflection on the findings