The Coordinate-Wise Core for Multiple-Type Housing Markets is Second-Best Incentive Compatible

We consider the generalization of Shapley and Scarf''s (1974) model of trading indivisible objects (houses) to so-called multiple-type housing markets. We show (Theorem 1) that the prominent solution for these markets, the coordinate-wise core rule, is second-best incentive compatible. In other words, there exists no other strategy-proof trading rule that Pareto dominates the coordinate-wise core rule. Given that for multiple-type housing markets Pareto efficiency, strategy-proofness, and individual rationality are not compatible, by Theorem 1 we show that applying the coordinate-wise core rule is a minimal concession with respect to Pareto efficiency while preserving strategy-proofness and individual rationality.microeconomics ;

Trade rules for uncleared markets

We analyze markets in which the price of a traded commodity is such that the supply and the demand are unequal. Under standard assumptions, the agents then have single peaked preferences on their consumption or production choices. For such markets, we propose a class of Uniform Trade rules each of which determines the volume of trade as the median of total demand, total supply, and an exogenous constant. Then these rules allocate this volume 'uniformly' on either side of the market. We evaluate these 'trade rules' on the basis of some standard axioms in the literature. We show that they uniquely satisfy Pareto optimality, strategy proofness, no-envy, and an informational simplicity axiom that we introduce. We also analyze the implications of anonymity, renegotiation proofness, and voluntary trade on this domain.market disequilibrium, trade rule, efficiency, strategy proofness, anonymity, no-envy, renegotiation proofness, voluntary trade

Efficiency in Multiple-Type Housing Markets

We consider multiple-type housing markets (Moulin, 1995), which extend Shapley-Scarf housing markets (Shapley and Scarf, 1974) from one dimension to higher dimensions. In this model, Pareto efficiency is incompatible with individual rationality and strategy-proofness (Konishi et al., 2001). Therefore, we consider two weaker efficiency properties: coordinatewise efficiency and pairwise efficiency. We show that these two properties both (i) are compatible with individual rationality and strategy-proofness, and (ii) help us to identify two specific mechanisms. To be more precise, on various domains of preference profiles, together with other well-studied properties (individual rationality, strategy-proofness, and non-bossiness), coordinatewise efficiency and pairwise efficiency respectively characterize two extensions of the top-trading-cycles mechanism (TTC): the coordinatewise top-trading-cycles mechanism (cTTC) and the bundle top-trading-cycles mechanism (bTTC). Moreover, we propose several variations of our efficiency properties, and we find that each of them is either satisfied by cTTC or bTTC, or leads to an impossibility result (together with individual rationality and strategy-proofness). Therefore, our characterizations can be primarily interpreted as a compatibility test: any reasonable efficiency property that is not satisfied by cTTC or bTTC could be considered incompatible with individual rationality and strategy-proofness. For multiple-type housing markets with strict preferences, our characterization of bTTC constitutes the first characterization of an extension of the prominent TTC mechanis

Strategy-proofness and Markets

If a market is considered to be a social choice function, then the domain of admissible preferences is restricted and standard social choice theorems do not apply. A substantial body of analysis, however, strongly supports the notion that attractive strategy-proof social choice functions do not exist in market settings. Yetprice theory, which implicityly assumes the strategy-proofness of markets, performs quie well in describing many real markets. This paper resolves this paradox in two steps. First, given that a market is not strategy-proof, it should be modeled as a Bayesian game of incomplete information. Second, a double auction market, which is perhaps the simplest operationalization of supply and demand as a Bayesian game, is approximately strategy-proof even when the number of traders on each side of the market is quite moderate.

Exploiting Weak Supermodularity for Coalition-Proof Mechanisms

Under the incentive-compatible Vickrey-Clarke-Groves mechanism, coalitions of participants can influence the auction outcome to obtain higher collective profit. These manipulations were proven to be eliminated if and only if the market objective is supermodular. Nevertheless, several auctions do not satisfy the stringent conditions for supermodularity. These auctions include electricity markets, which are the main motivation of our study. To characterize nonsupermodular functions, we introduce the supermodularity ratio and the weak supermodularity. We show that these concepts provide us with tight bounds on the profitability of collusion and shill bidding. We then derive an analytical lower bound on the supermodularity ratio. Our results are verified with case studies based on the IEEE test systems

Bundling in Exchange Markets with Indivisible Goods

We study efficient and individually rational exchange rules for markets with heterogeneous indivisible goods that exclude the possibility that an agent benefits by bundling goods in her endowment. Even if agents'' preferences are additive, no such rule exists.microeconomics ;

Matching under Preferences

Matching theory studies how agents and/or objects from different sets can be matched with each other while taking agents\u2019 preferences into account. The theory originated in 1962 with a celebrated paper by David Gale and Lloyd Shapley (1962), in which they proposed the Stable Marriage Algorithm as a solution to the problem of two-sided matching. Since then, this theory has been successfully applied to many real-world problems such as matching students to universities, doctors to hospitals, kidney transplant patients to donors, and tenants to houses. This chapter will focus on algorithmic as well as strategic issues of matching theory. Many large-scale centralized allocation processes can be modelled by matching problems where agents have preferences over one another. For example, in China, over 10 million students apply for admission to higher education annually through a centralized process. The inputs to the matching scheme include the students\u2019 preferences over universities, and vice versa, and the capacities of each university. The task is to construct a matching that is in some sense optimal with respect to these inputs. Economists have long understood the problems with decentralized matching markets, which can suffer from such undesirable properties as unravelling, congestion and exploding offers (see Roth and Xing, 1994, for details). For centralized markets, constructing allocations by hand for large problem instances is clearly infeasible. Thus centralized mechanisms are required for automating the allocation process. Given the large number of agents typically involved, the computational efficiency of a mechanism's underlying algorithm is of paramount importance. Thus we seek polynomial-time algorithms for the underlying matching problems. Equally important are considerations of strategy: an agent (or a coalition of agents) may manipulate their input to the matching scheme (e.g., by misrepresenting their true preferences or underreporting their capacity) in order to try to improve their outcome. A desirable property of a mechanism is strategyproofness, which ensures that it is in the best interests of an agent to behave truthfully