People interested in the research are advised to contact the author for the final version of the ... more People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Tucker's well-known combinatorial lemma states that, for any given symmetric triangulation of the... more Tucker's well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1, ±2,. .. , ±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1, ±2,. .. , ±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0, 1} n + q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations under certain natural conditions. An economic application is provided.
We study a decentralised and uncoordinated market where heterogeneous self-interested firms and w... more We study a decentralised and uncoordinated market where heterogeneous self-interested firms and workers meet directly and randomly in pursuit of higher payoff over time. Each firm hires several workers and each worker has preferences over firms and salaries, taking at most one job. Neither firms nor workers possess perfect knowledge of the market. At any time any firm and any group of workers can form a new coalition if doing so makes no member of the coalition worse off and at least one member strictly better off. In this process, the firm may recruit workers from other firms and dismiss some of its own workers, the deserted firms and red workers can be worse off. This process is called the coalition improvement. We establish that starting from an arbitrary market state of a matching between firms and workers with a system of salaries, a decentralised random dynamic market process where each possible coalition improvement occurs with a positive probability converges with probabilit...
PROOF OF LEMMA 1: Suppose that p∗ is an equilibrium price vector. Then we know from Gul and Stacc... more PROOF OF LEMMA 1: Suppose that p∗ is an equilibrium price vector. Then we know from Gul and Stacchetti (1999, Lemma 6) that for any efficient allocation π∗, (p∗ π∗) constitutes an equilibrium. Clearly, ∑ i∈I u i(π∗(i))= R(N) the market value of the objects. Furthermore, we have L(p∗)= ∑i∈I V i(p∗)+ ∑ βh∈N p ∗ h = ∑ i∈I(u i(π∗(i))− ∑βh∈π∗(i) ph)+ ∑βh∈N ph =R(N). Note that for any p ∈ R and i ∈ I, V (p) ≥ ui(π∗(i)) − ∑βh∈π∗(i) ph. Thus for any p ∈ R, we have
We examine the implementation of reduced-form allocation rules in mechanism design problems. To h... more We examine the implementation of reduced-form allocation rules in mechanism design problems. To handle the problem, we adopt a conic approach which uses a lift-and-project method to construct a projection cone and find its finite generators. This results in a set of implementable reduced forms for implementation. We then characterize projection cones for several typical mechanism design problems including single-item auctions, bilateral trade, compromise, and multiple-item auctions with group capacity constraints. We find that the implementation condition in general has a linear characterization by a class of sign functions, which is larger and richer than the well-known class of characteristic functions found by Border. These results admit meaningful economic interpretations.
This paper considers a general and practical kidney exchange model with compatible or incompatibl... more This paper considers a general and practical kidney exchange model with compatible or incompatible patient-donor pairs, single donors, and patients on the waiting list. Efficient exchange procedures are proposed with dichotomous preferences in which only one-way, two-way, three, or four-way chains or cycles of exchange are used. We derive a tight upper bound of the possible number of feasible kidney transplants in each case of exchange and provide substantial simulation results. We find that two-way cycles and chains of exchange can substantially increase the number of feasible transplants, threeway can have a visible effect, and at most four-way cycles and chains suffice to capture all potential gains of exchange. Our results are not only theoretically interesting but also have important and novel policy implications.
Following Jansen et al. (2012), we examine an unconventional Cournot model of the European Union ... more Following Jansen et al. (2012), we examine an unconventional Cournot model of the European Union natural gas market with three major suppliers Russian Gazprom, Norwegian Statoil, and Algerian Sonatrach. To reflect Russia's other strategic consideration besides profit, we incorporate a relative market share into Gazprom's objective function. We prove that when Gazprom pursues the control of market share along with profit, it will be good news for consumers but bad news for its pure profit maximising rivals. We further show that by seeking a proper market share, Gazprom can achieve the same profit of a Stackelberg leader in a simultaneous move model as in the standard sequential move leader-follower model. Compared with Jansen et al.'s, our approach makes the analysis considerably simpler and more transparent.
We develop a new model of addictive behavior that takes as a starting point the classic rational ... more We develop a new model of addictive behavior that takes as a starting point the classic rational addiction model of Becker and Murphy, but incorporates uncertainty. We model uncertainty through the Wiener stochastic process. This process captures both random events such as anxiety, tensions and environmental cues which can precipitate and exacerbate addictions, and those sober and thought-provoking episodes that discourage addictions. We derive closed-form expressions for optimal (and expected optimal) addictive consumption and capital trajectories and examine their global and local properties. Our theory provides plausible explanations of several important patterns of addictive behavior, and has novel implications for addiction control policy.
'I'hc abovc Lhcorctn extcnds an carlicr result o(Scarf for n-'L. In I,his note a constructive pro... more 'I'hc abovc Lhcorctn extcnds an carlicr result o(Scarf for n-'L. In I,his note a constructive proof of the theorern is proposed.
International Journal of Game Theory, Oct 29, 2014
An auctioneer wishes to sell several heterogeneous indivisible items to a group of potential bidd... more An auctioneer wishes to sell several heterogeneous indivisible items to a group of potential bidders. Each bidder has valuations over the items but might face a budget constraint and may therefore not be able to pay up to his values. In such markets, a competitive equilibrium typically fails to exist. We develop a novel dynamic auction and prove that the auction always finds a core allocation. The core allocation consists of an assignment of the items and its associated supporting price vector and is Pareto efficient.
We present a constructive proof for the well-known Ky Fan's coincidence theorem through a simplic... more We present a constructive proof for the well-known Ky Fan's coincidence theorem through a simplicial algorithm. In a finite number of steps the algorithm generates a simplex containing an approximate coincidence point. In the limit, when the mesh size converges to zero, the sequence of approximations converges to a coincidence point.
Journal of Optimization Theory and Applications, Feb 1, 2004
People interested in the research are advised to contact the author for the final version of the ... more People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
People interested in the research are advised to contact the author for the final version of the ... more People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Tucker's well-known combinatorial lemma states that, for any given symmetric triangulation of the... more Tucker's well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1, ±2,. .. , ±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1, ±2,. .. , ±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0, 1} n + q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations under certain natural conditions. An economic application is provided.
We study a decentralised and uncoordinated market where heterogeneous self-interested firms and w... more We study a decentralised and uncoordinated market where heterogeneous self-interested firms and workers meet directly and randomly in pursuit of higher payoff over time. Each firm hires several workers and each worker has preferences over firms and salaries, taking at most one job. Neither firms nor workers possess perfect knowledge of the market. At any time any firm and any group of workers can form a new coalition if doing so makes no member of the coalition worse off and at least one member strictly better off. In this process, the firm may recruit workers from other firms and dismiss some of its own workers, the deserted firms and red workers can be worse off. This process is called the coalition improvement. We establish that starting from an arbitrary market state of a matching between firms and workers with a system of salaries, a decentralised random dynamic market process where each possible coalition improvement occurs with a positive probability converges with probabilit...
PROOF OF LEMMA 1: Suppose that p∗ is an equilibrium price vector. Then we know from Gul and Stacc... more PROOF OF LEMMA 1: Suppose that p∗ is an equilibrium price vector. Then we know from Gul and Stacchetti (1999, Lemma 6) that for any efficient allocation π∗, (p∗ π∗) constitutes an equilibrium. Clearly, ∑ i∈I u i(π∗(i))= R(N) the market value of the objects. Furthermore, we have L(p∗)= ∑i∈I V i(p∗)+ ∑ βh∈N p ∗ h = ∑ i∈I(u i(π∗(i))− ∑βh∈π∗(i) ph)+ ∑βh∈N ph =R(N). Note that for any p ∈ R and i ∈ I, V (p) ≥ ui(π∗(i)) − ∑βh∈π∗(i) ph. Thus for any p ∈ R, we have
We examine the implementation of reduced-form allocation rules in mechanism design problems. To h... more We examine the implementation of reduced-form allocation rules in mechanism design problems. To handle the problem, we adopt a conic approach which uses a lift-and-project method to construct a projection cone and find its finite generators. This results in a set of implementable reduced forms for implementation. We then characterize projection cones for several typical mechanism design problems including single-item auctions, bilateral trade, compromise, and multiple-item auctions with group capacity constraints. We find that the implementation condition in general has a linear characterization by a class of sign functions, which is larger and richer than the well-known class of characteristic functions found by Border. These results admit meaningful economic interpretations.
This paper considers a general and practical kidney exchange model with compatible or incompatibl... more This paper considers a general and practical kidney exchange model with compatible or incompatible patient-donor pairs, single donors, and patients on the waiting list. Efficient exchange procedures are proposed with dichotomous preferences in which only one-way, two-way, three, or four-way chains or cycles of exchange are used. We derive a tight upper bound of the possible number of feasible kidney transplants in each case of exchange and provide substantial simulation results. We find that two-way cycles and chains of exchange can substantially increase the number of feasible transplants, threeway can have a visible effect, and at most four-way cycles and chains suffice to capture all potential gains of exchange. Our results are not only theoretically interesting but also have important and novel policy implications.
Following Jansen et al. (2012), we examine an unconventional Cournot model of the European Union ... more Following Jansen et al. (2012), we examine an unconventional Cournot model of the European Union natural gas market with three major suppliers Russian Gazprom, Norwegian Statoil, and Algerian Sonatrach. To reflect Russia's other strategic consideration besides profit, we incorporate a relative market share into Gazprom's objective function. We prove that when Gazprom pursues the control of market share along with profit, it will be good news for consumers but bad news for its pure profit maximising rivals. We further show that by seeking a proper market share, Gazprom can achieve the same profit of a Stackelberg leader in a simultaneous move model as in the standard sequential move leader-follower model. Compared with Jansen et al.'s, our approach makes the analysis considerably simpler and more transparent.
We develop a new model of addictive behavior that takes as a starting point the classic rational ... more We develop a new model of addictive behavior that takes as a starting point the classic rational addiction model of Becker and Murphy, but incorporates uncertainty. We model uncertainty through the Wiener stochastic process. This process captures both random events such as anxiety, tensions and environmental cues which can precipitate and exacerbate addictions, and those sober and thought-provoking episodes that discourage addictions. We derive closed-form expressions for optimal (and expected optimal) addictive consumption and capital trajectories and examine their global and local properties. Our theory provides plausible explanations of several important patterns of addictive behavior, and has novel implications for addiction control policy.
'I'hc abovc Lhcorctn extcnds an carlicr result o(Scarf for n-'L. In I,his note a constructive pro... more 'I'hc abovc Lhcorctn extcnds an carlicr result o(Scarf for n-'L. In I,his note a constructive proof of the theorern is proposed.
International Journal of Game Theory, Oct 29, 2014
An auctioneer wishes to sell several heterogeneous indivisible items to a group of potential bidd... more An auctioneer wishes to sell several heterogeneous indivisible items to a group of potential bidders. Each bidder has valuations over the items but might face a budget constraint and may therefore not be able to pay up to his values. In such markets, a competitive equilibrium typically fails to exist. We develop a novel dynamic auction and prove that the auction always finds a core allocation. The core allocation consists of an assignment of the items and its associated supporting price vector and is Pareto efficient.
We present a constructive proof for the well-known Ky Fan's coincidence theorem through a simplic... more We present a constructive proof for the well-known Ky Fan's coincidence theorem through a simplicial algorithm. In a finite number of steps the algorithm generates a simplex containing an approximate coincidence point. In the limit, when the mesh size converges to zero, the sequence of approximations converges to a coincidence point.
Journal of Optimization Theory and Applications, Feb 1, 2004
People interested in the research are advised to contact the author for the final version of the ... more People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
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