Polyhedral Clinching Auctions for Two-Sided Markets

Mathematics of Operations Research ◽

10.1287/moor.2021.1124 ◽

2021 ◽

Author(s):

Hiroshi Hirai ◽

Ryosuke Sato

Keyword(s):

Pareto Optimality ◽

Network Flow ◽

Flow Model ◽

Incentive Compatibility ◽

The Internet ◽

Matching Markets ◽

Budget Balance ◽

Multiunit Auctions ◽

Exchange Markets ◽

Two Sided Markets

In this paper, we present a new model and mechanisms for auctions in two-sided markets of buyers and sellers, where budget constraints are imposed on buyers. Our model incorporates polymatroidal environments and is applicable to a variety of models that include multiunit auctions, matching markets, and reservation exchange markets. Our mechanisms are built on the polymatroidal network flow model by Lawler and Martel. Additionally, they feature nice properties such as the incentive compatibility of buyers, individual rationality, Pareto optimality, and strong budget balance. The first mechanism is a two-sided generalization of the polyhedral clinching auction by Goel et al. for one-sided markets. The second mechanism is a reduce-to-recover algorithm that reduces the market to be one-sided, applies the polyhedral clinching auction by Goel et al., and lifts the resulting allocation to the original two-sided market via the polymatroidal network flow. Both mechanisms are implemented by polymatroid algorithms. We demonstrate how our framework is applied to the Internet display advertisement auctions.

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Efficient multiunit auctions for normal goods

Theoretical Economics ◽

10.3982/te3430 ◽

2020 ◽

Vol 15 (1) ◽

pp. 361-413 ◽

Cited By ~ 1

Author(s):

Brian Baisa

Keyword(s):

Incentive Compatibility ◽

Dominant Strategy ◽

Impossibility Theorem ◽

Budget Balance ◽

Auction Design ◽

Vickrey Auction ◽

Multiunit Auctions ◽

Private Values ◽

Multidimensional Types ◽

Normal Goods

I study multiunit auction design when bidders have private values, multiunit demands, and non‐quasilinear preferences. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. I give conditions under which we can design a mechanism that retains the Vickrey auction's desirable incentive and efficiency properties: (1) individual rationality, (2) dominant strategy incentive compatibility, and (3) Pareto efficiency. I show that there is a mechanism that retains the desired properties of the Vickrey auction if there are two bidders who have single‐dimensional types. I also present an impossibility theorem that shows that there is no mechanism that satisfies Vickrey's desired properties and weak budget balance when bidders have multidimensional types.

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Randomized Wagering Mechanisms

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33011845 ◽

2019 ◽

Vol 33 ◽

pp. 1845-1852

Author(s):

Yiling Chen ◽

Yang Liu ◽

Juntao Wang

Keyword(s):

Pareto Optimality ◽

Design Space ◽

Incentive Compatibility ◽

Ground Truth ◽

Impossibility Result ◽

Individual Rationality ◽

Budget Balance ◽

Information Elicitation ◽

Recent Extension ◽

Noisy Labels

Wagering mechanisms are one-shot betting mechanisms that elicit agents’ predictions of an event. For deterministic wagering mechanisms, an existing impossibility result has shown incompatibility of some desirable theoretical properties. In particular, Pareto optimality (no profitable side bet before allocation) can not be achieved together with weak incentive compatibility, weak budget balance and individual rationality. In this paper, we expand the design space of wagering mechanisms to allow randomization and ask whether there are randomized wagering mechanisms that can achieve all previously considered desirable properties, including Pareto optimality. We answer this question positively with two classes of randomized wagering mechanisms: i) one simple randomized lottery-type implementation of existing deterministic wagering mechanisms, and ii) another family of randomized wagering mechanisms, named surrogate wagering mechanisms, which are robust to noisy ground truth. Surrogate wagering mechanisms are inspired by an idea of learning with noisy labels (Natarajan et al. 2013) as well as a recent extension of this idea to the information elicitation without verification setting (Liu and Chen 2018). We show that a broad set of randomized wagering mechanisms satisfy all desirable theoretical properties.

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An Axiomatic View of the Parimutuel Consensus Mechanism

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/35 ◽

2018 ◽

Cited By ~ 1

Author(s):

Rupert Freeman ◽

David M. Pennock

Keyword(s):

Pareto Optimality ◽

Incentive Compatibility ◽

The Other ◽

Individual Rationality ◽

Budget Balance ◽

Incentive Compatible

We consider an axiomatic view of the Parimutuel Consensus Mechanism defined by Eisenberg and Gale (1959). The parimutuel consensus mechanism can be interpreted as a parimutuel market for wagering with a proxy that bets optimally on behalf of the agents, depending on the bets of the other agents. We show that the parimutuel consensus mechanism uniquely satisfies the desirable properties of Pareto optimality, individual rationality, budget balance, anonymity, sybilproofness and envy-freeness. While the parimutuel consensus mechanism does violate the key property of incentive compatibility, it is incentive compatible in the limit as the number of agents becomes large. Via simulations on real contest data, we show that violations of incentive compatibility are both rare and only minimally beneficial for the participants. This suggests that the parimutuel consensus mechanism is a reasonable mechanism for eliciting information in practice.

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Operation of a CCHP System Using an Optimal Energy Dispatch Algorithm

ASME 2008 2nd International Conference on Energy Sustainability, Volume 1 ◽

10.1115/es2008-54096 ◽

2008 ◽

Cited By ~ 4

Author(s):

Heejin Cho ◽

Sandra D. Eksioglu ◽

Rogelio Luck ◽

Louay M. Chamra

Keyword(s):

Energy Efficiency ◽

Energy Cost ◽

Network Flow ◽

Flow Model ◽

Energy Requirement ◽

Optimal Operation ◽

Operational Conditions ◽

Optimal Energy ◽

Network Flow Model ◽

The Cost

The Combined Cooling, Heating, and Power (CCHP) systems have been widely recognized as a key alternative for thermal and electric energy generation because of the outstanding energy efficiency, reduced environmental emissions, and relative independence from centralized power grids. Nevertheless, the total energy cost of CCHP systems can be highly dependent on the operation of individual components and load balancing. The latter refers to the process of fulfilling the thermal and electrical demand by partitioning or “balancing” the energy requirement between the available sources of energy supply. The energy cost can be optimized through an energy dispatch algorithm which provides operational/control signals for the optimal operation of the equipment. The algorithm provides optimal solutions on decisions regarding generating power locally or buying power from the grid. This paper presents an initial study on developing an optimal energy dispatch algorithm that minimizes the cost of energy (i.e., cost of electricity from the grid and cost of natural gas into the engine and boiler) based on energy efficiency constrains for each component. A deterministic network flow model of a typical CCHP system is developed as part of the algorithm. The advantage of using a network flow model is that the power flows and efficiency constraints throughout the CCHP components can be readily visualized to facilitate the interpretation of the results. A linear programming formulation of the network flow model is presented. In the algorithm, the inputs include the cost of the electricity and fuel and the constraints include the cooling, heating, and electric load demands and the efficiencies of the CCHP components. This algorithm has been used in simulations of several case studies on the operation of an existing micro-CHP system. Several scenarios with different operational conditions are presented in the paper to demonstrate the economical advantages resulting from optimal operation.

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