Full Substitutability in Trading Networks

Hatfield, John William; Kominers, Scott Duke; Nichifor, Alexandru; Ostrovsky, Michael; Westkamp, Alexander

doi:10.1145/2764468.2764472

Cited by 11 publications

(10 citation statements)

References 4 publications

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“…At each iteration of the price-adjustment process for the forward and real-time P2P energy markets, each agent is offered a set of contracts by its neighbours in the contract network. Since the agent preferences satisfy full substitutability, the agent utility functions exhibit the single improvement property [39]. The single improvement property states that an agent with a suboptimal bundle of contracts can be made better off by taking one of the following options: 1) Accepting a new upstream or downstream contract.…”

Section: Contract Selectionmentioning

confidence: 99%

“…In this appendix, it is shown that the agent preferences from Section III satisfy full substitutability. The following definition for an agent's indirect utility function, from [39], is needed. The preferences of an agent are fully substitutable, if and only if they induce a submodular indirect utility function V mi .…”

Section: Appendixmentioning

confidence: 99%

“…The preferences of an agent are fully substitutable, if and only if they induce a submodular indirect utility function V mi . To show V mi is submodular, it is enough to show that for any two trades φ, ψ ∈ Ω mi and prices p Ω mi ∈ R |Ωmi\{ψ,φ}| , p h φ ≥ p φ , p h ψ ≥ p ψ [39],…”

Section: Appendixmentioning

confidence: 99%

See 2 more Smart Citations

Bilateral Contract Networks for Peer-to-Peer Energy Trading

Morstyn

Teytelboym

McCulloch

2019

IEEE Trans. Smart Grid

428

265

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This paper proposes bilateral contract networks as a new scalable market design for peer-to-peer energy trading. Coordinating small-scale distributed energy resources to shape overall demand could offer significant value to power systems, by alleviating the need for investments in upstream generation and transmission infrastructure, increasing network efficiency and increasing energy security. However, incentivising coordination between the owners of large-scale and smallscale energy resources at different levels of the power system remains an unsolved challenge. This paper introduces real-time and forward markets, consisting of energy contracts offered between generators with fuel-based sources, suppliers acting as intermediaries and consumers with inflexible loads, timecoupled flexible loads and/or renewable sources. For each type of agent, utility-maximising preferences for real-time contracts and forward contracts are derived. It is shown that these preferences satisfy full substitutability conditions essential for establishing the existence of a stable outcome-an agreed network of contracts specifying energy trades and prices, which agents do not wish to mutually deviate from. Important characteristics of energy trading are incorporated, including upstream-downstream energy balance and forward market uncertainty. Full substitutability ensures a distributed price-adjustment process can be used, which only requires local agent decisions and agent-to-agent communication between trading partners.

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Section: Contract Selectionmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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Bilateral Contract Networks for Peer-to-Peer Energy Trading

Morstyn

Teytelboym

McCulloch

2019

IEEE Trans. Smart Grid

428

265

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show abstract

“…Hatfield and Milgrom [18] argue that most important examples of valuation functions arising in matching markets belong to the class of gross substitutes. Gross substitutes have been used to guarantee the convergence of salary adjustment processes in the job market [21], to guarantee the existence of stable matchings in a variety of settings [25,43], to show the stability of trading networks [17,20], to design combinatorial auctions [1,30] and even to analyze settings with complementarities [16,46].…”

Section: Walrasian Equilibrium For Gross Substitutes Inõ(nt Ad + N 3 )mentioning

confidence: 99%

Computing Walrasian equilibria: fast algorithms and structural properties

Leme

Wong

2018

Math. Program.

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We present the first polynomial time algorithm for computing Walrasian equilibrium in an economy with indivisible goods and general buyer valuations having only access to an aggregate demand oracle, i.e., an oracle that given prices on all goods, returns the aggregated demand over the entire population of buyers. For the important special case of gross substitute valuations, our algorithm queries the aggregate demand oracle O(n) times and takes O(n 3 ) time, where n is the number of goods and the O(·) notation denotes an asymptotic bound up to polylogarithmic factors. Both algorithms are randomized. At the heart of our solution is a method for exactly minimizing certain convex functions which cannot be evaluated but for which the subgradients can be computed. We also give the fastest known algorithm for computing Walrasian equilibrium for gross substitute valuations in the value oracle model. Our algorithm has running time O((mn + n 3 )T V ) where T V is the cost of querying the value oracle.A key technical ingredient is to regularize a convex programming formulation of the problem in a way that subgradients are cheap to compute. En route, we give necessary and sufficient conditions for the existence of robust Walrasian prices, i.e., prices for which each agent has a unique demanded bundle and the demanded bundles clear the market. When such prices exist, the market can be perfectly coordinated by solely using prices. Mathematics Subject Classification 90C25 (Convex programming) · 91B26 (Market models)A shorter conference version of this paper appeared in the ACM-SIAM Symposium on Discrete Algorithms (SODA17) and has been posted on arXiv (https://arxiv.org/abs/1511.04032). The conference version is attached to this submission for the records.

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“…Hatfield and Milgrom [HM05] argue that most important examples of valuation functions arising in matching markets belong to the class of gross substitutes. Gross substitutes were used to guarantee the convergence of salary adjustment processes in the job market [KC82], to guarantee the existence of stable matchings in many settings [Rot84,KTY14], to show the stability of trading networks [HKN + 15], to design combinatorial auctions [AM02,MSY13] and even to analyze settings with complementarities [SY06,HK15].…”

Section: From Telescopes To Augmenting Lensesmentioning

confidence: 99%

Computing Walrasian Equilibria: Fast Algorithms and Structural Properties

Leme

Wong

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We present the first polynomial time algorithm for computing Walrasian equilibrium in an economy with indivisible goods and general buyer valuations having only access to an aggregate demand oracle, i.e., an oracle that given prices on all goods, returns the aggregated demand over the entire population of buyers. For the important special case of gross substitute valuations, our algorithm queries the aggregate demand oracle O(n) times and takes O(n 3 ) time, where n is the number of goods. At the heart of our solution is a method for exactly minimizing certain convex functions which cannot be evaluated but for which the subgradients can be computed.We also give the fastest known algorithm for computing Walrasian equilibrium for gross substitute valuations in the value oracle model. Our algorithm has running time O((mn + n 3 )T V ) where T V is the cost of querying the value oracle. A key technical ingredient is to regularize a convex programming formulation of the problem in a way that subgradients are cheap to compute. En route, we give necessary and sufficient conditions for the existence of robust Walrasian prices, i.e., prices for which each agent has a unique demanded bundle and the demanded bundles clear the market. When such prices exist, the market can be perfectly coordinated by solely using prices.

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Full Substitutability in Trading Networks

Cited by 11 publications

References 4 publications

Bilateral Contract Networks for Peer-to-Peer Energy Trading

Bilateral Contract Networks for Peer-to-Peer Energy Trading

Computing Walrasian equilibria: fast algorithms and structural properties

Computing Walrasian Equilibria: Fast Algorithms and Structural Properties

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