Pricing under information asymmetry for a large population of users

Shen, Hongxia; Başar, Tamer

doi:10.1007/s11235-010-9306-2

Cited by 14 publications

(7 citation statements)

References 13 publications

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“…This work represents a small step towards establishing a general framework of understanding incomplete information in dynamic spectrum sharing. As the next step plan, we will consider more incomplete information structures: (1) the PU does not know the distribution of SUs' types, and (2) each SU knows other SUs' types but PU does not know (a similar setting with a different application has been studied in [35]). We also want to understand how to design contracts in a market with multiple PUs and multiple SUs.…”

Section: Discussionmentioning

confidence: 99%

Contract-based cooperative spectrum sharing

Duan

Gao

Huang

2011

2011 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN)

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Providing proper economic incentives is essential for the success of dynamic spectrum sharing. Cooperative spectrum sharing is one effective way to achieve this goal. In cooperative spectrum sharing, secondary users (SUs) relay traffics for primary users (PUs), in exchange for dedicated transmission time for the SUs' own communication needs. In this paper, we study the cooperative spectrum sharing under incomplete information, where SUs' types (capturing their heterogeneity in relay channel gains and evaluations of power consumptions) are private information and not known by PUs. Inspired by the contract theory, we model the network as a labor market. The single PU is the employer who offers a contract to the SUs. The contract consists of a set of contract items representing combinations of spectrum accessing time (i.e., reward) and relaying power (i.e., contribution). The SUs are employees, and each of them selects the best contract item to maximize his payoff. We study the optimal contract design for both weak and strong incomplete information scenarios. First, we provide necessary and sufficient conditions for feasible contracts in both scenarios. In the weak incomplete information scenario, we further derive the optimal contract that achieves the same maximum PU's utility as in the complete information benchmark. In the strong incomplete information scenario, we propose a Decompose-and-Compare algorithm that achieves a close-to-optimal contract. We future show that the PU's average utility loss due to the suboptimal algorithm and the strong incomplete information are both relatively small (less than 2% and 1.3%, respectively, in our numerical results with two SU types).

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Section: Discussionmentioning

confidence: 99%

Contract-based cooperative spectrum sharing

Duan

Gao

Huang

2011

2011 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN)

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“…Price formation has been studied in several contexts and with different techniques. In [37] and [7], Stackelberg games to maximize the producer's revenue were used. A Cournot model was introduced in [16], which specifies the price dynamics with noise from a Brownian motion and a jump process.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning architectures for price formation models

Gomes¹,

Gutiérrez²,

Laurière³

2022

Preprint

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Here, we study machine learning (ML) architectures to solve a mean-field games (MFGs) system arising in price formation models. We formulate a training process that relies on a min-max characterization of the optimal control and price variables. Our main theoretical contribution is the development of a posteriori estimates as a tool to evaluate the convergence of the training process. We illustrate our results with numerical experiments for a linear-quadratic model.

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“…In [4], the price equilibrium is obtained for a finite number of agents who optimally control their production and trading rates in order to satisfy a demand subjected to common noise. Stackelberg games for price formation under revenue optimization were proposed in [13] and [40], and Cournot models in [21]. A MFG of optimal switching was presented in [5] to model the transition to renewable energies.…”

Section: Introductionmentioning

confidence: 99%

A Variational Approach For Price Formation Models In One Dimension

Ashrafyan¹,

Bakaryan²,

Gomes³

et al. 2022

Preprint

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In this paper, we study a class of first-order mean-field games (MFGs) that model price formation. Using Poincaré Lemma, we eliminate one of the equations and obtain a variational problem for a single function. This variational problem offers an alternative approach for the numerical solution of the original MFGs system. We show a correspondence between solutions of the MFGs system and the variational problem. Moreover, we address the existence of solutions for the variational problem using the direct method in the calculus of variations. We end the paper with numerical results for a linear-quadratic model.

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Pricing under information asymmetry for a large population of users

Cited by 14 publications

References 13 publications

Contract-based cooperative spectrum sharing

Contract-based cooperative spectrum sharing

Machine Learning architectures for price formation models

A Variational Approach For Price Formation Models In One Dimension

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