Page 121 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1
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ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1 4.4 Equilibrium and its uniqueness mated as follows: In this section we ind the equilibrium and establish its ℎ uniqueness. ≈ ℎ − 2 , (33) + ℎ Theorem 2 In the game Γ( , , ), Nash equilibrium , ≤ , 2 ( , ) is unique. (...) Proposition 4 implies that, for negligible background Then, the Nash equilibrium ( , ) can be approximated as noise at the receivers, the equilibrium strategies of the follows: transmitter and the jammer are proportional to ratio / . 1 Note that, in the SLCC problem solved in [14, 15] for ≈ (Ω , 0) = 1 + 1 + 4 Ω , (39) 0 0 negligible background noise at the receiver, equilibrium 2Ω 0 ∈ ℎ strategies are given in closed form. Proposition 4 also supplies the equilibrium strategies in closed form for the ≈ / for ∈ , (40) MLCC problem.
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Page 121 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1
Basic HTML Version
Table of Contents
View Full Version
Page 121 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1
P. 121
ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1 4.4 Equilibrium and its uniqueness mated as follows: In this section we ind the equilibrium and establish its ℎ uniqueness. ≈ ℎ − 2 , (33) + ℎ Theorem 2 In the game Γ( , , ), Nash equilibrium , ≤ , 2 ( , ) is unique. (...) Proposition 4 implies that, for negligible background Then, the Nash equilibrium ( , ) can be approximated as noise at the receivers, the equilibrium strategies of the follows: transmitter and the jammer are proportional to ratio / . 1 Note that, in the SLCC problem solved in [14, 15] for ≈ (Ω , 0) = 1 + 1 + 4 Ω , (39) 0 0 negligible background noise at the receiver, equilibrium 2Ω 0 ∈ ℎ strategies are given in closed form. Proposition 4 also supplies the equilibrium strategies in closed form for the ≈ / for ∈ , (40) MLCC problem.
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Score: 1245695.5
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SOLUTION OF THE GAME In this section we ind equilibrium strategies in closed − form using a constructive approach via inding all solu‑ ℎ ( , ) = , (7) tions of the best response equations. (...) Thus, (13) correspondingly). ( , ) is the payoff to the transmitter, while for the jam‑ Proposition 1 Each equilibrium ( , ) of the game mer ( , ) is the cost function. (...) We look for the Nash equilibrium [2]. Re‑ call that ( , ) is a Nash equilibrium in a zero‑sum game ∗ ∗ = ( , ) if and only if the following inequalities hold: 2 2 ⎧ , ≤ , ( , ) ≤ ( , ) ≤ ( , ) for all ( , ) ∈ × . ⎪ ℎ ℎ ∗ ∗ ∗ ∗ (9) ⎪ ℎ Let ≜ 1 + 1 + 4 + ⎨ ℎ 2 2 ( , ) = ln( ( , )) ⎪ ℎ , ℎ > ⎪ 2 + ℎ ⎩ = ln − . (10) ℎ + ℎ (14) ∈ ∈ and Since ln(⋅) is an increasing function, the problem to ind the Nash equilibrium with payoff ( , ) to the transmit‑ = ( , ) ter is equivalent to inding the Nash equilibrium with pay‑ off ( , ) to the transmitter, i.e., such ( , ) that ℎ ∗ ∗ ⎢ ⎥ ⎢ 1 + 1 + 4 ℎ + ⎥ ( , ) ≤ ( , ) ≤ ( , ) for all ( , ) ∈ × . ⎢ 1 ℎ ⎥ ∗ ∗ ∗ ∗ (11) ≜ ⎢ − ℎ ⎥ , (15) Denote this game by Γ = Γ( , , ). ⎢ 2 + ⎥ Note that the transmitter’s equilibrium strategy also re‑ ⎣ ⎦ + lects the most fair power resource allocation to main‑ tain communication with all the receiversunder the worst where ∈ and ⌊ ⌋ ≜ max{ , 0}.
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Considerations and challenges when choosing a Partial Equilibrium modelling (PE) and Computable General Equilibrium modelling (CGE) for global long-term analysis of food and agriculture | Global Perspectives Studies | Food and Agriculture Organization of the United Nations
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Considerations and challenges when choosing a Partial Equilibrium modelling (PE) and Computable General Equilibrium modelling (CGE) for global long-term analysis of food and agriculture
Year: 2017
Presentation by Marc Müller, Aikaterini Kavallari, Dominik Wisser and Lorenzo G. (...) This presentation outlines the challenges in using Partial Equilibrium (PE) and Computable General Equilibrium (CGE) models for simulating future scenarios in long-term foresight exercises. (...) Available in:
http://www.fao.org/3/CA2252EN/ca2252en.pdf
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Foresight methods , General equilibrium modelling , Partial equilibrium modelling
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Score: 1228771.5
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https://www.fao.org/global-per...resources/detail/en/c/1161760/
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SOLUTION OF THE GAME In this section we ind equilibrium strategies in closed − form using a constructive approach via inding all solu‑ ℎ ( , ) = , (7) tions of the best response equations. (...) Thus, (13) correspondingly). ( , ) is the payoff to the transmitter, while for the jam‑ Proposition 1 Each equilibrium ( , ) of the game mer ( , ) is the cost function. (...) We look for the Nash equilibrium [2]. Re‑ call that ( , ) is a Nash equilibrium in a zero‑sum game ∗ ∗ = ( , ) if and only if the following inequalities hold: 2 2 ⎧ , ≤ , ( , ) ≤ ( , ) ≤ ( , ) for all ( , ) ∈ × . ⎪ ℎ ℎ ∗ ∗ ∗ ∗ (9) ⎪ ℎ Let ≜ 1 + 1 + 4 + ⎨ ℎ 2 2 ( , ) = ln( ( , )) ⎪ ℎ , ℎ > ⎪ 2 + ℎ ⎩ = ln − . (10) ℎ + ℎ (14) ∈ ∈ and Since ln(⋅) is an increasing function, the problem to ind the Nash equilibrium with payoff ( , ) to the transmit‑ = ( , ) ter is equivalent to inding the Nash equilibrium with pay‑ off ( , ) to the transmitter, i.e., such ( , ) that ℎ ∗ ∗ ⎢ ⎥ ⎢ 1 + 1 + 4 ℎ + ⎥ ( , ) ≤ ( , ) ≤ ( , ) for all ( , ) ∈ × . ⎢ 1 ℎ ⎥ ∗ ∗ ∗ ∗ (11) ≜ ⎢ − ℎ ⎥ , (15) Denote this game by Γ = Γ( , , ). ⎢ 2 + ⎥ Note that the transmitter’s equilibrium strategy also re‑ ⎣ ⎦ + lects the most fair power resource allocation to main‑ tain communication with all the receiversunder the worst where ∈ and ⌊ ⌋ ≜ max{ , 0}.
Language:English
Score: 1228020.5
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It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
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Score: 1217114.5
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https://shop.un.org/series/review-maritime-transport
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It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
Language:English
Score: 1217114.5
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https://shop.un.org/es/taxonomy/term/2351
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It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
Language:English
Score: 1217114.5
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https://shop.un.org/fr/taxonomy/term/2351
Data Source: un
It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
Language:English
Score: 1217114.5
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https://shop.un.org/ru/taxonomy/term/2351
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It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
(...) It takes a look at supply/demand equilibrium in containerized shipping, shipbuilding and ship scrapping, the development of ports, privatization and freight markets among other...
Language:English
Score: 1217114.5
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https://shop.un.org/ar/taxonomy/term/2351
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