Como ficar milionário, só que ao contrário!Vinícius Hax
Apresentação feita no IV Fórum do Engenheiro Empreendedor. Apresenta alguns erros que cometi e desafios que enfrentei nos meus empreendimentos. Ao final deixo algumas dicas de como começar a empreender.
Este documento describe las características de un software de hoja de cálculo llamado CALC. CALC permite crear tablas y calcular y analizar datos. Algunas de sus características incluyen la capacidad de aplicar bordes a múltiples selecciones de celdas, mejoras en la función de autorrelleno, preguntar al usuario si desea ampliar la selección al ordenar datos, y permitir pegar celdas combinadas sin errores.
This document provides a list of common cardiac medications organized into categories including beta blockers, ACE inhibitors, angiotensin receptor blockers, calcium channel blockers, antiarrhythmics, antiplatelet agents, antilipids, diuretics, miscellaneous drugs, direct thrombin inhibitors, anti-platelets, and nitrates. Each medication is listed with its brand name and generic name.
The document provides information about 9 free downloadable products/guides related to domains/hosting, installing WordPress offline, Google AdSense, creating an Amazon store on Facebook, paid reviews, WordPress secrets, automatic Amazon stores, YouTube marketing, and becoming an eBay seller. It also provides the download links, passwords, and number of downloads for each product. At the end, it provides login credentials for the user to access membership pages on the site.
Como ficar milionário, só que ao contrário!Vinícius Hax
Apresentação feita no IV Fórum do Engenheiro Empreendedor. Apresenta alguns erros que cometi e desafios que enfrentei nos meus empreendimentos. Ao final deixo algumas dicas de como começar a empreender.
Este documento describe las características de un software de hoja de cálculo llamado CALC. CALC permite crear tablas y calcular y analizar datos. Algunas de sus características incluyen la capacidad de aplicar bordes a múltiples selecciones de celdas, mejoras en la función de autorrelleno, preguntar al usuario si desea ampliar la selección al ordenar datos, y permitir pegar celdas combinadas sin errores.
This document provides a list of common cardiac medications organized into categories including beta blockers, ACE inhibitors, angiotensin receptor blockers, calcium channel blockers, antiarrhythmics, antiplatelet agents, antilipids, diuretics, miscellaneous drugs, direct thrombin inhibitors, anti-platelets, and nitrates. Each medication is listed with its brand name and generic name.
The document provides information about 9 free downloadable products/guides related to domains/hosting, installing WordPress offline, Google AdSense, creating an Amazon store on Facebook, paid reviews, WordPress secrets, automatic Amazon stores, YouTube marketing, and becoming an eBay seller. It also provides the download links, passwords, and number of downloads for each product. At the end, it provides login credentials for the user to access membership pages on the site.
This document provides instructions for connecting an RFID reader to an Arduino board. The Arduino's transmit pin connects to the RFID reader's receive pin, grounds are shared, digital pin 2 on the Arduino is connected to the RFID reader's enable pin to power it, and the RFID reader's power input connects to the Arduino's +5 volt supply.
This document appears to be a practice exam containing math problems. It includes a table with 10 rows listing Peruvian currency amounts from 1 to 10 soles and their corresponding decimal values. The document also contains phrases in Spanish encouraging being successful and achieving success.
La Citta' invisibile; Le informazioni digitali nei contesti urbaniPaolo Nesi
Incontri con la città. Leggere il presente per comprendere il futuro L'Ateneo fiorentino, nel quadro delle iniziative culturali e divulgative volte a rinsaldare il legame con il territorio, organizza un ciclo di incontri aperti al pubblico, in cui docenti e ricercatori discutono su temi d'attualità legati alle loro competenze disciplinari. In programma la presentazione di un argomento di interesse per i fiorentini, svolta da un docente affiancato da un ricercatore, che dialoga con il pubblico, stimolandone il dibattito e il confronto di idee Universita' degli Studi di Firenze, Aula Magna, Piazza S. Marco 4, Firenze, 11 Gennaio 2015. La città invisibile. Le informazioni digitali nei contesti urbani". Relatore Paolo Nesi ordinario di Sistemi di elaborazione delle informazioni. Introduce e coordina Maria Grazia Giovannini. Paolo Nesi dirige il DISIT (Distributed Systems and Internet Technologies) Lab e si occupa di modellazione della conoscenza, sistemi distribuiti, smart city, elaborazione semantica, supporto alle decisioni. Al riguardo ha coordinato numerosi progetti di ricerca internazionali. Le città stanno attraendo un numero crescente di cittadini, offrendo maggiori opportunità e servizi. Gli incrementi di efficienza e della qualità della vita sono sempre più spesso abilitati da soluzioni che usano informazioni digitali sui: servizi pubblici, comportamenti dei cittadini, sensori ambientali ed energetici, mezzi pubblici, dati statistici, fattori di rischio, etc. Le soluzioni che permettono lo sfruttamento intelligente di queste informazioni rientrano nel quadro delle Smart City. Comprendere, è il primo passo per usare al meglio le opportunità delle nuove tecnologie superando le problematiche per vivere nelle future Smart City!
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Mobiilioppimisympäristön kehittäminen ammatillisessa oppilaitoksessa vaatii monenlaista pohjatyötä ja suunnittelua. Tämä esitys antaa vinkkejä asioihin, joita kannattaa miettiä, ennen mobiililaitteiden käyttöönottoa ja mobiilioppimisen aloittamista.
El documento describe la cultura y el arte del Imperio Bizantino. El Imperio Bizantino fue el Estado sucesor del Imperio Romano ubicado en el Mediterráneo oriental, con capital en Constantinopla. La cultura bizantina se caracterizó por el lujo y la diversidad cultural con influencias griegas, romanas, orientales y cristianas. La arquitectura bizantina incluye estilos como la basílica de Santa Sofía, y usó plantas de cruz griega. Las formas de arte bizantino incluyeron mosa
Este documento contiene cuatro secciones breves que describen varias fotografías tomadas en diferentes lugares de Argentina, incluyendo la Esma, la basílica de Luján, Mar del Plata y el centro de Buenos Aires, mostrando estatuas, iglesias, esculturas y edificios históricos.
Incredible Paper Sculptures- By Carlos Meiramaditabalnco
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise boosts blood flow, releases endorphins, and promotes changes in the brain which help enhance one's emotional well-being and mental clarity.
Este documento presenta una guía didáctica sobre el uso de herramientas de la Web 2.0 en la educación. Explica qué es la Web 2.0 e introduce varias herramientas como blogs, wikis, SlideShare y Moodle. Detalla los propósitos de cada herramienta y cómo pueden usarse para mejorar la enseñanza y el aprendizaje de manera colaborativa y centrada en el estudiante. El objetivo general es conocer estas herramientas para que los docentes puedan aplicar nuevas estrategias acordes a la te
La Teoría General del Control es esencial para la Cibernética porque ambas disciplinas se ocupan del estudio de los fenómenos de control y comunicación. La Teoría General del Control provee los fundamentos matemáticos para el diseño y construcción de máquinas y sistemas de inteligencia artificial, al identificar los mecanismos de control en humanos, animales y máquinas. Wiener redefinió la Cibernética como el estudio analítico de la estructura de las comunicaciones en diferentes sistemas, entendiendo que existe un "isom
This document provides instructions for connecting an RFID reader to an Arduino board. The Arduino's transmit pin connects to the RFID reader's receive pin, grounds are shared, digital pin 2 on the Arduino is connected to the RFID reader's enable pin to power it, and the RFID reader's power input connects to the Arduino's +5 volt supply.
This document appears to be a practice exam containing math problems. It includes a table with 10 rows listing Peruvian currency amounts from 1 to 10 soles and their corresponding decimal values. The document also contains phrases in Spanish encouraging being successful and achieving success.
La Citta' invisibile; Le informazioni digitali nei contesti urbaniPaolo Nesi
Incontri con la città. Leggere il presente per comprendere il futuro L'Ateneo fiorentino, nel quadro delle iniziative culturali e divulgative volte a rinsaldare il legame con il territorio, organizza un ciclo di incontri aperti al pubblico, in cui docenti e ricercatori discutono su temi d'attualità legati alle loro competenze disciplinari. In programma la presentazione di un argomento di interesse per i fiorentini, svolta da un docente affiancato da un ricercatore, che dialoga con il pubblico, stimolandone il dibattito e il confronto di idee Universita' degli Studi di Firenze, Aula Magna, Piazza S. Marco 4, Firenze, 11 Gennaio 2015. La città invisibile. Le informazioni digitali nei contesti urbani". Relatore Paolo Nesi ordinario di Sistemi di elaborazione delle informazioni. Introduce e coordina Maria Grazia Giovannini. Paolo Nesi dirige il DISIT (Distributed Systems and Internet Technologies) Lab e si occupa di modellazione della conoscenza, sistemi distribuiti, smart city, elaborazione semantica, supporto alle decisioni. Al riguardo ha coordinato numerosi progetti di ricerca internazionali. Le città stanno attraendo un numero crescente di cittadini, offrendo maggiori opportunità e servizi. Gli incrementi di efficienza e della qualità della vita sono sempre più spesso abilitati da soluzioni che usano informazioni digitali sui: servizi pubblici, comportamenti dei cittadini, sensori ambientali ed energetici, mezzi pubblici, dati statistici, fattori di rischio, etc. Le soluzioni che permettono lo sfruttamento intelligente di queste informazioni rientrano nel quadro delle Smart City. Comprendere, è il primo passo per usare al meglio le opportunità delle nuove tecnologie superando le problematiche per vivere nelle future Smart City!
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Mobiilioppimisympäristön kehittäminen ammatillisessa oppilaitoksessa vaatii monenlaista pohjatyötä ja suunnittelua. Tämä esitys antaa vinkkejä asioihin, joita kannattaa miettiä, ennen mobiililaitteiden käyttöönottoa ja mobiilioppimisen aloittamista.
El documento describe la cultura y el arte del Imperio Bizantino. El Imperio Bizantino fue el Estado sucesor del Imperio Romano ubicado en el Mediterráneo oriental, con capital en Constantinopla. La cultura bizantina se caracterizó por el lujo y la diversidad cultural con influencias griegas, romanas, orientales y cristianas. La arquitectura bizantina incluye estilos como la basílica de Santa Sofía, y usó plantas de cruz griega. Las formas de arte bizantino incluyeron mosa
Este documento contiene cuatro secciones breves que describen varias fotografías tomadas en diferentes lugares de Argentina, incluyendo la Esma, la basílica de Luján, Mar del Plata y el centro de Buenos Aires, mostrando estatuas, iglesias, esculturas y edificios históricos.
Incredible Paper Sculptures- By Carlos Meiramaditabalnco
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise boosts blood flow, releases endorphins, and promotes changes in the brain which help enhance one's emotional well-being and mental clarity.
Este documento presenta una guía didáctica sobre el uso de herramientas de la Web 2.0 en la educación. Explica qué es la Web 2.0 e introduce varias herramientas como blogs, wikis, SlideShare y Moodle. Detalla los propósitos de cada herramienta y cómo pueden usarse para mejorar la enseñanza y el aprendizaje de manera colaborativa y centrada en el estudiante. El objetivo general es conocer estas herramientas para que los docentes puedan aplicar nuevas estrategias acordes a la te
La Teoría General del Control es esencial para la Cibernética porque ambas disciplinas se ocupan del estudio de los fenómenos de control y comunicación. La Teoría General del Control provee los fundamentos matemáticos para el diseño y construcción de máquinas y sistemas de inteligencia artificial, al identificar los mecanismos de control en humanos, animales y máquinas. Wiener redefinió la Cibernética como el estudio analítico de la estructura de las comunicaciones en diferentes sistemas, entendiendo que existe un "isom
The document discusses concurrency and synchronization in distributed computing. It provides an overview of Petr Kuznetsov's research at Telecom ParisTech, which includes algorithms and models for distributed systems. Some key points discussed are:
- Concurrency is important due to multi-core processors and distributed systems being everywhere. However, synchronization between concurrent processes introduces challenges.
- Common synchronization problems include mutual exclusion, readers-writers problems, and producer-consumer problems. Tools for synchronization include semaphores, transactional memory, and non-blocking algorithms.
- Characterizing distributed computing models and determining what problems can be solved in a given model is an important area of research, with implications for distributed system design.
The document discusses weakly supervised learning from video and images using convolutional neural networks. It describes using scripts as weak supervision for learning actions from movies without explicit labeling. Methods are presented for jointly learning actors and actions from scripts, and for action learning with ordering constraints. The use of CNNs for object and action recognition in images is also summarized, including work on training CNNs using only image-level labels without bounding boxes.
This document discusses common C++ bugs and tools to find them. It describes various types of memory access bugs like buffer overflows on the stack, heap, and globals that can lead to crashes or security vulnerabilities. Threading bugs like data races, deadlocks, and race conditions on object destruction are also covered. Other undefined behaviors like initialization order issues, lack of sequence points, and integer overflows are explained. The document provides examples of each type of bug and emphasizes that undefined behavior does not guarantee a predictable result. It concludes with a quiz to find bugs in a code sample and links to additional reading materials.
AddressSanitizer, ThreadSanitizer, and MemorySanitizer are compiler-based tools that detect bugs like buffer overflows, data races, and uninitialized memory reads in C/C++ programs. AddressSanitizer instruments loads and stores to detect out-of-bounds memory accesses. ThreadSanitizer intercepts synchronization calls to detect data races between threads. MemorySanitizer tracks initialized and uninitialized memory using shadow memory to find uses of uninitialized values. The tools have found thousands of bugs with low overhead. Future work includes supporting more platforms and languages and detecting additional bug classes.
This document discusses common C++ bugs and tools to find them. It describes various types of memory access bugs like buffer overflows on the stack, heap, and globals that can lead to crashes or security vulnerabilities. Threading bugs like data races, deadlocks, and race conditions on object destruction are also covered. Other undefined behaviors like initialization order issues, lack of sequence points, and integer overflows are explained. The document provides examples of each type of bug and quizzes the reader to find bugs in a code sample. It recommends resources for further reading on debugging techniques and thread sanitizers that can detect races and data races.
This document provides examples and snippets of code for MapReduce, Pig, Hive, Spark, Shark, and Disco frameworks. It also includes two sections of references for related papers and Disco documentation. The examples demonstrate basic MapReduce jobs with drivers, mappers, and reducers in Java, Pig and Hive queries, Spark and Shark table operations, and a Disco MapReduce job.
13. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Âûïëàòà â àóêöèîíå ñ ðåçåðâíîé öåíîé
r
Òåïåðü òîòD êòî ñòàâèò D îæèäàåò çàïëàòèòü ïðîñòî rG (r )
r
@ìåíüøå íå áûâàåòAF
r
À òîòD êòî ñòàâèò áîëüøå D îæèäàåò çàïëàòèòü
x
m(x , r ) = rG (r ) + yg (y )dy .
r
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
14. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Àóêöèîí ïåðâîé öåíû ñ ðåçåðâíîé öåíîé
Íåìíîæêî îòâëå÷¼ìñÿ è åù¼ ðàç ïðîèëëþñòðèðóåì
ïðèíöèï ýêâèâàëåíòíîñòè äîõîäíîñòèF
 àóêöèîíå ïåðâîé öåíû àíàëèç áóäåò òî÷íî òàêèì æåD êàê
ðàíüøåD òîëüêî òåïåðü ó÷àñòíèê ñ öåííîñòüþ < âîîáùå x r
íå áóäåò ó÷àñòâîâàòüD è îñòàíåòñÿ
x
β( ) = E [m—x{ Y1, r }|Y1 < x ]
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
15. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Àóêöèîí ïåðâîé öåíû ñ ðåçåðâíîé öåíîé
 àóêöèîíå ïåðâîé öåíû àíàëèç áóäåò òî÷íî òàêèì æåD êàê
ðàíüøåD òîëüêî òåïåðü ó÷àñòíèê ñ öåííîñòüþ < âîîáùå x r
íå áóäåò ó÷àñòâîâàòüD è îñòàíåòñÿ
x
β( ) = E [m—x{ Y1, r }|Y1 < x ] =
=r
G (r ) + I x yg (y )dy
G (x ) G (x ) r
Gx
Óìíîæàÿ íà ( )D ïîëó÷èì òó æå ñàìóþ äîõîäíîñòü @òó æå
âûïëàòó äëÿ àãåíòà AF i
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
16. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Äîõîäíîñòü
ÍîD õîòü äîõîäíîñòü è îäèíàêîâàÿ ó äâóõ àóêöèîíîâD ìîæåò
áûòüD îíà èçìåíèëàñü ïî ñðàâíåíèþ ñ àóêöèîíàìè áåç
ðåçåðâíîé öåíûc
ω
E [m(X , r )] = m(x , r )f (x )dx =
r
ω x
= rG (r ) + yg (y )dy f (x )dx =
r r
ω
= rG (r )(I − F (r )) + y (I − F (y ))g (y )dy .
r
@ìû ìåíÿëè ïîðÿäîê èíòåãðèðîâàíèÿ âî âòîðîì
ñëàãàåìîìAF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
17. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Êàê ìàêñèìèçèðîâàòü?
Êàê ïðîäàâöó ìàêñèìèçèðîâàòü äîõîäíîñòüc
x
Îáîçíà÷èì ÷åðåç 0 åãî ñîáñòâåííóþ öåííîñòü îáúåêòà @âî
ñêîëüêî îí îöåíèâàåò òîò ôàêòD ÷òî îáúåêò îñòàíåòñÿ ó
íåãîAF
Òîãäà åãî îáùèé äîõîä îò ðåçåðâíîé öåíû r ïîëó÷àåòñÿ êàê
Π0 = N E [m(X , r )] + F (r )N x0.
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
18. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Êàê ìàêñèìèçèðîâàòü?
Π0 = N E [m(X , r )] + F (r )N x0.
Íàäî ìàêñèìèçèðîâàòüY ïðîäèôôåðåíöèðóåì ïî X r
d Π0 = N (I − F (r ) − rf (r ))G (r ) + NG (r )f (r )x .
dr 0
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
19. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ôóíêöèÿ ðèñêà
 ñòàòèñòèêå åñòü òàêàÿ ôóíêöèÿ ðèñêàX
λ(x ) =
f (x ) .
I − F (x )
Îíà ïîêàçûâàåòD ãðóáî ãîâîðÿD ìãíîâåííóþ âåðîÿòíîñòü
¾ñìåðòè¿F
F
Åñëè " âåðîÿòíîñòü òîãîD ÷òî ñîáûòèå ñëó÷èòñÿ äî
x x
âðåìåíè D òî λ( ) " ìãíîâåííàÿ âåðîÿòíîñòü òîãîD ÷òî
ñîáûòèå ñëó÷èòñÿ âî âðåìÿ x ïðè óñëîâèè
D ÷òî ðàíüøå íå
ñëó÷èëîñüF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
20. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ôóíêöèÿ ðèñêà
Ïðè x → ω λ(x ) → ∞F
Ìîæíî âûðàçèòü è íàîáîðîòX
x d
−λ( ) =
dx ln(I − F (x )), çíà÷èò,
F (x ) = I − e − 0 λ(t )dt .
x
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
21. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Êàê ìàêñèìèçèðîâàòü?
 òåðìèíàõ ôóíêöèè ðèñêà ïîëó÷àåòñÿ
d Π0 = N (I − (r − x )λ(r ))(I − F (r ))G (r ).
dr 0
ÒFåF ïðè x0 > H ddr 0 â x0 ïîëîæèòåëüíàD òFåF ïðîäàâöó
Π
âûãîäíî óñòàíîâèòü ðåçåðâíóþ öåíó r > x0 F
Ïðè x0 = H òîæå âûãîäíî @ïðîâåðüòåAF Èíà÷å ãîâîðÿD
ðåçåðâíàÿ öåíà äîëæíà áûòü âûøå öåííîñòè ïðîäóêòà äëÿ
ïðîäàâöàF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
22. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Êàê ìàêñèìèçèðîâàòü?
d Π0 = N (I − (r − x )λ(r ))(I − F (r ))G (r ).
dr 0
À ìàêñèìóì ïîëó÷èòñÿD åñëè
r x0)λ(r ) = I,
( − èëè r ∗ − λ(I∗) = x0.
r
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
23. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ïðèìåð
Ïîäñ÷èòàåì îïòèìàëüíóþ ðåçåðâíóþ öåíó äëÿ
ðàâíîìåðíîãî ðàñïðåäåëåíèÿ öåííîñòåé àãåíòîâ íà [H, I]F
Íóæíî íàéòè îæèäàåìûé äîõîä ó ïðîäàâöà â îáîèõ
ñëó÷àÿõF
ÂîEïåðâûõD ïîñêîëüêó öåííîñòè ðàâíîìåðíî ðàñïðåäåëåíû
íà [H, I]D
Fx
( )= , x fx
( ) = I.
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
24. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ïðèìåð
Ýòî çíà÷èòD ÷òî
x f (x ) = I .
I − F (x ) I−x
λ( ) =
Ïîäñ÷èòàåì îïòèìàëüíóþ ðåçåðâíóþ öåíó r ∗X
x0 = r ∗ − λ(I∗) = Pr ∗ − I.
r
Ïóñòü x0 = HD òîãäà r ∗ = 1 " èñêîìàÿ ðåçåðâíàÿ öåíàF
2
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
25. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ïðèìåð
Íàéä¼ì òåïåðü îæèäàåìûé äîõîä ïðîäàâöàX
1
Π0 = NrG (r ) Fr
I− ( ) + y F y g (y )dy + F (r )N x0.
I− ( )
r
Ïîñêîëüêó G (x ) = x N D à çíà÷èòD g (x ) = Nx N −1D
N2 Nr N +1 − PNr N +2 .
(N + I)(N + P) N +I N +P
Π0 = +
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
26. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ïðèìåð
ÑëåäîâàòåëüíîD îæèäàåìûé äîõîä ïðîäàâöà áåç ðåçåðâíîé
r
öåíû @ = HA ðàâåí (N +1N N +2) F
2
)(
À ïðè ðîñòå ðåçåðâíîé öåíû îæèäàåìûå äîõîäû ïîíåìíîãó
ðàñòóòD äîñòèãàÿ ìàêñèìóìà ïðè = 1 F
2 r
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
27. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ïëàòà çà ó÷àñòèå
Âìåñòî ðåçåðâíîé öåíû ìîæíî ââåñòè ïëàòó çà ó÷àñòèåF
r
Ðåçåðâíàÿ öåíà îòñåêàåò ó÷àñòíèêîâ ñ öåííîñòÿìè x < rF
Òî æå ñàìîå ïîëó÷èòñÿD åñëè çàñòàâèòü ¾çà âõîä¿
çàïëàòèòü r
= e ( ) , G y dy
0
òFåF îæèäàåìûé äîõîä ó÷àñòíèêà ñ öåííîñòüþ ðîâíî F r
Íî ýòî âåðíîD òîëüêî åñëè àãåíòû íåéòðàëüíû ê ðèñêóF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
28. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Îáùàÿ ïîñòàíîâêà
Òåïåðü âåðí¼ìñÿ ê íàøåé áîëåå îáùåé ñèòóàöèèF
Äëÿ ïðÿìîãî ìåõàíèçìà (Q , M ) ìû ìàêñèìèçèðóåì
N
E (R ) = E [mi (Xi )],
i =1
ãäå mi (Xi ) " âûïëàòà àãåíòà i @Xi " åãî ðàñïðåäåëåíèåAF
Äàâàéòå ýòî ÿâíî ïîäñ÷èòàåìF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
29. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Âñïîìíèì îáîçíà÷åíèÿ
qi (zi ) " îæèäàåìàÿ äîõîäíîñòü àãåíòà i D êîãäà îí ãîâîðèò
zi D à îñòàëüíûå ãîâîðÿò ïðàâäóX
qi (zi ) = Qi (zi , x −i )f−i (x −i )dx −i .
X−i
mi (zi ) " îæèäàåìàÿ âûïëàòà àãåíòà i X
mi (zi ) = Mi (zi , x −i )f−i (x −i )dx −i .
X−i
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
30. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Âûâîä îæèäàåìîãî äîõîäà ïðîäàâöà
ωi
E [mi (Xi )] = mi (xi )fi (xi )dxi =
0
ωi ωi x
mi (H) + qi (xi )xi fi (xi )dxi − qi (ti )fi (xi )dti dxi .
i
=
0 0 0
Ïîìåíÿåì ïîðÿäîê èíòåãðèðîâàíèÿX
ωi x ωi ωi
qi (ti )fi (xi )dti dxi = qi (ti )fi (xi )dxi dti =
i
0 0 0 t i
ωi
= F t q t dt
(I − i ( i )) i ( i ) i .
0
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
31. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Âûâîä îæèäàåìîãî äîõîäà ïðîäàâöà
ωi
E [mi (Xi )] = mi (xi )fi (xi )dxi =
0
ωi ωi x
mi (H) + qi (xi )xi fi (xi )dxi − qi (ti )fi (xi )dti dxi .
i
=
0 0 0
Èòîãî @âñïîìíèì îïðåäåëåíèå i AX q
xi − I − (Fxi ()xi ) qi (xi )fi (xi )dxi =
ωi
E [mi (Xi )] = mi (H)+
0 fi i
= xi − I − (Fxi ()xi ) Qi (x )f (x )d x .
fi i
X
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
32. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Âûâîä îæèäàåìîãî äîõîäà ïðîäàâöà
Èòîãî äîõîä ïðîäàâöà ïîëó÷àåòñÿ êàê
N
E [R ] = E [mi (Xi )] =
i =1
N N
= mi (H) + xi − I − (Fxi ()xi ) Qi (x )f (x )d x .
f
i =1 i =1 X i i
Åãî íóæíî îïòèìèçèðîâàòü ïðè ñëåäóþùèõ óñëîâèÿõX
ïðàâäèâîñòüD ÷òî ðàâíîñèëüíî íåóáûâàíèþ i Y q
ðàöèîíàëüíîñòüD ÷òî ðàâíîñèëüíî i (H) ≤ HF m
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
33. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Âèðòóàëüíûå öåííîñòè
Ìû ââåä¼ì ïîíÿòèå âèðòóàëüíîé öåííîñòè ïðåäìåòà äëÿ
i
àãåíòà X
I − Fi (xi )
ψi (xi ) = xi −
fi (xi ) .
Êàê äîêàçàòüD ÷òî E [ψi (Xi )] = Hc
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
34. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Âèðòóàëüíûå öåííîñòè
ÏåðåïèøåìX
E [ψi (Xi )] = E (Xi ) −
F x
I − i( i)
Xi
f x f x dx
i( i)
( i) i =
= E (Xi ) − (I − Fi (xi )) dxi .
X i
Ðàññìîòðèì òåïåðü îòäåëüíî èíòåãðàë ñïðàâàD ïîìåíÿâ
ïîðÿäîê èíòåãðèðîâàíèÿX
ωi ωi ωi
F x dxi =
(I − i ( i )) fi (y )dy dxi =
0 0 x i
ωi y ωi
= dxi fi (y )dy = fi (y )ydy = E (Xi ).
0 0 0
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
35. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ðåãóëÿðíûå çàäà÷è
Çàäà÷à äèçàéíà ìåõàíèçìîâ íàçûâàåòñÿ ðåãóëÿðíîé
D åñëè
i
äëÿ âñåõ ψi ÿâëÿåòñÿ âîçðàñòàþùåé ôóíêöèåé îò i F x
Ýòî ýêâèâàëåíòíî òîìóD ÷òî ôóíêöèÿ ðèñêà λi âîçðàñòàåòD
òFêF
I
x
ψi ( i ) = i − x
λi ( i )
.
x
 äàëüíåéøåì áóäåì ðàññìàòðèâàòü òîëüêî ðåãóëÿðíûå
çàäà÷èF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
36. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ïîñìîòðèì íà ôóíêöèþ âíèìàòåëüíî
Ïîñìîòðèì íà íàøó ôóíêöèþ âíèìàòåëüíîX
N N
mi (H) + x Q f dx.
ψi ( i ) i (x ) (x )
i =1 i =1 X
Äàâàéòå ïîêà ñêîíöåíòðèðóåìñÿ íà ïîäûíòåãðàëüíîì
âûðàæåíèèX
N
x Q
ψi ( i ) i (x ).
i =1
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
37. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ïîñìîòðèì íà ôóíêöèþ âíèìàòåëüíî
Äàâàéòå ïîêà ñêîíöåíòðèðóåìñÿ íà ïîäûíòåãðàëüíîì
âûðàæåíèèX
N
x Q
ψi ( i ) i (x ).
i =1
Q ïîõîæà íà âåñîâóþ ôóíêöèþD âçâåøèâàþùóþ ψi F
Ðåçîííî áûëî áû äàòü ìàêñèìàëüíûé âåñ ìàêñèìàëüíîìó
ψi @åñëè îí ïîëîæèòåëüíûéAD à íà îñòàëüíûå ïëþíóòüF
Ýòî áû ìàêñèìèçèðîâàëî ôóíêöèþ â êàæäîé òî÷êå D
çíà÷èòD è èíòåãðàë òîæåF
Ýòî è áóäåò èäååé êîíñòðóêöèèD íî ìû åù¼ íå ó÷èòûâàëè
îãðàíè÷åíèÿ @ïðàâäèâîñòü è ðàöèîíàëüíîñòüAF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
38. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Êîíñòðóêöèÿ îïòèìàëüíîãî ìåõàíèçìà
Ðàññìîòðèì ïðÿìîé ìåõàíèçì (Q , M )D â êîòîðîìX
Q ðàñïðåäåëÿåò îáúåêò ïîêóïàòåëþ i ñ ïîëîæèòåëüíîé
x x
âåðîÿòíîñòüþ i' ψi ( i ) = m—xj =1..N ψj ( j )X
Qi (x ) > H i' ψi (xi ) = j =1..N ψj (xj ) ≥ H.
m—x
ïëàòà M ðàâíà
x
Mi (x ) = Qi (x )xi − Qi (zi , x −i )dzi .
i
0
Ìû ñåé÷àñ äîêàæåìD ÷òî ýòî è åñòü îáåùàííûé
îïòèìàëüíûé ìåõàíèçì @åñëè çàäà÷à ðåãóëÿðíàAF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
39. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ïðàâäèâîñòü
Qi (x ) > H i' ψi (xi ) = j =1..N ψj (xj ) ≥ H.
m—x
x
Mi (x ) = Qi (x )xi − Qi (zi , x −i )dzi .
i
0
z x
Ïóñòü i < i F ÒîãäàD ïî ðåãóëÿðíîñòèD ψi ( i ) < ψi ( i )D èDz x
Q z Q z
çíà÷èòD äëÿ âñåõ x −i i ( i , x −i ) ≤ i ( i , x −i )F
q
Çíà÷èòD i íåóáûâàþùàÿD òFåF ìåõàíèçì ïðàâäèâûéF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
40. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Ðàöèîíàëüíîñòü
Qi (x ) > H i' ψi (xi ) = j =1..N ψj (xj ) ≥ H.
m—x
x
Mi (x ) = Qi (x )xi − Qi (zi , x −i )dzi .
i
0
M
Î÷åâèäíîD ÷òî i (H, x −i ) = HD çíà÷èòD mi (H) = HD è
ìåõàíèçì ðàöèîíàëüíûéF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
41. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Èòîãî
Qi (x ) > H i' ψi (xi ) = j =1..N ψj (xj ) ≥ H.
m—x
x
Mi (x ) = Qi (x )xi − Qi (zi , x −i )dzi .
i
0
Ýòî ðàöèîíàëüíûé ïðàâäèâûé ìåõàíèçìF
Îí îïòèìàëåíD òFêF ìàêñèìèçèðóåò êàæäîå èç äâóõ
ñëàãàåìûé ôîðìóëû äîõîäà ïî îòäåëüíîñòèF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
43. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Åãî ñâîéñòâà
Ðàññìîòðèì íîâóþ ôóíêöèþ
yi (x −i ) = inf {zi | ψi (zi ) > H è ∀j = i ψi (zi ) ≥ ψj (xj )}.
ÒFåF ýòî ìèíèìàëüíîå çíà÷åíèå ñòàâêè èãðîêà i D êîòîðîå
âûèãðûâàåò ó âñåõ îñòàëüíûõF
Òîãäà îïðåäåëåíèå Q áóäåò òàêèìX
Qi (zi , x −i ) = I, zi > yi (x −i ),
H, zi < yi (x −i ).
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
44. Îïòèìàëüíûå ìåõàíèçìû Ââåäåíèå
Ýôôåêòèâíûå ìåõàíèçìû Àóêöèîí âòîðîé öåíû ñ ðåçåðâíîé öåíîé
AGV è budget balance Îáùàÿ ïîñòàíîâêà: äîõîä ïðîäàâöà
Åãî ñâîéñòâà
ÌîæíîD çíà÷èòD è èíòåãðàë ïîñ÷èòàòüX
Qi (zi , x −i )dzi = xi − yi (x −i ), xi > yi (x −i ),
x i
0 H, xi < yi (x −i ).
Çíà÷èòD
Mi (x ) = yi (x −i ), xi > yi (x −i ),
H, xi < yi (x −i ).
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
66. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Budget balance
Ìû áû õîòåëèD ÷òîáû ó íàøèõ ìåõàíèçìîâ ñõîäèëñÿ
áàëàíñ @˜udget ˜—l—n™e propertyAF
Èíà÷å ãîâîðÿD ÷òîáû îíè ìîãëè ñóùåñòâîâàòü áåç âíåøíèõ
âëèâàíèéF
Ôîðìàëüíî ýòî âûðàæàåòñÿ êàê
N
Mi (x ) = H,
i =1
òFåF ñóììà âûïëàò âñåõ àãåíòîâ ðàâíà íóëþF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
67. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Ìåõàíèçì AGV
eq† îò errow!d9espremont!q¡r—rdE†—retF
e
Èñòîðèÿ òîæå íåïðîñòàÿX
Äâå íåçàâèñèìûõ ðàáîòû errow @IWUWA è
d9espremont!q¡r—rdE†—ret @IWUWAF
e
Áîëåå òîãîD q¡r—rdE†—ret ýòî îäèí ÷åëîâåêD à íå äâàF XA
e
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
68. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Ìåõàíèçì AGV
Ýòîò ìåõàíèçì òîæå ýôôåêòèâåí @òFåF èñïîëüçóåò Q ∗ AF
Åãî âûïëàòû MA îïðåäåëÿþòñÿ êàê
MiA(x ) = N I I
−
E X − [W−j (xj , X −j )]−E X − [W−i (xi , X −i )].
j i
j =i
Òåïåðü î÷åâèäíîD ÷òî äëÿ âñåõ x
N
MiA(x ) = H.
i =1
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
69. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Ìåõàíèçì AGV
Ìåõàíèçì eq† ïðàâäèâX åñëè äðóãèå àãåíòû ãîâîðÿò x −i D à
i z
àãåíò ãîâîðèò i D îí ïîëó÷àåò
E X − [Qi∗ (zi , X −i ) + W−i (zi , X −i )]−
i
I
− EX− E X − [W−j (Xj , X −j )] .
i
N −I
j =i
j
z
Âû÷èòàåìîå íå çàâèñèò îò i D à ïåðâîå ìàêñèìèçèðóåòñÿ
z
ïðè i = i F x
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
70. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Òåîðåìà
Òåîðåìà
Ýôôåêòèâíûé, ïðàâäèâûé è ðàöèîíàëüíûé ìåõàíèçì, ó
êîòîðîãî ñõîäèòñÿ áàëàíñ, ñóùåñòâóåò òîãäà è òîëüêî òîãäà,
êîãäà ìåõàíèçì VCG äà¼ò ïîëîæèòåëüíóþ îæèäàåìóþ ïðèáûëü
àóêöèîíåðó.
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
71. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Äîêàçàòåëüñòâî
 îäíó ñòîðîíó òðèâèàëüíîX †gq äîëæåí äàâàòü ïðèáûëüD
ïîòîìó ÷òî îí ñàìûé ýôôåêòèâíûéF
Íàì íóæíî äîêàçàòü â äðóãóþ ñòîðîíóX ïðåäúÿâèòü
êîíñòðóêöèþ òàêîãî çàìå÷àòåëüíîãî ìåõàíèçìà â òîì
ñëó÷àåD êîãäà †gq äà¼ò ïðèáûëüF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
72. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Äîêàçàòåëüñòâî
Íà÷í¼ì ñ ìåõàíèçìà eq† MA F Ïðèíöèï ýêâèâàëåíòíîñòè
äîõîäíîñòè íàì ãîâîðèòD ÷òî åñòü òàêèå êîíñòàíòû iA D ÷òî c
UiA(xi ) = E [W (xi , X −i )] − ciA.
Äëÿ †gq ýòî òîæå âåðíîX ñóùåñòâóþò òàêèå êîíñòàíòû iV D c
÷òî
A U x Wx V
i ( i ) = E [ ( i , X −i )] − i . c
Ìû ñåé÷àñ ïîäïðàâèì eq† òàêD ÷òîáû îí ïðèáûëü äàâàëD
îñòàâàÿñü ðàöèîíàëüíûìF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
73. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Äîêàçàòåëüñòâî
ÄàíîD ÷òî †gq ïðèíîñèò ïðèáûëüX
N
E MiV (X ) ≥ H.
i =1
Ïîñêîëüêó eq† ïî îïðåäåëåíèþ â íóëåX
N N
E MiV (X ) ≥ E MiA(X ) .
i =1 i =1
ÈëèD â òåðìèíàõ íàøèõ êîíñòàíòD
N N
ciV ≥ ciA.
i =1 i =1
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
74. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Äîêàçàòåëüñòâî
N c V ≥ N c A.
i =1 i i =1 i
Îïðåäåëèì òåïåðü ïîïðàâêèX äëÿ i = P..N
N
di = ciA − ciV , d1 = − di .
i =2
Èñêîìûì ìåõàíèçìîì áóäåò
Mi (x ) = MiA(x ) + di .
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
75. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Äîêàçàòåëüñòâî
Mi (x ) = MiA(x ) + di F
Î÷åâèäíîD áàëàíñ ñõîäèòñÿ @ýòî M A D ïîäïðàâëåííûé íà
êîíñòàíòûD êîòîðûå â ñóììå äàþò HAF
Ìåõàíèçì ïðàâäèâûéD ïîòîìó ÷òî âûïëàòû àãåíòà
îòëè÷àþòñÿ îò âûïëàò ïðàâäèâîãî M A íà êîíñòàíòóF
Íàäî òîëüêî ïðîâåðèòüD ÷òî îí ðàöèîíàëüíûéD òî åñòü
îæèäàíèå êàæäîãî àãåíòà áîëüøå íóëÿF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
76. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Äîêàçàòåëüñòâî
i
Äëÿ = I
Ui (xi ) = UiA(xi ) + di = UiA(xi ) + ciA − ciV = UiV (x ) ≥ H.
Äëÿ ïåðâîãî àãåíòà âñ¼ òî æå ñàìîåD íóæíî òîëüêî
çàìåòèòüD ÷òî
N N
d1 = − di = c c c
( iV − iA ) ≥ 1 − 1 ,
A V c
i =2 i =2
òFêF îáùàÿ ñóììà N cV ≥ N c AF
i =1 i i =1 i
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû
77. Îïòèìàëüíûå ìåõàíèçìû Ìåõàíèçì AGV
Ýôôåêòèâíûå ìåõàíèçìû Budget balance ó õîðîøèõ ìåõàíèçìîâ
AGV è budget balance
Ñïàñèáî çà âíèìàíèå!
ve™ture notes è ñëàéäû áóäóò ïîÿâëÿòüñÿ íà ìîåé
homep—geX
http://logic.pdmi.ras.ru/∼sergey/index.php?page=teaching
Ïðèñûëàéòå ëþáûå çàìå÷àíèÿD ðåøåíèÿ óïðàæíåíèéD
íîâûå ÷èñëåííûå ïðèìåðû è ïðî÷åå ïî àäðåñàìX
sergey@logic.pdmi.ras.ruD snikolenko@gmail.com
Çàõîäèòå â ÆÆ smartnikF
Ñåðãåé Íèêîëåíêî Îïòèìàëüíûå è ýôôåêòèâíûå ìåõàíèçìû