CN107463443A - A kind of distribution method based on the parallel mechanism insensitive to identity - Google Patents
A kind of distribution method based on the parallel mechanism insensitive to identity Download PDFInfo
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- CN107463443A CN107463443A CN201710567045.0A CN201710567045A CN107463443A CN 107463443 A CN107463443 A CN 107463443A CN 201710567045 A CN201710567045 A CN 201710567045A CN 107463443 A CN107463443 A CN 107463443A
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Abstract
The invention discloses a kind of distribution method based on the parallel mechanism insensitive to identity, step (1) is in each step of assigning process, according to specified " parallel mechanism ", some open reports oneself favorite article in remaining all items will be selected, then article will be allocated away；Step (2) wants some article simultaneously if multiple Agent, then which Agent these determine to obtain the article at random by way of lot, then proceed to, until all articles are all allocated away.Using technical scheme by using parallel mechanism distribution method, computational efficiency has arrived raising；It make use of and to the insensitive property of identity, ensure that fairness in advance when each Agent selects the article of oneself favorite, effectively solve the inequitable shortcoming of resource allocation, while also improve economic benefit, and there is good practicality and social equality.
Description
Technical field
The present invention relates to artificial intelligence and Agent system field, and in particular to it is a kind of based on insensitive to identity and
The distribution method of row mechanism.
Background technology
In recent years, some by computational efficiency account for scope research to distribution system design problem find it is various not
System (such as VCG systems) computational efficiency for considering private information but thoroughly closing down single Agent behaviour's lane behavior is very low, and various examines
Consider private information and situation that the very high system of computational efficiency can not thoroughly prevent from obtaining additional benefit by dishonest conduct goes out
It is existing.Consideration to computational efficiency makes thinking of the people to distribution system reasonable in design have new pragmatic direction：Although can not
The possibility that dishonest conduct occurs thoroughly is eliminated, but if it can be its band that each Agent wants to find under some distribution system
Come the dishonest conduct (such as behaviour's lane behavior and collusion behavior) of additional benefit so they will face and be difficult to the flood tide that receives and calculate
Task (such as related computational problem be NP-hard), the then it is considered that system is limited reliably (to participate in the distribution
Agent is tended to using honest behavior).
Therefore design towards it is multiple from sharp Agent distribution system when, it is necessary to consider:
(1) in the case where respective sharp Agent honestly participates in the distribution process, can is (i.e. in multinomial
In) allocation result for taking into account economic benefit and social equality is calculated；
(2) if some or some non-honest action schemes that additional benefit can be brought from sharp Agent attempt searchings, then
Whether the calculating task that they are faced is arduous abnormal.
In recent years the scholars of artificial intelligence field begin attempt to and meanwhile from the research of above these two aspects how to design towards
Multiple distribution systems from sharp Agent.Bouveret and Lang have studied a kind of serially resource allocation system framework without induction.
Under this system frame, it is each since sharp Agent without submitting any information before assigning process, only need to be according to a finger
Fixed rotation takes out oneself favorite resource from surplus resources set.They ask for the distribution of some specific scales
Topic have found substandard optimal in economic benefit or social equality (when each Agent uses dishonest behavior) by experiment
Agent orders；Again under conditions of some Agent knows other Agent preference informations in advance, initial analysis Agent behaviour
Do the computational complexity of allocation result.
There is, according to specified order, to identity sensitivity, caused in Agent resource allocation process for above-mentioned prior art
Justice is owed in economic benefit, social equality, computational efficiency distribution, and efficiency owes the shortcomings that high.
The content of the invention
In view of the shortcomings of the prior art, problem solved by the invention is that how to solve to pass through in Agent resource allocation process
Ji benefit, social equality, the more superior problem of computational efficiency.
In order to solve the above technical problems, the technical solution adopted by the present invention is a kind of based on the parallel machine insensitive to identity
The distribution method of system, comprises the following steps：
Step (1) defines a tripleWith O={ o1,o2,o3... expression article, N number of Agent,
Each Agent is to the preference ordering of articleEach Agent by according to oneself
Preference ordering Oneself favorite article is selected, then this article will be divided
With going out.
Step (2) has multiple Agent while wants some article, then by way of lot if in the step
Which Agent is determined at random to obtain the article, then proceedes to step (1), until all articles are all allocated away, finally
Social welfare maximization can be obtained.
In step (1) and step (2),
The value of article obtained by each Agent is weighed using revenue function：
The social welfare that parallel assigning process is realized is weighed with following two kinds of criterions：
Utilitarianism standard：
Equalitarianism standard：
In above-mentioned formula,Represent Agent i revenue function；2O→ R, g are that a score function to successively decrease includes
(1)lexicographic gL(k)=2|O|-k, and (2) BordagB(k)=| O |-k+1；ai(k) thing of Agent i reports is represented
Product, no(k) expression Agent in k wheels needs the number of article, Γ is represented
Agent it is possible that sequence set, | Γ |=(| O |！)|N|,It is 1/ | Γ |, have k Agent while want some thing
Product, then the probability that each Agent obtains article is 1/k.
In step (1) and step (2), if there is
The value of article obtained by each Agent is weighed using probability distribution：
The social welfare that parallel assigning process is realized is weighed with following two kinds of criterions：
Utilitarianism standard：
Equalitarianism standard：
In above-mentioned formula：O is an indivisible article set；N is that Agent gathers, 2≤| N |≤| O |；It is each
Agent likes article an ordered set of degree, the article o ∈ O sequence r for liking degree in the minds of Agent ii
(o) represent, that is to say, thatSo that
Using technical scheme, using parallel mechanism distribution method, computational efficiency has arrived raising；It make use of to body
The insensitive property of part, ensure that the fairness in advance when each Agent selects the article of oneself favorite, effectively solves resource
Malapportioned shortcoming, while economic benefit is also improved, and there is good practicality and social equality.
Brief description of the drawings
Fig. 1 is the ordering of optimization preference that each Agent most likes in the heart article to oneself；
Fig. 2 is that each Agent is assigned to an allocation result for oneself most liking article under order mechanism；
Fig. 3 is that each Agent is assigned to an assigning process for oneself most liking article under parallel mechanism；
Fig. 4 is the comparison of order mechanism and parallel mechanism allocation result in the case of utilitarianism and score function g；
Fig. 5 is the comparison of order mechanism and parallel mechanism allocation result in the case of equalitarianism and score function g.
Embodiment
The embodiment of the present invention is further described with reference to the accompanying drawings and examples, but is not to this hair
Bright restriction.
Fig. 1 is the ordering of optimization preference that Agent most likes in the heart article to oneselfWherein, arcri(1) represent
The article that Agenti is reported in the first round, arcri（2）Represent that Agenti takes turns reported thing t second, by that analogy, below
Numeral such as " o1、o2、o3、o4、o5" etc. representative be article.
Fig. 2 is a kind of resource allocation methods based under serial mechanism, the kth wheel that wherein k is represented, π (k)：π (1)=1, π
(2)=2, π (3)=3, π (4)=3, π (2)=2, when representing the first round respectively, first Agent selects o1, during the second wheel, the
Two Agent select o2, during third round, the 3rd Agent selects o3, during fourth round, the 3rd Agent selects o4, the 5th wheel
When, second Agent selects o2。
Fig. 3 is a kind of resource allocation methods based under parallel mechanism, and is divided using the insensitive form to identity
Process with resource, each Agent identity is had no effect allocation result, ensure that society during resource allocation puts down
Etc. property.
Fig. 4 and Fig. 5 is order mechanism and parallel mechanism distribution knot in the case of utilitarianism and score function g respectively
The comparison of fruit and in the case of equalitarianism and score function g, the comparison of order mechanism and parallel mechanism allocation result.
Embodiment one：
A kind of distribution method based on the parallel mechanism insensitive to identity, comprises the following steps：
Step (1) and step (2), it is the ordering of optimization preference that each Agent most likes in the heart article to oneself in Fig. 1,
According to respective ordering of optimization preference.Each Agent is the same as the favorite article of Times oneself, multiple same things of Agent simultaneous selections
During product, then these are equiprobable by way of lot to determine to obtain the article at random by which Agent.Then proceed to straight
All it is allocated away to all articles.
In Fig. 3, ai(k) article of Agent i reports, O are representedkThe selected article collection when k takes turns is represented,Table
Show in k wheels, o1By two Agent simultaneous selections,Represent in k wheels, o4By an Agent selection by that analogy,
Under Borda score functions, r1(o1)=1, gB(r1(o1))=5, r1(o2)=2, gB(r1(o2))=4, r1(o3)=5, gB(r1
(o5))=1, andThen SimilarlyThen In fact existIn the case of unknown,
In order to more preferably embody the superiority of the distribution method of the parallel mechanism insensitive to identity；
Embodiment two：
In fig. 2 it can be seen that each Agent selecting sequence π=12332, in Borda score functions
Under, In fact existIn the case of unknown,
The distribution method that the insensitive parallel mechanism of identity is can be seen that from embodiment one and example two is distributed than order mechanism
Method has more preferable superiority in economic benefit and social equality.It relatively refer to Fig. 4 and Fig. 5 in more detail
As a result emulate：
It is can be seen that by the result of above-mentioned example and Fig. 4, Fig. 5 either under utilitarianism or in equalitarianism
Under, the distribution method of the insensitive parallel mechanism of identity has more preferably than order mechanism distribution method in economic benefit and social equality
Superiority.
Using technical scheme, by using parallel mechanism distribution method, computational efficiency has arrived raising；It make use of
To the insensitive property of identity, the fairness in advance when each Agent selects the article of oneself favorite is ensure that, is effectively solved
The inequitable shortcoming of resource allocation, while economic benefit is also improved, and there is good practicality and social equality.
Embodiments of the present invention are made that with detailed description above in association with drawings and examples, but the present invention is not limited to
Described embodiment.To those skilled in the art, without departing from the principles and spirit of the present invention, it is right
These embodiments carry out various change, modification, replacement and modification and still fallen within protection scope of the present invention.
Claims (3)
- A kind of 1. distribution method based on the parallel mechanism insensitive to identity, it is characterised in that：Comprise the following steps：Step (1) defines a triple (0, N, ＞), with 0={ o1,o2,o3... expression article, N number of Agent, each Agent is ＞={ ＞ to the preference ordering of article1, ＞2, ＞3..., each Agent is by according to the preference ordering ＞ of oneself1= {o1, o2, o3, o4, o5..., ＞2={ o4, o2, o5, o1, o3..., ＞3={ o1, o3, o5, o4, o2... ..., select oneself most The article liked, then this article will be allocated away；Step (2) has multiple Agent while wants some article if in the step, then random by way of lot Which Agent is determined to obtain the article, then proceedes to step (1), until all articles are all allocated away, eventually To social welfare maximization.
- 2. the distribution method according to claim 1 based on the parallel mechanism insensitive to identity, it is characterised in that：In step Suddenly in (1) and step (2),The value of article obtained by each Agent is weighed using revenue function：<mrow> <msubsup> <mi>u</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mo>></mo> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo>&Sigma;</mo> <mrow> <mn>1</mn> <mo>&le;</mo> <mi>k</mi> <mo>&le;</mo> <mi>K</mi> </mrow> </munder> <mfrac> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>n</mi> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>The social welfare that parallel assigning process is realized is weighed with following two kinds of criterions：Utilitarianism standard：Equalitarianism standard：In above-mentioned formula,Represent Agent i revenue function；G is that a score function to successively decrease includes (1)lexicographic gL(k)=2|O|-k, and (2) Borda gB(k)=| O |-k+1；ai(k) Agent i reports are represented Article, no(k) expression Agent in k wheels needs the number of article, Γ tables Show Agent it is possible that sequence set, | Γ |=(| O |!)|N|, ＞ ∈ Γ are 1/ | Γ |, have k Agent while want certain Individual article, then the probability that each Agent obtains article is 1/k.
- 3. the distribution method according to claim 1 based on the parallel mechanism insensitive to identity, it is characterised in that：In step Suddenly in (1) and step (2), if there is ＞ it is unknown in the case of,The value of article obtained by each Agent is weighed using probability distribution：<mrow> <mover> <msubsup> <mi>u</mi> <mi>l</mi> <mo>*</mo> </msubsup> <mo>~</mo> </mover> <mo>=</mo> <munder> <mo>&Sigma;</mo> <mrow> <mo>></mo> <mo>&Element;</mo> <mi>&Gamma;</mi> </mrow> </munder> <mfrac> <mrow> <msubsup> <mi>u</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mo>></mo> <mo>)</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mi>&Gamma;</mi> <mo>|</mo> </mrow> </mfrac> <mo>=</mo> <munder> <mo>&Sigma;</mo> <mrow> <mo>></mo> <mo>-</mo> <mo>&Element;</mo> <mi>&Gamma;</mi> </mrow> </munder> <mfrac> <mrow> <msubsup> <mi>u</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mo>></mo> <mo>)</mo> </mrow> </mrow> <msup> <mrow> <mo>(</mo> <mo>|</mo> <mi>O</mi> <mo>|</mo> <mo>!</mo> <mo>)</mo> </mrow> <mrow> <mo>|</mo> <mi>N</mi> <mo>|</mo> </mrow> </msup> </mfrac> </mrow>The social welfare that parallel assigning process is realized is weighed with following two kinds of criterions：Utilitarianism standard：Equalitarianism standard：In above-mentioned formula：O is an indivisible article set；N is that Agent gathers, 2≤| N |≤| O |；＞ is each Agent pairs Article likes an ordered set of degree, the article o ∈ O sequence r for liking degree in the minds of Agent ii(o) table is carried out Show, that is to say, that o ＞io*So that ri(o) ＜ ri(o*)。
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2017
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Patent Citations (4)
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|---|---|---|---|---|
| CN103854208A (en) * | 2014-03-11 | 2014-06-11 | 湖州师范学院 | Cloud market multi-type resource allocation pricing mechanism and implementation algorithm thereof |
| CN104915742A (en) * | 2014-03-12 | 2015-09-16 | 株式会社理光 | User preference-based resource allocation method and apparatus |
| CN105578602A (en) * | 2015-10-21 | 2016-05-11 | 中国人民解放军理工大学 | Satellite heterogeneous network resource allocation method based on graph theory |
| CN106922002A (en) * | 2017-04-26 | 2017-07-04 | 重庆邮电大学 | A kind of network section virtual resource allocation method based on internal auction mechanism |
Non-Patent Citations (2)
| Title |
|---|
| WEI HUANG等: ""Allocating Indivisible Objects With a Parallel Method Insensitive to Identities"", 《IEEE ACCESS》 * |
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