CN109816089A - Bayes's operating method of Two-Agent under parallel distribution system - Google Patents
Bayes's operating method of Two-Agent under parallel distribution system Download PDFInfo
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Abstract
Bayes's operating method of the invention discloses a kind of under parallel distribution system Two-Agent, it is related to artificial intelligence and Agent system technical field, solve the problems, such as it is how to find an energy Successful Operation under parallel distribution system and obtain the operating method of the maximum sequence of taking of expected utility.In the method, when operator Agent-A and participant Agent-B is in certain wheel while when wanting the same article, in Bayes, then it can use participant that can obtain the method for the article with same probability to be allocated.Can oneself favorite article successively can be put into sequence of taking and carry out judging realize, until distributing all items, obtain the highest sequence of taking of an expected utility value by operator according to other participants to the hobby sequence of distribution article.Operator Agent-A can be made to find the maximum sequence of taking of an expected utility value using technical solution of the present invention.
Description
Technical field
The present invention relates to artificial intelligence and Agent system technical fields, more particularly to the Two- under parallel distribution system
Bayes's operating method of Agent.
Background technique
In research both domestic and external recent years, it is some by computational efficiency account for range to distribution system design problem
The study found that the various systems for not considering private information but can thoroughly close down single Agent behaviour's lane behavior, such as VCG system, meter
It is very low to calculate efficiency, and the various consideration private informations and very high system of computational efficiency can not thoroughly prevent from obtaining by dishonest conduct
The case where obtaining additional benefit occurs.People are made to have new business to the thinking of design reasonable distribution system the considerations of computational efficiency
Real direction: although a possibility that dishonest conduct occurs can not thoroughly be eliminated, but if each Agent thinks under certain distribution system
The dishonest conduct that additional benefit can be brought for it, such as operation behavior and collusion behavior are found, then they will face difficulty
With the flood tide calculating task of receiving, such as relevant computational problem is NP-hard, it may be considered that the system is limited reliable
The i.e. Agent that participates in the distribution tend to using honest behavior.
Therefore it when design is towards multiple distribution systems of benefit Agent certainly, needs to consider: (1) all sincere in respective benefit Agent
In the case where process of participating in the distribution on the spot, it can be calculated effectively i.e. in polynomial time and take into account economic benefit and society
The allocation result of meeting equality；(2) if some or certain find from benefit Agent attempt can bring the non-honesty of additional benefit to take action
Scheme, then whether the calculating task that they are faced is abnormal huge.The scholars of artificial intelligence field begin trying in recent years
How to design from the above these two aspects research towards multiple distribution systems from benefit Agent simultaneously.
In recent years the scholars of artificial intelligence field begin trying simultaneously from the above these two aspects research how to design towards
Multiple distribution systems from benefit Agent.The parallel distribution system frame of one novel no induction of Huang wei researching and designing is
Parallel distribution system.Using a kind of simple distributorship agreement that will not change with problem scale under the frame, and by it with most
Excellent order-assigned agreement makees experiment and Theory comparison, such as Bouveret and Lang is published in the opinion of IJCAI 2011 at them
Wen Li proposes optimal guess, and Kalinowski and Walsh then give proof in the paper that they are published in IJCAI 2013.
It was found that the agreement is all defeated corresponding optimal suitable under these standards no matter under economic benefit or the standard of social equality
Sequence distributorship agreement, and further inquired into progress target resource set under such an arrangement and grasped with maximum security gain and done computational
The computational complexity of behaviour's lane behavior is realized in problem also preliminary analysis under the system frame.
A kind of Publication No.: CN109034361A title are as follows: " pessimistic behaviour based on Two-Agent under parallel distribution system
Make method " Chinese invention disclose a kind of distribution method, comprising steps of (1) in each step of assigning process, according to
Specified " parallel mechanism " will select open report oneself favorite article in remaining all items, and then article will
It is assigned away；(2) it when Agent wants the same article simultaneously, is then determined at random by way of throwing coin, but when operation
Person Agent-A is under pessimistic strategy, and when two Agent are in same wheel while when reporting the same article, pessimistic thinks default
Oneself can not take the article, can avoid reporting some article simultaneously with other operators；(3) operator Agent-A shifts to an earlier date
Know that the article of other Agent likes sequence, by the pessimistic operation strategy of oneself, allows and oneself obtain optimal article collection, directly
It is assigned to article.How the technical proposal research of invention behaviour lane person obtains optimal article collection, reality under pessimistic scenario
The operation strategy of existing benefit.But be not that Agent can be pessimistic think not getting in the assignment procedure and other
The article of Agent competition does not discuss that the i.e. same article of more universal Bayes's situation in competition, can not be known each
The expected utility of Agent is how many, reaches and really maximizes interests.
Summary of the invention
In view of the deficiencies of the prior art, technical problem solved by the invention how is found under parallel distribution system
One energy Successful Operation obtains the operating method of the maximum sequence of taking of expected utility.
In order to solve the above technical problems, the technical solution adopted by the present invention is that one kind Two- under parallel distribution system
Bayes's operating method of Agent, includes the following steps:
(1) triple is definedWithIndicate assigned object
Product set；Indicate the article set that operator has 50% probability to take；Indicate the article set that operator does not get；N
=2, it indicates the quantity of operator Agent of participating in the distribution, is indicated with Agent-A and Agent-B；Each Agent is to the inclined of article
Good sequence set by
It indicates；In each round of distribution article, operator respectively selects oneself most desired article taken, and selected article will be by
It dispenses；
It (2), then can be using every when operator Agent-A and participant Agent-B takes turns while wanting the same article
The method that a participant can obtain the article with identical probability；
(3) for operator Agent-A in Bayes, the operation strategy used is according to oneself to distribution article
Hobby sequenceThe article of the i-th wheel (i=1,2,3... and i≤n) is successively put into sequence of taking to carry out judging that success is inserted
Enter in sequence, after distributing all items, obtains the maximum article of expected utility and take sequence, detailed process is such as
Under:
1) setting operation person Agent-A is aware of participant Agent-B to the preference ordering of article in advanceAnd
The honest preference ordering according to oneself of Agent-B meetingReport each round is gone to want the article taken；
2) judge that article is put into sequence δ success of taking, need to meet following condition:
In above-mentioned formula,Indicate the article set that current i-th wheel is not taken, o indicates that current i-th wheel attempts to join and takes
The article of sequence δ,Indicate all assigned article set,Indicate that participant Agent-B thinksCollection
Article collection good than o article in conjunction, δ indicate the optimal sequence of taking of operator, and IPOS indicates that article o is inserted in sequence of taking
The position entered,Indicate the article set that operator has 50% probability to take；
Current i-th wheel will be inserted into the article o for the sequence δ that takes, if meeting equation (1), so that it may think in the object of taking
Before product, participant Agent-B, which can take good article number than article o and take more than or equal to behaviour lane person Agent-A, compares object
Product o will be good number of articles；Therefore the i-th wheel behaviour lane person Agent-A has probability to take article o；When equation (1) takes greater-than sign, then
Article o can centainly take；When equation (1) takes equal to number, then the probability that article o is brought into is 50%, and is put intoSet
In；
3) article o meets equation (1) insertion and takes after sequence δ, whether needs to examine article in other sequence δ that take
Because the insertion of article o is taken, probability is changed, and needs the entire sequence δ that takes of primary inspection；Whether judge article
It needs to examine, needs to meet following condition:
In above-mentioned formula, j successively indicates to take sequence δ from 1 to | δ | position, δ (j) then indicate in the sequence δ that takes j this
Article on a position；If belonging in the sequence δ that takesArticle in set and identical with position IPOS is currently inserted into
Article, without the probability of taking of item inspecting；Article on remaining position judges whether probability change of taking, and needs under satisfaction
The condition in face:
If article δ (j) is unsatisfactory for the decision condition of equation (3), article o is inserted into the position IPOS for sequence of taking then
It needs to move one backward, IPOS=IPOS+1；Then it returns equation (1) to continue to determine, examines, examine successfully again after success
It can be just added in the sequence δ that takes at last later；And be inserted into article o number byValue determine, if
Article o is successively inserted into and belongs toSet, then EXPNUMO subtracts 0.5；It is successfully singly not belonging to if be inserted intoSet, then
EXPNUMO subtracts 1；Until the value of EXPNUMO is 0, do not continue to insertion article o and enter take sequence δ, and sequence of taking at this time
Arranging δ is the sequence δ that takes in the case of optimal Bayes.
Compared with prior art, using technical solution of the present invention, based under parallel distribution system, when meeting condition:
For
Then may be used
To guarantee the article preference ordering based on operator Agent-AThe sequence δ that takes can be found, obtain expectation effect
The maximum article collection of benefit.
Detailed description of the invention
Fig. 1 is operation of the present invention flow chart；
Can Fig. 2 be that an article is examined to be inserted into series of operations flow chart of taking；
Fig. 3 is the ordering of optimization preference that two Agent most like in the heart article to oneself；
The Optimum Operation sequence and true hobby sequence, the true hobby sequence of Agent-B that Fig. 4 is operator Agent-A；
In the case that Fig. 5 is two Agent honesty, each Agent, which is assigned to, oneself most likes that one of article is distributed
As a result；
Fig. 6 is that operator Agent-A carries out bayes strategy operation, in the case where Agent-B honesty, each Agent
It is assigned to an allocation result of article；
Fig. 7 is score situation of two Agent to each article；
Fig. 8 is the algorithm of optimal sequence of taking in the case of finding a Bayes；
Can Fig. 9 be the algorithm for examining an article be inserted into sequence of taking under bayes strategy operation.
Specific embodiment
A specific embodiment of the invention is further described with reference to the accompanying drawings and examples, but is not to this hair
Bright restriction.
Fig. 1 shows Bayes's operating method of the Two-Agent under parallel distribution system, includes the following steps:
(1) triple is definedWithIndicate assigned object
Product set；Indicate the article set that operator has 50% probability to take；Indicate the article set that operator does not get；N
=2, it indicates the quantity of operator Agent of participating in the distribution, is indicated with Agent-A and Agent-B；Each Agent is to the inclined of article
Good sequence set by
It indicates；In each round of distribution article, operator respectively selects oneself most desired article taken, and selected article will be by
It dispenses；
It (2), then can be using every when operator Agent-A and participant Agent-B takes turns while wanting the same article
The method that a participant can obtain the article with identical probability, such as: throwing coin, go to determine the ownership of this article of the wheel
Power；
(3) for operator Agent-A in Bayes, the operation strategy used is according to oneself to distribution article
Hobby sequence, the article of the i-th wheel (i=1,2,3... and i≤n) is successively put into sequence of taking and carries out judging that success is inserted
Enter in sequence, after distributing all items, obtains the maximum article of expected utility and take sequence, be specifically inserted into
Journey is as shown in Figure 2:
1) setting operation person Agent-A is aware of participant Agent-B to the preference ordering of article in advanceAnd
The honest preference ordering according to oneself of Agent-B meetingReport each round is gone to want the article taken；
2) judge that article is put into sequence δ success of taking, need to meet following condition:
In above-mentioned formula,Indicate the article set that current i-th wheel is not taken, o indicates that current i-th wheel attempts to join and takes
The article of sequence δ is taken,Indicate all assigned article set,Indicate that participant Agent-B thinks
Article collection good than o article in set, δ indicate the optimal sequence of taking of operator, and IPOS indicates article o in sequence of taking
The position of insertion,Indicate the article set that operator has 50% probability to take；
Current i-th wheel will be inserted into the article o for the sequence δ that takes, if meeting equation (1), so that it may think in the object of taking
Before product, participant Agent-B, which can take good article number than article o and take more than or equal to behaviour lane person Agent-A, compares object
Product o will be good number of articles；Therefore the i-th wheel behaviour lane person Agent-A has probability to take article o；When equation (1) takes greater-than sign, then
Article o can centainly take；When equation (1) takes equal to number, then the probability that article o is brought into is 50%, and is put intoSet
In；
3) article o meets equation (1) insertion and takes after sequence δ, whether needs to examine article in other sequence δ that take
Because the insertion of article o is taken, probability is changed, and needs the entire sequence δ that takes of primary inspection；Whether judge article
It needs to examine, needs to meet following condition:
In above-mentioned formula, j successively indicates to take sequence δ from 1 to | δ | position, δ (j) then indicate in the sequence δ that takes j this
Article on a position；If belonging in the sequence δ that takesArticle in set and identical with position IPOS is currently inserted into
Article, without the probability of taking of item inspecting；Article on remaining position judges whether probability change of taking, and needs under satisfaction
The condition in face:
If article δ (j) is unsatisfactory for the decision condition of equation (3), article o is inserted into the position IPOS for sequence of taking then
It needs to move one backward, IPOS=IPOS+1；Then it returns equation (1) to continue to determine, examines, examine successfully again after success
It can be just added in the sequence δ that takes at last later；And be inserted into article o number byValue determine, if
Article o is successively inserted into and belongs toSet, then EXPNUMO subtracts 0.5；It is successfully singly not belonging to if be inserted intoSet, then
EXPNUMO subtracts 1；Until the value of EXPNUMO is 0, do not continue to insertion article o and enter take sequence δ, and sequence of taking at this time
Arranging δ is the sequence δ that takes in the case of optimal Bayes.
Fig. 3 is the ordering of optimization preference that each Agent most likes in the heart article to oneselfThe more preceding representative of ranking more by
Agent likes, and successively reduces.Intermediate number such as " o1、o2、o3、o4、o5" etc. representatives be article.
Fig. 4 is the sequence of taking for grasping lane person Agent-A operation strategy in BayesWith taking under truth
Take sequence δAAnd the sequence δ that takes of Agent-B under real conditionsB。
Fig. 5 is under parallel distribution system, and the two Agent all honest hobby according to oneself reports that each round is wanted to take
The article taken, then first round operator Agent-A reports o4, Agent-B report o1, successively go on, until article is divided
With complete, their expected value is calculated separately out to the situation of scoring of each article according to two Agent of Fig. 5.
Fig. 6 is under parallel distribution system, and operator Agent-A uses Bayes's operation strategy, and Agent-B remains sincere
It is real to be reported according to oneself hobby, then operator Agent-A can then report o in the first round5, Agent-B still reports
o1, remaining each round report is as shown in fig. 6, and calculate separately out the expected value of two Agent in this case.
Fig. 7 is expected value of two Agent to each article.
Fig. 8 is within the polynomial time, and finding one, expected utility is optimal takes for operator Agent-A
Sequence.
Fig. 9 is one current sequence of taking of article success insertion of verifying.
Embodiment:
In one kind, based on being obtained under parallel distribution system using Bayes's operation strategy, an expected utility is maximum to take
Sequence includes the following steps:
Step (1), step (2) and step (3), be in Fig. 3 two Agent oneself is most liked in the heart one of article partially
Good sequence, according to respectively to the ordering of optimization preference of article.Oneself favorite article is reported while each operator Agent honesty,
When the same article of multiple operator Agent simultaneous selections, then these are equiprobable come random by way of throwing coin
Which Agent is determined to obtain the article.It then proceedes to all be assigned away until all articles.Last allocation result is such as
Shown in Fig. 5.
It is then to be aware of the article hobby sequence of Agent-B in advance in operator Agent-A, and use Bayes in Fig. 6
Operation strategy, and the Agent-B still honest article hobby sequence report article according to oneself, the operator in the first round
Agent-A reports o5, Agent-B report o1；Second wheel, operator Agent-A report o2, Agent-B report o2；Third round, behaviour
Author Agent-A reports o4, operator Agent-B report o3；Fourth round, operator Agent-A report o6, operator Agent-B
Report o6.Under the Borda score function of such as Fig. 7, uA(o1)=35, uA(o2)=40, uA(o3)=20, vA(o4)=70, uA
(o5)=65, uA(o6)=10；uB(o1)=100, uB(o2)=80, uB(o3)=70, uB(o4)=55, uB(o5)=30, uB(o6)
=10.Under operation distribution and honest distribution, the expected value that two Agent are respectively obtained, respectively as illustrated in figures 6 and 5, really
It is real to distribute lower UA=150, UB=220；Operation distributes lower UA=160, UB=220.
It is last true when operator Agent-A carries out Bayes's operation to obtain more expected utilities in distribution
It is real that bigger expected utility is obtained by operation.
As a result it emulates:
It can be seen that in the case where two Agent all honest participations by the result of above-mentioned example and Fig. 5, Fig. 6
The expected utility U of Agent-AA=150, and take the expected utility U of Agent-A in the case of Bayes's operation strategyA=160, really
For real storage under the distribution method in the parallel mechanism insensitive to identity, Bayes's operation strategy of Two-Agent makes operator
Expected utility increased, specific operative algorithm is as shown in Figure 8 and Figure 9.
Using technical solution of the present invention, under parallel distribution system, Bayes's operational circumstances of Two-Agent are deposited really
In order to guarantee the fairness of distribution system, preventing cheating, the Agent for needing to participate in the distribution protects oneself to article
The private informations such as hobby sequence, or increase the operator's Agent quantity participated in the distribution, operation difficulty is increased, guarantees the public affairs of distribution
Levelling.
Take Bayes's operation strategy that can find one based under parallel distribution system using technical solution of the present invention
The maximum sequence of taking of the expected utility obtained at feature operation.
Detailed description is made that embodiments of the present invention in conjunction with the accompanying drawings and embodiments above, 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, right
These embodiments progress various change, modification, replacement and variant are still fallen in protection scope of the present invention.
Claims (2)
1. a kind of Bayes's operating method of the Two-Agent under parallel distribution system, characterized by the following steps:
(1) triple is definedWithIndicate assigned article collection
It closes；Indicate the article set that operator has 50% probability to take；Indicate the article set that operator does not get；N=2,
It indicates the quantity of operator Agent of participating in the distribution, is indicated with Agent-A and Agent-B；Each Agent is suitable to the preference of article
Ordered sets by
It indicates；In each round of distribution article, operator respectively selects oneself most desired article taken, and selected article will be by
It dispenses；
(2) when operator Agent-A and participant Agent-B takes turns while wanting the same article, then each ginseng can be used
The method that the article can be obtained with person with identical probability；
(3) for operator Agent-A in Bayes, the operation strategy used is according to oneself hobby to distribution article
SequentiallyThe article of the i-th wheel (i=1,2,3... and i≤n) is successively put into sequence of taking to carry out judging that success is inserted into sequence
In column, after distributing all items, obtains the maximum article of expected utility and take sequence.
2. Bayes's operating method of the Two-Agent according to claim 1 under parallel distribution system, feature exist
In: in step (3), detailed process is as follows for Bayes's situation operation strategy:
1) setting operation person Agent-A is aware of participant Agent-B to the preference ordering of article in advanceAnd Agent-B meeting
The honest preference ordering according to oneselfReport each round is gone to want the article taken；
2) judge that article is put into sequence δ success of taking, need to meet following condition:
In above-mentioned formula,Indicate the article set that current i-th wheel is not taken,oIndicate that current i-th wheel attempts to join sequence of taking
The article of δ,Indicate all assigned article set,Indicate that participant Agent-B thinksSet
Middle good article collection than o article, δ indicate the optimal sequence of taking of operator, and IPOS indicates that article o is inserted into sequence of taking
Position,Indicate the article set that operator has 50% probability to take；
Current i-th wheel will be inserted into the article o of the sequence δ that takes, if meeting equation (1), so that it may think take the article it
Before, participant Agent-B can take good article number than article o and take than article o more than or equal to behaviour lane person Agent-A
Good number of articles；Therefore the i-th wheel behaviour lane person Agent-A has probability to take article o；When equation (1) takes greater-than sign, then article o
It can centainly take；When equation (1) takes equal to number, then the probability that article o is brought into is 50%, and is put intoIn set；
3) article o meets equation (1) insertion and takes after sequence δ, need to examine article in other sequence δ that take whether because
The insertion of article o probability of taking is changed, so needing primary to examine the sequence δ that entirely takes；Judge whether article needs
It examines, needs to meet following condition:
In above-mentioned formula, j successively indicates to take sequence δ from 1 to | δ | position, δ (j) then indicates this position j in the sequence δ that takes
The article set；If belonging in the sequence δ that takesArticle and article identical with position IPOS is currently inserted into set,
Without the probability of taking of item inspecting；Article on remaining position judges whether probability change of taking, and needs to meet following
Condition:
If article δ (j) is unsatisfactory for the decision condition of equation (3), the position IPOS that article o is inserted into sequence of taking then needs
One is moved backward, IPOS=IPOS+i；Then it returns equation (1) to continue to determine, be examined again after success, after examining successfully
It can be just added in the sequence δ that takes at last；And be inserted into article o number byValue determine, if article
O is successively inserted into and belongs toSet, then EXPNUMO subtracts 0.5；It is successfully singly not belonging to if be inserted intoSet, then
EXPNUM0 subtracts 1；Until the value of EXPNUMO is 0, do not continue to insertion article o and enter take sequence δ, and sequence of taking at this time
Arranging δ is the sequence δ that takes in the case of Bayes.
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