CN110390560A - A kind of mobile intelligent perception multitask pricing method based on Stackelberg game - Google Patents

A kind of mobile intelligent perception multitask pricing method based on Stackelberg game Download PDF

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CN110390560A
CN110390560A CN201910574705.7A CN201910574705A CN110390560A CN 110390560 A CN110390560 A CN 110390560A CN 201910574705 A CN201910574705 A CN 201910574705A CN 110390560 A CN110390560 A CN 110390560A
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鲁剑锋
段佳昂
戴情
杨沙沙
韩建民
彭浩
胡兆龙
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Zhejiang Normal University CJNU
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Abstract

The mobile intelligent perception multitask pricing method based on game that the invention discloses a kind of, comprising: (1) obtain current all user roles and its corresponding task；(2) when the income of acquisition worker and the income of requestor maximize it respectively, the relationship of the two and unit reward；(3) it determines that unit is rewarded, obtains task set of rewards；(4) determine that the unified of the system pays the mechanism of determination；(5) according to Stackelberg Model Nash Equilibrium state, the optimal perception planning strategy of worker and the optimal detecting period strategy of each worker are determined；(6) the true unit value of submitting for given requestor for task formulates optimal γ ° of publishing policy of reward based on Stackelberg Model Nash Equilibrium state.The present invention is designed as a three stage Continuous Games for gunz perception task is moved, and the technical issues of gunz perception task provides pricing strategy cannot be moved for multiple leaders and multiple follower by solving the prior art.

Description

A kind of mobile intelligent perception multitask pricing method based on Stackelberg game
Technical field
The invention belongs to novel perceptual computing fields, are based on Stackelberg more particularly, to one kind (Stackelberg) the mobile intelligent perception multitask pricing method of game.
Background technique
With mobile calculation technique fast development and built-in multiple sensors mobile device (such as: smart phone, Smartwatch, intelligent glasses etc.) it is universal make mobile gunz perceive as collecting for perception data, analysis and the new tool explored, And the range that can be explored is considerably beyond pervious mode.Currently, the extensive application program based on intelligent perception occurs, these Using cover people life various aspects, such as smart city, traffic monitoring, environmental monitoring, map tag and it is some its In terms of him.However, existing intelligent perception application is it is difficult to ensure that user plays an active part in, it is voluntary that most of applications are all based on user It participates in, because providing mobile gunz aware services inevitably consumes battery capacity, mobile data stream, manual work and sense Know the time, and by sharing sensing data with personal information, is exposed to user in potential privacy leakage threat.
As one of most important application program in mobile intelligent perception, service switching application, which has become, to be allowed to use Family exchanges the medium of valuable service.The service quality of typical service switching application generally depends on leaping up for a large number of users The high quality perception data that jump participates in and these users provide, however perceived cost the mentioning with degree of participation of service is provided It is high and increase.Therefore, the user of a rationality and selfishness will not generate interest to perception task is participated in, unless there are satisfactory It rewards to compensate the perceived cost of user.(or payment is very few) will will lead to Oversensing (or perception be not however, excess disbursement Foot), long-term gain can be reduced for ISP.In addition, rationality, selfish user merely desire to maximize personal income, " hitchhiking " and " false report " may be in the case where not having suitably punish to these behaviors.In this case, It will appear multitask when selfish user tends to request service without being to provide service to exchange problem (MSE), meanwhile, also deposit Cooperation between non-serving requestor and ISP.Therefore, effective incentive mechanism is designed to motivate user actively to join With and the perception data of high quality be provided be necessary, to realize the service of high quality, make in mobile intelligent perception Multitask exchanges successfully.
Many researchs based on game theory provide such as price, reputation and the incentive mechanism of Stackelberg game The methods of, to motivate user to participate in mobile gunz aware services.However, presently, there are three to prevent these research extensions everywhere The main reason for managing the MSE problem in mobile intelligent perception: (i) in each stage, user, which can become one with unrestricted choice, to be asked Person's of asking (i.e. service requester) or a worker (i.e. ISP), therefore it is that have must that balanced service request is provided with service It wants.Otherwise, selfish user is more likely to request service and obtains low receipts without being to provide service, and in short-term balance Benefit；(ii) each worker can be with unrestricted choice perception task and perception level.Further, since the diversity of worker's ability causes The perceived cost of worker is different, and therefore, each user carefully determines task selection policy and detecting period strategy To maximize personal income.(iii) each stage has multiple requestors to issue multiple perception tasks, wherein the valence of perception task Be worth it is different, and the value of task be secrecy, only requestor oneself knows, then requestor may have motivation to pass through It lies about a reference value and carrys out steerable system.In short, there is also competitions between requestor not there is only competition between worker.These relationships Between game be Incompletely information games.MSE problem is very common in mobile gunz aware application, however, This problem is more complicated so that well solving scheme not yet.It mainly all concentrates at present and solves single leader and more This special circumstances of a follower.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides one kind to be based on Stackelberg game Mobile intelligent perception multitask pricing method, its object is to it is given unified pay the mechanism of determination under, by mobile gunz sense Know that multitask bidding fashion is divided into reward statement determination and perception plan determines two game stages, it is rich by Stackelberg The calculating for playing chess Nash Equilibrium is provided so that community income is maximized, guarantees that requestor (leader) and worker (follower) will not Thus the pricing mechanism for having motivation to deviate solves the existing pricing mechanism game stage that only regard perceptual plan determines, causes Not the technical issues of not can solve the mobile intelligent perception multitask price of multiple leaders and multiple follower.
To achieve the above object, according to one aspect of the present invention, a kind of mobile intelligent perception based on game is provided Multitask pricing method, which comprises the following steps:
(1) current all user roles and its corresponding task are obtained, that is, is obtained:
Requestor set R={ r1..., rm, requestor rjThe task τ of publicationjSet of tasks T={ the τ of composition1..., τmAnd task τjUnit value κjThe unit value set K={ κ of composition1..., κm}；And:
Worker set W={ w1..., wn, each worker wiUnit cost ciThe unit cost set C=of composition {c1..., cn}；
(2) according to the user role of step (1) acquisition and its corresponding task, worker w is obtainediIncome viAnd requestor rjIncome ujWhen maximizing it respectively, the relationship of the two and unit reward γ；
(3) the worker w that the user role and its corresponding task and step (2) obtained according to step (1) obtainsiReceipts Beneficial viAnd requestor rjIncome ujWith unit reward γ relationship, determine unit reward γ, obtain task set of rewards Γ= {γ1..., γm}；
(4) it rewards γ according to the unit obtained in step (3), determines that the unified of the system pays the mechanism of determination, i.e., (R, T, K, W, C, Γ)；Wherein R is requestor's set R={ r1..., rm, T is the set of tasks T={ τ of publication1..., τm, K The unit value set K={ κ answered for the set of tasks T-phase of publication1..., κm, C is worker's set W={ w1..., wnPhase The unit cost set answered, C={ c1..., cn, and c1≤…≤cn, Γ is the set of rewards that the set of tasks T-phase of publication is answered Γ={ γ1..., γm, γ1≥…≥γm, γj=κjγ, γ are unit reward；
(5) in the case where the given unified payment of step (4) acquisition determines mechanism i.e. (R, T, K, W, C, Γ), according to Stark that Burger model Nash Equilibrium state determines the optimal perception planning strategy Π of worker*And each worker wiOptimal detecting period Strategy
(6) the optimal perception planning strategy of worker obtained according to step (5)Given is asked The task τ that the person of asking submitsjTrue unit valueBased on Stackelberg Model Nash Equilibrium State formulates optimal γ ° of publishing policy of reward, makes community income's V=∑ for all γ >=0I ∈ [1, n]vi+∑J ∈ [1, m]ujIt is maximum Change, wherein viFor worker wiIncome, ujFor requestor rjIncome.
Preferably, the mobile intelligent perception multitask pricing method based on game, step (1) the worker wi's Income viIt maximizes, it may be assumed that
Wherein, citijIt is the perceived cost w of workeri, ci∈ C is the unit cost of worker, C={ c1..., cnIt is worker The unit cost set of worker, t can be used in set WijIt is worker wiTo task τjDetecting period, txjIt is worker wxTo task τj Detecting period, vijFor user wiParticipate in task τjWhen income, viFor vi=maxJ≤[1, m]vij, γj=κjγ, γ are units Reward.
Preferably, the mobile intelligent perception multitask pricing method based on game, step (1) the requestor rj Income ujIt maximizes, it may be assumed that
Wherein,It is requestor rjTo worker's detecting period collection WjEvaluation function；txjIt is worker wxTo task τjDetecting period；κjIt is task τjUnit value；γj=κjγ, γ are unit rewards；θ ∈ (0,1), so that ujInIn be strictly concave function, reflect the universal phenomenon of marginal income decreasing in economics.
Preferably, the mobile intelligent perception multitask pricing method based on game, step (3) wherein reward by unit γ meets:
Wherein, V is social integral benefit, viFor worker wiIncome vi=maxJ≤[1, m]vij, vijFor worker wiParticipation task τjWhen income (see formula 1), ujFor requestor rjIncome (see formula 2), siTo select task τiWorker set selected by Set of tasks, ti>=0 is artificial detecting period, κj>=0 is task τjUnit value.
For set of tasks T={ τ1..., τmTask τj, task reward γj=κjγ remembers task set of rewards Γ ={ γ1..., γm}。
Preferably, the mobile intelligent perception multitask pricing method based on game, step (5) worker are optimal Perceive planning strategy For using worker w when OPTIMAL TASK selection strategyiChoosing The set of tasks selected,For using worker w when OPTIMAL TASK selection strategyiDetecting period；Worker wiOptimal detecting period plan SlightlyIt is for allSo thatIt maximizes；t-ijTo remove other than worker i, other workers ginseng With task τjDetecting period collection.
Preferably, the mobile intelligent perception multitask pricing method based on game, step (5) worker wi's is optimal Detecting period strategyThe specific method is as follows for acquisition:
Worker w1With the smallest unit cost c1, determine that its OPTIMAL TASK selection strategy isThat is worker w1Choosing It selects and rewards γ with highest1Task τ1, and so on worker will press its competitiveness sequential selection task:
It is given that there is corresponding reward γjPerception task τjWith the set W of interested workerj={ w1..., wl, and Optimal detecting period strategyWherein:
By WjIn worker according to CjMiddle unit cost is ranked up, i.e. c1≤c2≤…≤cl, enable ε is a sufficiently small positive number, and l is to task τjInterested worker's number Amount.
For giving γj, Wj={ w1..., wlAnd its corresponding cost set Cj={ c1..., cl, worker wj∈Wj Maximum returnAre as follows:
Wherein c1≤c2≤…≤cl, and
Preferably, the mobile intelligent perception multitask pricing method based on game, step (6) specifically includes following Step:
The task τ that (6-1) acquisition request person submitsjTrue unit valueGive
(6-2) is according to the true unit value obtained in step (6-1)And in step (5) The optimal perception planning strategy of the worker of acquisitionBased on Stackelberg Model Nash Equilibrium state The optimum value for obtaining requestor states strategy
(6-3) states strategy according to the optimum value that step (6-2) obtains, and determines ratio inhibiting factor φ, obtains optimal γ ° of publishing policy of reward.
Preferably, the mobile intelligent perception multitask pricing method based on game, step (6-2) optimum value sound Bright strategy obtains according to the following steps:
Existing set of tasks T={ τ1..., τm, Γ be publication set of tasks T-phase answer set of rewards Γ= {γ1..., γm, γ1≥…≥γm, γj=κjγ, γ are unit reward；For not yet stating unit valence in set of tasks T Highest task τ is rewarded in all tasks of valuej, its unit value of initialization statementAnd appoint according to currently stating The unit value of businessThe unit value stated when being higher than all tasks of the task using optimal statement strategy with reward Iteration updates the unit value of its statementUntil its requestor income obtained, which increases, is less than default threshold Value, then using the unit value for the task stated at this time as the sound when requestor is tactful using optimal statement to the task Bright unit value.
All tasks that the unit value for the task that the basis is currently stated and reward are higher than the task use The calculation method for the unit value that the unit value iteration stated when optimal statement strategy updates its statement is as follows:
Wherein, (0,1) θ ∈, txjFor the optimal perception planning strategy Π of worker*Lower worker wXParticipate in the task τjPerception Time,The task τ that requestor submitsjTrue unit value,
The income method for calculating its requestor is shown in formula (2).
Preferably, the mobile intelligent perception multitask pricing method based on game, step (6-3) the ratio suppression Factor φ processed meets following constraint:
Preferably, the mobile intelligent perception multitask pricing method based on game, step (6-3) the optimal prize γ ° of publishing policy is encouraged, γ ° is the maximum value for meeting the following γ constrained:
Wherein,
Wherein, (0,1) θ ∈, θ make u in this rangejInIn be strictly concave function；cxFor detecting period tij The unit cost of >=0 worker, x are variable, indicate some worker；cyFor worker wyUnit cost；In order to see formula Succinctly, to enable zj=| Wj| -1,For using worker w when OPTIMAL TASK selection strategyiThe set of tasks of selection,
In general, through the invention it is contemplated above technical scheme is compared with the prior art, can obtain down and show Beneficial effect:
(1) the MSE problem in MCS is designed as comprising more leaders with more follower based on Stackelberg by we The multiservice switching problem of game, the game are a three stage Continuous Games.First stage, user's unrestricted choice are known as one Requestor (i.e. leader) either worker (i.e. follower).Second stage, each requestor issue perception task and State corresponding unit value.Phase III, each worker formulate respective perceptual strategy to maximize personal income；It solves The prior art cannot move the technical issues of gunz perception task provides pricing strategy for multiple leaders and multiple follower.
(2) payments mechanism, i.e. ideal money are determined invention introduces unified, thus the service request between balancing user It is provided with service, wherein user provides (or reception) service to earn (or consumption) ideal money, therefore nobody can be not It is serviced in the case that service is provided.We are using ideal money rather than the reason of real money is that ideal money is only limitted to Circulation in system, and convert very convenient.
(3) unique Nash Equilibrium of perception planning strategy game, each worker are calculated we have proposed effective algorithm Optimal task selection policy and detecting period strategy are made, none of worker can be current by unilaterally deviateing Perceptual strategy improves personal income.Preferred embodiment, we have proposed a kind of new algorithms, walk process by m and realize low complexity Degree calculates, and unique Nash Equilibrium of reward statement strategy is found with a kind of alternative, and devises a kind of ratio inhibition side Method lies about the trend of the higher unit value of perception task to be compressed in Nash Equilibrium, therefore it improves societies to receive Benefit.
Simulation result further demonstrates that inner parameter (that is, the number of requestor, the number of worker, the multiplicity of task value Property, the diversity of worker's cost) to the quantity of runing time, participation worker, the influence of optimal reward and community income.Largely Numerically modeling shows that our method is with good performance, this truly states the unit of its perception task with each requestor The special circumstances of value are suitable.
Detailed description of the invention
Fig. 1 is the mobile gunz sensory perceptual system structural schematic diagram using multitask pricing method provided by the invention；
Fig. 2 is the unified runing time and inner parameter relational graph for paying (UPD) mechanism of determination, when wherein Fig. 2 (a) is run Between with requestor's quantity m relational graph；Fig. 2 (b) is runing time and number of workers n relational graph；
Fig. 3 is to participate in number of workers to the interior influence in parameter；Wherein Fig. 3 (a) is to participate in number of workers to be worth task Diversity influence；Fig. 3 (b) is to participate in number of workers to influence the diversity of worker's cost；
Fig. 4 is γ ° of optimal reward unit and inherent parameter-relation chart；Wherein Fig. 4 (a) is γ ° of optimal reward unit and ask The person's of asking quantity m relational graph；Fig. 4 (b) is γ ° of optimal reward unit and number of workers n relational graph；Fig. 4 (c) is optimal reward unit The γ ° of diversity relational graph being worth with task；Fig. 4 (d)；It is the diversity relational graph of optimal γ ° of unit of reward and worker's cost；
Fig. 5 is the normalization performance for inner parameter；Wherein Fig. 5 (a) is normalization performance and requestor's quantity m relationship Figure；Fig. 5 (b) is normalization performance and number of workers n relational graph；Fig. 5 (c) is the diversity pass for normalizing performance and task value System's figure；Fig. 5 (d)；It is the diversity relational graph for normalizing performance and worker's cost.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below each other it Between do not constitute conflict and can be combined with each other.
The mobile intelligent perception multitask pricing method based on game that the present invention provides a kind of, comprising the following steps:
(1) current all user roles and its corresponding task are obtained, that is, is obtained:
Requestor set R={ r1..., rm, requestor rjThe task τ of publicationjSet of tasks T={ the τ of composition1..., τmAnd task τjUnit value κjThe unit value set K={ κ of composition1..., κm}；And:
Worker set W={ w1..., wn, each worker wiUnit cost ciThe unit cost set C=of composition {c1..., cn}；
(2) according to the user role of step (1) acquisition and its corresponding task, worker w is obtainediIncome viAnd requestor rjIncome ujWhen maximizing it respectively, the relationship of the two and unit reward γ；
The worker wiIncome viIt maximizes, it may be assumed that
Wherein, citijIt is the perceived cost w of workeri, ci∈ C is the unit cost of worker, C={ c1..., cnIt is worker The unit cost set of worker, t can be used in set WijIt is worker wiTo task τjDetecting period, txjIt is worker wxTo task τj Detecting period, vijFor user wiParticipate in task τjWhen income, viFor vi=maxJ≤[1, m]vij, γj=κjγ, γ are units Reward.
The requestor rjIncome ujIt maximizes, it may be assumed that
Wherein,It is requestor rjTo worker's detecting period collection WjEvaluation function；txjIt is worker wxTo task τjDetecting period；κjIt is task τjUnit value；γj=kjγ, γ are unit rewards；θ ∈ (0,1), so that ujInIn be strictly concave function, reflect the universal phenomenon of marginal income decreasing in economics.
(3) the worker w that the user role and its corresponding task and step (2) obtained according to step (1) obtainsiReceipts Beneficial viAnd requestor rjIncome ujWith unit reward γ relationship, determine unit reward γ, obtain task set of rewards Γ= {γ1..., γm}；Wherein unit reward γ meets:
Wherein, V is social integral benefit, viFor worker wiIncome vi=maxJ≤[1, m]vij, vijFor worker wiParticipation task τjWhen income (see formula 1), ujFor requestor rjIncome (see formula 2), siTo select task τiWorker set selected by Set of tasks, ti>=0 is artificial detecting period, κj>=0 is task τjUnit value.
For set of tasks T={ τ1..., τmTask τj, task reward γj=κjγ remembers task set of rewards Γ ={ γ1..., γm}；
(4) it rewards γ according to the unit obtained in step (3), determines that the unified of the system pays the mechanism of determination, i.e., (R, T, K, W, C, Γ)；Wherein R is requestor's set R={ r1..., rm, T is the set of tasks T={ τ of publication1..., τm, K The unit value set K={ κ answered for the set of tasks T-phase of publication1..., κm, C is worker's set W={ w1..., wnPhase The unit cost set answered, C={ c1..., cn, and c1≤…≤cn, Γ is the set of rewards that the set of tasks T-phase of publication is answered Γ={ γ1..., γm, γ1≥…≥γm, γj=κjγ, γ are unit reward.
(5) in the case where the given unified payment of step (4) acquisition determines mechanism i.e. (R, T, K, W, C, Γ), according to Stark that Burger model Nash Equilibrium state determines the optimal perception planning strategy Π of worker*And each worker wiOptimal detecting period Strategy
The optimal perception planning strategy of worker To use optimal Worker w when business selection strategyiThe set of tasks of selection,For using worker w when OPTIMAL TASK selection strategyiDetecting period； Worker wiOptimal detecting period strategyIt is for allSo that worker wj∈WjIncome It maximizes and obtains worker wj∈WjMaximum return
Wherein c1≤c2≤…≤cl, andL is to task τjSense The number of workers of interest；t-ijTo remove other than worker i, other workers participate in task τjDetecting period collection.
The specific method is as follows:
Worker w1With the smallest unit cost c1, determine that its OPTIMAL TASK selection strategy isThat is worker w1Choosing It selects and rewards γ with highest1Task τ1, and so on worker will press its competitiveness sequential selection task:
It is given that there is corresponding reward γjPerception task τjWith the set W of interested workerj={ w1..., wl, and Optimal detecting period strategyWherein:
By WjIn worker according to CjMiddle unit cost is ranked up, i.e. c1≤c2≤…≤cl, enable ε is a sufficiently small positive number, is 0.01 or smaller, and l is to task τj Interested number of workers.
For giving γj, Wj={ w1..., wlAnd its corresponding cost set Cj={ c1..., cl, worker wj∈Wj Maximum returnAre as follows:
Wherein c1≤c2≤…≤cl, and
(6) the optimal perception planning strategy of worker obtained according to step (5)Given is asked The task τ that the person of asking submitsjTrue unit valueBased on Stackelberg Model Nash Equilibrium shape State formulates optimal γ ° of publishing policy of reward, makes community income's V=∑ for all γ >=0I ∈ [1, n]vi+∑J ∈ [1, m]ujIt maximizes, Wherein viFor worker wiIncome, ujFor requestor rjIncome.
Specific step is as follows:
The task τ that (6-1) acquisition request person submitsjTrue unit valueGive
(6-2) is according to the true unit value obtained in step (6-1)And in step (5) The optimal perception planning strategy of the worker of acquisitionIt is obtained based on Stackelberg Model Nash Equilibrium state The optimum value for the person of calling request states strategy
Optimum value statement strategy obtains according to the following steps:
Existing set of tasks T={ τ1..., τm, Γ be publication set of tasks T-phase answer set of rewards Γ= {γ1..., γm, γ1≥…≥γm, γj=κjγ, γ are unit reward；For not yet stating unit valence in set of tasks T Highest task τ is rewarded in all tasks of valuej, its unit value of initialization statementAnd appoint according to currently stating The unit value of businessThe unit value stated when being higher than all tasks of the task using optimal statement strategy with reward Iteration updates the unit value of its statementUntil its requestor income obtained, which increases, is less than default threshold Value, then using the unit value for the task stated at this time as the sound when requestor is tactful using optimal statement to the task Bright unit value.
All tasks that the unit value for the task that the basis is currently stated and reward are higher than the task use The calculation method for the unit value that the unit value iteration stated when optimal statement strategy updates its statement is as follows:
Wherein, (0,1) θ ∈, txjFor the optimal perception planning strategy Π of worker*Lower worker wXParticipate in the task τjPerception Time,The task τ that requestor submitsjTrue unit value,
The income method for calculating its requestor is shown in formula (2).
(6-3) states strategy according to the optimum value that step (6-2) obtains, and determines ratio inhibiting factor φ, obtains optimal γ ° of publishing policy of reward.
The ratio inhibiting factor φ meets following constraint:
γ ° of publishing policy of optimal reward, γ ° is the maximum value for meeting the following γ constrained:
Wherein,
Wherein, (0,1) θ ∈, θ make u in this rangejInIn be strictly concave function；cxFor detecting period tij The unit cost of >=0 worker, x are variable, indicate some worker；cyFor worker wyUnit cost；In order to see formula Succinctly, to enable zj=| Wj| -1,For using worker w when OPTIMAL TASK selection strategyiThe set of tasks of selection,
The following are embodiments:
System model:
As shown in Figure 1, MSE application program is made of the MCS platform with multiple smart phone users, wherein in system Each user can provide service to other users.The example of service includes expertise, information resources, computing capability, storage The process of the .MSE application program such as space can be described as follows:
1. firstly, each user in system can choose as requestor or worker；
2. each requestor issues perception task with its unit value, which is sent to MCS platform；
3. after platform receives a group task, each worker selects to participate in perception task after reading its particular content；
4. each worker determines the personal detecting period to task；
5. after worker collects perception plan, MCS platform calculates the expense of each required by task payment, and to requestor's rope Pay expense；
6. by reimbursement of expense to worker；
7. selected worker will execute perception task and be sent to the perception data for the service that requestor is required to meet Requestor.This completes MSE processes.
When worker selects to participate in the multi-task, it is considered as multiple workers；When requestor issues multiple perception tasks, it is considered as Multiple requestors.
The mobile intelligent perception multitask pricing method based on game applied to the system model, comprising the following steps:
(1) current all user roles and its corresponding task are obtained, that is, is obtained:
Requestor set R={ r1..., rm, requestor rjThe task τ of publicationjSet of tasks T={ the τ of composition1..., τmAnd task τjUnit value κjThe unit value set K={ κ of composition1..., κm}；And:
Worker set W={ w1..., wn, each worker wiUnit cost ciThe unit cost set C=of composition {c1..., cn}；
In MSE system, user decides whether request service (being selected to requestor or worker).If user selects As requestor, then need to pay enough rewards to attract worker as much as possible to participate in the task of its publication, this is usually Requestor with high budget provides competitive advantage.If user selection be known as worker, will by study publication task and The information of other users selfishly determines personal perception plan noti, to maximize personal income.Decision is sequential: The decision of role selecting is made first, followed by rewards decision, is finally perception planning decision-making.
(2) according to the user role of step (1) acquisition and its corresponding task, worker w is obtainediIncome viAnd requestor rjIncome ujWhen maximizing it respectively, the relationship of the two and unit reward γ；
The worker wiIncome viIt maximizes, it may be assumed that
Wherein, citijIt is the perceived cost w of workeri, ci∈ C is the unit cost of worker, C={ c1..., cnIt is worker The unit cost set of worker, t can be used in set WijIt is worker wiTo task τjDetecting period, txjIt is worker wxTo task τj Detecting period, vijFor user wiParticipate in task τjWhen income, viFor vi=maxJ≤[1, m]vij, γj=κjγ, γ are units Reward.
The requestor rjIncome ujIt maximizes, it may be assumed that
Wherein,It is requestor rjTo worker's detecting period collection WjEvaluation function；txjIt is worker wxTo task τjDetecting period；κjIt is task τjUnit value；γj=κjγ, γ are unit rewards；θ ∈ (0,1), so that ujInIn be strictly concave function, reflect the universal phenomenon of marginal income decreasing in economics.
(3) the worker w that the user role and its corresponding task and step (2) obtained according to step (1) obtainsiReceipts Beneficial viAnd requestor rjIncome ujWith unit reward γ relationship, determine unit reward γ, obtain task set of rewards Γ= {γ1..., γm}；Wherein unit reward γ meets:
Wherein, V is social integral benefit, viFor worker wiIncome vi=maxJ≤[1, m]vij, vijFor worker wiParticipation task τjWhen income (see formula 1), ujFor requestor rjIncome (see formula 2), siTo select task τiWorker set selected by Set of tasks, ti>=0 is artificial detecting period, κj>=0 is task τjUnit value.
For set of tasks T={ τ1..., τmTask τj, task reward γj=κjγ remembers task set of rewards Γ ={ γ1..., γm}；
(4) it rewards γ according to the unit obtained in step (3), determines that the unified of the system pays the mechanism of determination, i.e., (R, T, K, W, C, Γ)；Wherein R is requestor's set R={ r1..., rm, T is the set of tasks T={ τ of publication1..., τm, K The unit value set K={ κ answered for the set of tasks T-phase of publication1..., κm, C is worker's set W={ w1..., wnPhase The unit cost set answered, C={ c1..., cn, and c1≤…≤cn, Γ is the set of rewards that the set of tasks T-phase of publication is answered Γ={ γ1..., γm, γ1≥…≥γm, γj=κjγ, γ are unit reward.
In order to encourage rationality, selfish user more energetically to participate in perception task, and the positive contribution in the task of participation The perception data of high quality, we introduce the concept of ideal money in systems, are only limitted to recycle in system.We devise It is a kind of by ideal money rather than the incentive mechanism of monetary incentive, this incentive mechanism are opened by indirect reciprocal key concepts Hair.Under this mechanism, user is obtained when being selected to worker for providing the ideal money of service, and is being selected to ask Consumption is for receiving the ideal money of service when the person of asking.Requestor in MSE system contends with one other to attract work as much as possible On the one hand people participates in the task of themselves publication, on the other hand, contend with one other between worker to obtain higher reward.We Propose it is a kind of MSE, referred to as UPD are solved the problems, such as based on the incentive mechanism of ideal money, this is that a kind of unified payment determines (Unified Payment DEtermination abbreviation), the unit reward of the perception task for determining all publications.
(5) in the case where the given unified payment of step (4) acquisition determines mechanism i.e. (R, T, K, W, C, Γ), according to Stark that Burger model Nash Equilibrium state determines the optimal perception planning strategy Π of worker*And each worker wiOptimal detecting period Strategy
The optimal perception planning strategy of worker To use optimal Worker w when business selection strategyiThe set of tasks of selection,For using worker w when OPTIMAL TASK selection strategyiDetecting period；Work People wiOptimal detecting period strategyIt is for allSo thatIt maximizes；t-ijIt is used to remove Other than the i of family, other users participate in task τjDetecting period collection.
The specific method is as follows:
Worker w1With the smallest unit cost c1, determine that its OPTIMAL TASK selection strategy isThat is worker w1Choosing It selects and rewards γ with highest1Task τ1, and so on worker will press its competitiveness sequential selection task:
It is given that there is corresponding reward γjPerception task τjWith the set W of interested workerj={ w1..., wl, and Optimal detecting period strategyWherein:
By WjIn worker according to CjMiddle unit cost is ranked up, i.e. c1≤c2≤…≤cl, enable ε is a sufficiently small positive number, is 0.01 or smaller, and l is to task τj Interested number of workers.
For giving γj, Wj={ w1..., wlAnd its corresponding cost set Cj={ c1..., cl, worker wj∈Wj Maximum returnAre as follows:
Wherein c1≤c2≤…≤cl, and
The purpose of design UPD mechanism is to establish balanced (SE) point of an ideal Stackelberg, and requestor and worker are Motivation deviation is not had, and realizes the case where cooperating with each other with each user selection comparable high-performance.For given one Group reward solves perception first and plans to determine (SPD) game.Then the optimal solution Π of the worker obtained is utilized*, we solve to encourage It encourages and states to determine (RDD) game to obtain the set K of optimal issuing unit's value*。
Under the assumptions, the SPD game Nash Equilibrium that this method obtains is unique Nash Equilibrium of SPD game.
Following algorithm specifically can be used:
The time complexity of algorithm 1 is O (mnlog n), this is dominated by circulation.
According to equation (4) and equation (5), we conclude that, the unit cost of worker is lower, more competitive.By In worker w1With the smallest unit cost c1, the OPTIMAL TASK selection strategy of the worker is(3-4 row).According to Lemma 2, even if there is other workers to select participation task t1, worker w1Its task selection policy will not be changedDue to ability The arrival of weak worker, the strong worker of ability will not select to abandon its currently participating in for task.Worker will be by the suitable of its competitiveness Sequence selects task (5-20 row).
Next, we can calculate the optimal detecting period strategy of each worker according to equation (4) (21-22 row). According to lemma 1, if the unit cost of a worker is sufficiently high, which is from the income for participating in obtaining in all tasks Negative, then the optimal policy of the worker is exactly to be not involved in any task (23-24 row).
As a result, the output of algorithm 1 is unique NE of SPD game.
Showing that the lesser worker of unit cost has stronger competitiveness, this worker will contribute more detecting periods, And obtain higher income.The worker of rationality tends to participate in the higher task of reward, and as much as possible not with other Worker's competition.This generates the concepts of OPTIMAL TASK selection strategy, the i.e. Nash Equilibrium of RDD game.
(6) the optimal perception planning strategy of worker obtained according to step (5)Given is asked The task τ that the person of asking submitsjTrue unit valueBased on Stackelberg Model Nash Equilibrium State formulates optimal γ ° of publishing policy of reward, makes community income's V=∑ for all γ >=0I ∈ [1, n]vi+∑J ∈ [1, m]ujIt is maximum Change, wherein viFor worker wiIncome, ujFor requestor rjIncome.
Specific step is as follows:
The task τ that (6-1) acquisition request person submitsjTrue unit valueGive
(6-2) is according to the true unit value obtained in step (6-1)And in step (5) The optimal perception planning strategy of the worker of acquisitionIt is obtained based on Stackelberg Model Nash Equilibrium state The optimum value for the person of calling request states strategy
Optimum value statement strategy obtains according to the following steps:
Existing set of tasks T={ τ1..., τm, Γ be publication set of tasks T-phase answer set of rewards Γ= {γ1..., γm, γ1≥…≥γm, γj=κjγ, γ are unit reward；For not yet stating unit valence in set of tasks T Highest task τ is rewarded in all tasks of valuej, its unit value of initialization statementAnd appoint according to currently stating The unit value of businessThe unit value stated when being higher than all tasks of the task using optimal statement strategy with reward Iteration updates the unit value of its statementUntil its requestor income obtained, which increases, is less than default threshold Value, then using the unit value for the task stated at this time as the sound when requestor is tactful using optimal statement to the task Bright unit value.
All tasks that the unit value for the task that the basis is currently stated and reward are higher than the task use The calculation method for the unit value that the unit value iteration stated when optimal statement strategy updates its statement is as follows:
Wherein, (0,1) θ ∈, txjFor the optimal perception planning strategy Π of worker*Lower worker wXParticipate in the task τjPerception Time,The task τ that requestor submitsjTrue unit value,
The income method for calculating its requestor is shown in formula (2).
The present embodiment calculates Stackelberg Model Nash Equilibrium state using following algorithm
The algorithm guarantee restrain and export be RDD game unique Nash Equilibrium.Its time complexity mainly takes Certainly in ∈.
(6-3) states strategy according to the optimum value that step (6-2) obtains, and determines ratio inhibiting factor φ, obtains optimal γ ° of publishing policy of reward.
The ratio inhibiting factor φ meets following constraint:
γ ° of publishing policy of optimal reward, γ ° is the maximum value for meeting the following γ constrained:
Wherein,
Wherein, (0,1) θ ∈, θ make u in this rangejInIn be strictly concave function；cxFor detecting period tijThe unit cost of >=0 worker, x are variable, indicate some worker；cyFor worker wyUnit cost；In order to see formula Succinctly, to enable zj=| Wj| -1,For using worker w when OPTIMAL TASK selection strategyiThe set of tasks of selection,
Emulation experiment:
We provide numerical result to assess it is proposed that being the performance of the incentive mechanism of the MSE problem design in MCS. As shown in Figure 1, it will be assumed that exciting torque person explores user and (including all available ask from the angle of MCS platform The person of asking and worker) strategy, it is intended to maximize the summation of its income.
The realization of the incentive mechanism proposed includes four-stage:
(i) each user carries out role selecting first, then platform measuring inner parameter C={ c1..., cn, and ask The person of asking assesses the set of unit value corresponding with its perception task
(ii) requestor will be distributed according to the cost of worker assesses its prospective earnings, and reports effective unit value set.
(iii) community income of platform evaluation system calculates the optimal value of φ according to equation (7) and optimal design is joined γ ° of number.
(iv) by comparing the gap between the theoretical value and real value of social welfare, Protocol Design person updates design Practical value of the parameter to augment social welfare.
The aforementioned four stage is divided into two parts: (1) stage (i) by us, and the direct implementation of (ii) and (iii) is a wheel Implement, the assessment result obtained based on Section III part.(2) bargaining in (iv) stage is discussed in a manner of repetition test. This is because the possible Imperfect Rationality of user in true MCS scene, therefore Mechanism Design person should attempt gradually to update γ ° So as to closer theoretical value.
Performance indicators includes runing time, participates in number of workers, optimal reward unit and community income.In our experiment In, it will be assumed thatValue Gaussian distributed(we fix μ here1=50), And its boundary value is defined as (0,100).
WhereinBecause x ∈ (0,100) andWe have f (x) ∈ (0,100).
Similarly, it will be assumed that ci,Value Gaussian distributed(here we Fixed μ2=5), and by its boundary value it is defined as (0,10).
WhereinBecause y ∈ (0,10) andWe have f (y) ∈ (0,10).
The realization written in Java of our mechanism.All experiments are carried out on standard desktop computer, main Configuring is processor for Intel Conroe, and running frequency is the four core CPU i7-4790 of 3.6GHz, inside saves as DDR3L 16GB 1600MHz and operating system are 7 Ultimate of Microsoft Windows.For each example, 10 are run at random The test case of generation, and figure is generated using the average value of test result.
It is directed to runing time, Fig. 2 depicts the UPD mechanism of suggestion and runing time (a) available requests of inherent parameter The quantity m and (b) of person can use worker number n, and wherein we fixAs shown in the results, the runing time of UPD As the quantity of requestor is increased monotonically, as shown in Fig. 2 (a).Herein, we determined that n=500. is same, runing time with We determined that the number of workers of m=20 is increased monotonically, as shown in Fig. 2 (b).In general, runing time is influenced by worker's quantity Greater than the quantity of requestor, such result is consistent with the time complexity of algorithm 1, because of the runing time of calculation equation (8) It is dominated by algorithm 1.
It is directed to number of workers, Fig. 3, which is shown, participates in number of workers to the interior influence in parameter (a): (a)(b)(b)Influence.WhereinWithValue it is bigger, then the difference for organizing the value in K and C is bigger.In Fig. 3 (a), N=500, m=20 is arranged in we, and=1, and allowChange from 0.5 to 5, increment 0.5.It shows to participate in the quantity of worker It is increased monotonicallyThe main reason for this phenomenon behind is that task value variance is bigger, and the higher worker of cost is more possible to It avoids competing with inexpensive user, to there is more chances to participate in low value task.In Fig. 3 (b), n=500, m is arranged in we =20,And changeFrom 0.5 to 5, increment 0.5.It has been observed that participate in staff quantity withIt is single It adjusts and reduce few.This is because the unit cost difference between worker is bigger, Gao Chengben worker participates in task and is got over obtaining positive income Difficulty, therefore selection is abandoned.
It is directed to optimal reward unit, Fig. 4 has investigated n, m,WithInfluence to optimal reward unit γ.In Fig. 4 (a) in, it is observed that γ is with m monotonic increase, wherein n=500 is arranged in we,With requestor's quantity Increase and perception task quantity, worker has more selections freely.In order to attract worker to contribute more detecting periods, It is necessarily increased reward unit.From Fig. 4 (b) as can be seen that the value of γ is with n monotone decreasing, wherein we fix m=20, With the increase of number of workers, competition becomes fiercer.
Therefore unit reward can suitably be reduced.With intuition on the contrary, γ ° hardly byInfluence, such as Fig. 4 (c) institute Show.This is because participate in worker quantity withThe task of monotonic increase (see Fig. 3 (a)), high value can attract enough numbers The worker of amount, and the work of low value is often abandoned because attraction is insufficient.Therefore, γ ° value fluctuation, to entire effect compared with It is small.In Fig. 4 (d), with given n=500, m=20 andThe unit cost of worker becomes more diversified, optimal Return γ ° withMonotone decreasing.Main cause be participate in number of workers withMonotone decreasing (see Fig. 3 (b)), system need γ ° is reduced, this can inhibit the competitive advantage of inexpensive worker, and the participation for improving worker is horizontal, to augment social welfare.
It is directed to community income, Fig. 5 has evaluated proposed UPD mechanism to interior in parameter m, n,WithIt (is expressed as) performance.In order to compare, it is contemplated that the unit value for the perception task really stated based on requestor (is expressed as) The NE calculated with algorithm 2 (is expressed as) community income calculating.From Fig. 5 (a) as can be seen that with requestor's quantity Increase, we fix n=500 andWorker has more selections freely, keen competition is avoided, to improve Community income.Although fixed in Fig. 5 (b) m=20 andBut observe that community income is certain as n increases Show decreasing returns.This is because higher worker n introduces higher competition, to reduce total contribution aware time. In Fig. 5 (c), we fix n=500, m=20 andCommunity income's fluctuation, but overall return is still on 4.30 left sides It is right.It explains that this phenomenon needs to combine Fig. 3 (a) and Fig. 4 (c), as the unit cost of worker becomes more diversified, participates in work The quantity monotone decreasing of people, and unit reward is almost unchanged, becauseChange between 0.5 to 5, byWithIt calculates Community income keeps relative stability.Fig. 5 (d) is consistent with the situation in Fig. 5 (c), and reason is similar.Generally speaking,Reach Good performance, withQuite (it is not balance thus cannot achieve), but be higher than
Herein, it is proposed that the theoretical frame of the incentive mechanism based on Stackelberg game, to motivate user's Quality data is played an active part in and provides, to realize good service quality.Firstly, the MSE problem in MCS is modeled as being based on The MSE problem of the more follower's compositions of more leaders of Stackelberg game.Secondly, based on indirectly reciprocal key idea, In Balanced service request and service provide between user, and the concept of ideal money is introduced into the design of incentive mechanism.Third mentions A kind of effective algorithm is gone out and has determined unique Nash Equilibrium of game to calculate perception plan, and has proposed and a kind of walked by m The new algorithm that Cheng Shixian low complex degree calculates finds unique Nash Equilibrium that tactful game is stated in reward in another way.This Outside, a kind of ratio suppressing method is devised, for compressing the perception task unit value that do not state really in Nash Equilibrium, to mention High community income.Finally, simulation result further demonstrates how inherent parameter influences runing time, number of workers is participated in, most Excellent reward unit and community income.Most of all, our method realizes good performance, this is honest with each requestor State that the special circumstances of the unit value of its perception task are suitable in ground.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include Within protection scope of the present invention.

Claims (10)

1. a kind of mobile intelligent perception multitask pricing method based on game, which comprises the following steps:
(1) current all user roles and its corresponding task are obtained, that is, is obtained:
Requestor set R={ r1..., rm, requestor rjThe task τ of publicationjSet of tasks T={ the τ of composition1..., τm}、 And task τjUnit value κjThe unit value set K={ κ of composition1..., κm}；And:
Worker set W={ w1..., wn, each worker wiUnit cost ciThe unit cost set C={ c of composition1..., cn}；
(2) according to the user role of step (1) acquisition and its corresponding task, worker w is obtainediIncome viAnd requestor rj's Income ujWhen maximizing it respectively, the relationship of the two and unit reward γ；
(3) the worker w that the user role and its corresponding task and step (2) obtained according to step (1) obtainsiIncome viWith And requestor rjIncome ujWith unit reward γ relationship, determine unit reward γ, obtain task set of rewards Γ= {γ1..., γm}；
(4) it rewards γ according to the unit obtained in step (3), determines that the unified of the system pays the mechanism of determination, i.e., (R, T, K, W, C, Γ)；Wherein R is requestor's set R={ r1..., rm, T is the set of tasks T={ τ of publication1..., τm, K is hair The unit value set that the set of tasks T-phase of cloth is answered, K={ κ1..., κm, C is worker's set W={ w1..., wnCorresponding Unit cost set, C={ c1..., cn, and c1≤…≤cn, Γ be publication set of tasks T-phase answer set of rewards Γ= {γ1..., γm, γ1≥…≥γm, γj=κjγ, γ are unit reward；
(5) in the case where the given unified payment that step (4) obtain determines mechanism i.e. (R, T, K, W, C, Γ), according to Stackelberg mould Type Nash Equilibrium state determines the optimal perception planning strategy ∏ of worker*And each worker wiOptimal detecting period strategy
(6) the optimal perception planning strategy of worker obtained according to step (5)For given requestor The task τ of submissionjTrue unit valueBased on Stackelberg Model Nash Equilibrium state γ ° of publishing policy of optimal reward is formulated, community income's V=∑ is made for all γ >=0I ∈ [1, n]vi+∑J ∈ [1, m]ujIt maximizes, Middle viFor worker wiIncome, ujFor requestor rjIncome.
2. the mobile intelligent perception multitask pricing method based on game as described in claim 1, which is characterized in that step (1) with step (2) described worker wiIncome viIt maximizes, it may be assumed that
Wherein, citijIt is the perceived cost w of workeri, ci∈ C is the unit cost of worker, C={ c1..., cnIt is worker's set W In can use worker unit cost set, tijIt is worker wiTo task τjDetecting period, txjIt is worker wxTo task τjPerception Time,vijFor user wiParticipate in task τjWhen income, vi=maxJ≤[1, m]vij, γj=κjγ, γ are unit rewards.
3. the mobile intelligent perception multitask pricing method based on game as described in claim 1, which is characterized in that step (1) with step (2) described requestor rjIncome ujIt maximizes, it may be assumed that
Wherein,It is requestor rj to worker's detecting period collection WjEvaluation function；txjIt is worker wxIt is right Task τjDetecting period；κjIt is task τjUnit value；γj=κjγ, γ are unit rewards；θ ∈ (0,1), so that ujInIn be strictly concave function, reflect the universal phenomenon of marginal income decreasing in economics.
4. the mobile intelligent perception multitask pricing method based on game as described in claim 1, which is characterized in that step (3) wherein unit reward γ meets:
Wherein, V is social integral benefit, viFor worker wiIncome vi=maxJ≤[1, m]vij, vijFor worker wiParticipate in task τjWhen Income (see formula 1), ujFor requestor rjIncome (see formula 2), siTo select task τiWorker gather selected Business set, ti>=0 is worker's detecting period, κj>=0 is task τjUnit value.
For set of tasks T={ τ1..., τmTask τj, task reward γj=κjγ, note task set of rewards Γ= {γ1..., γm}。
5. the mobile intelligent perception multitask pricing method based on game as described in claim 1, which is characterized in that step (5) the optimal perception planning strategy of the worker To be selected using OPTIMAL TASK Worker w when selecting strategyiThe task of selection,For using worker w when OPTIMAL TASK selection strategyiDetecting period；Worker wiMost Excellent detecting period strategyIt is for allSo thatIt maximizes and obtains worker wj∈WjMaximum Incomet-ijTo remove other than worker i, other workers participate in task τjDetecting period collection.
6. the mobile intelligent perception multitask pricing method based on game as claimed in claim 5, which is characterized in that step (5) worker wiOptimal detecting period strategyThe specific method is as follows for acquisition:
Worker w1With the smallest unit cost c1, determine that its OPTIMAL TASK selection strategy isThat is worker w1Selection has Highest rewards γ1Task τ1, and so on worker will press its competitiveness sequential selection task:
It is given that there is corresponding reward γjPerception task τjWith the set W of interested workerj={ w1..., wlAnd it is optimal Detecting period strategyWherein:
By WjIn worker according to CjMiddle unit cost is ranked up, i.e. c1≤c2≤…≤cl, enable ε is a sufficiently small positive number, and l is to task τjInterested worker's number Amount.
For giving γj, Wj={ w1,…,wlAnd its corresponding cost set Cj={ c1,…,cl, worker wj∈WjMaximum IncomeAre as follows:
Wherein c1≤c2≤…≤cl, and
7. the mobile intelligent perception multitask pricing method based on game as described in claim 1, which is characterized in that step (6) specifically includes the following steps:
The task τ that (6-1) acquisition request person submitsjTrue unit valueGive
(6-2) is according to the true unit value obtained in step (6-1)And it is obtained in step (5) The optimal perception planning strategy of workerIt is asked based on Stackelberg Model Nash Equilibrium state The optimum value for the person of asking states strategy
(6-3) states strategy according to the optimum value that step (6-2) obtains, and determines ratio inhibiting factor φ, obtains optimal reward γ ° of publishing policy.
8. the mobile intelligent perception multitask pricing method based on game as claimed in claim 7, which is characterized in that step (6-2) optimum value statement strategy obtains according to the following steps:
Existing set of tasks T={ τ1,…,τm, Γ is set of rewards Γ={ γ that the set of tasks T-phase of publication is answered1,…, γm, γ1≥…≥γm, γj=κjγ, γ are unit reward；For not yet stating all of unit value in set of tasks T Highest task τ is rewarded in taskj, its unit value of initialization statementAnd according to the unit for the task currently stated ValueThe unit value iteration stated when being higher than all tasks of the task using optimal statement strategy with reward updates Its unit value stated Until its requestor income obtained, which increases, is less than preset threshold, then by this The unit value of the task of Shi Shengming is as the unit stated when requestor is tactful using optimal statement to the task Value.
The unit value for the task that the basis is currently stated and reward are higher than all tasks of the task using optimal The calculation method for the unit value that the unit value iteration stated when statement strategy updates its statement is as follows:
Wherein, (0,1) θ ∈, txjFor the optimal perception planning strategy Π of worker*Lower worker wXParticipate in the task τjDetecting period,The task τ that requestor submitsjTrue unit value,
The income method for calculating its requestor is shown in formula (2).
9. the mobile intelligent perception multitask pricing method based on game as claimed in claim 7, which is characterized in that step (6-3) described ratio inhibiting factor φ meets following constraint:
10. the mobile intelligent perception multitask pricing method based on game as claimed in claim 7, which is characterized in that step (6-3) described γ ° of publishing policy of optimal reward, γ ° is the maximum value for meeting the following γ constrained:
Wherein,
Wherein, (0,1) θ ∈, θ make u in this rangejInIn be strictly concave function；cxFor detecting period tij≥0 Worker unit cost, x is variable, indicates some worker；cyFor worker wyUnit cost；In order to seem formula Succinctly, z is enabledj=| Wj| -1,For using worker w when OPTIMAL TASK selection strategyiThe set of tasks of selection,
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