CN105760350A - Efficient calculation method for cooperative game value based on probability distribution - Google Patents

Abstract

The invention discloses an efficient calculation method for a cooperative game value based on probability distribution. The efficient calculation method includes the steps that the numbers of players and corresponding alliance payment data, on various alliance combination conditions, of a cooperative game are obtained; alliance types are distinguished according to the numbers of players on the various alliance combination conditions, the corresponding alliance payment data is combined, probability distribution is used for calculating the cooperative game value in steps from a conditional probability perspective, and therefore efficient calculation of the cooperative game value is realized. According to the scheme, the calculation amount of the cooperative game value is reduced substantially, whether being a Shapley value or a Banzhaf value, the cooperative game value can be calculated more efficiently, and application of cooperative game to the practice field is promoted.

Description

Efficient calculation method of cooperative game value based on probability distribution

Technical Field

The invention relates to the technical field of data processing, in particular to a high-efficiency calculation method of cooperative game values based on probability distribution.

Background

At present, the use of the cooperative game is more and more, and the cooperative game has various applications in various practical aspects such as emergency material storage, market company stock right analysis, cost allocation of environmental protection and the like. In the solving process of the application fields, the operation efficiency is greatly reduced along with the increase of the number of people in the game, and the application range of the cooperative game is severely limited. On the other hand, in the current research process of the cooperative game, axiomatic pictures are also emphasized too much, and the guiding performance of practice is insufficient.

Disclosure of Invention

The invention aims to provide a high-efficiency calculation method of a cooperative game value based on probability distribution, which greatly reduces the calculation amount of the cooperative game value, so that the cooperative game value can be calculated more efficiently no matter the cooperative game value is a Shapley value or a Banzhaf value, and the cooperative game is promoted to be applied to the practical field.

The purpose of the invention is realized by the following technical scheme:

a method for efficiently calculating cooperative game values based on probability distribution comprises the following steps:

acquiring the number of players in the game and corresponding alliance payment data of the cooperative game under each alliance combination condition;

and distinguishing the alliance types according to the number of people in the station under the condition of each alliance combination, and calculating the value of the cooperative game step by step at the angle of conditional probability by combining corresponding alliance payment data and using probability distribution, thereby realizing the high-efficiency calculation of the value of the cooperative game.

The step of distinguishing the alliance types according to the number of people in the station under each alliance combination condition, and calculating the value of the cooperative game step by step in the angle of the conditional probability by combining the corresponding alliance payment data and using the probability distribution comprises the following steps:

step S1, distinguishing the alliance types according to the number S of people in each alliance central office; the alliance with s being set to be 0 exists only, and the payment data of the alliance is 0; when s is equal to n, the coalition is the only big coalition, and n represents the total number of people in the cooperative game bureau;

step S2, determining a person i in the bureau needing to calculate the payment condition;

step S3, calculating an absolute value of a difference between the payment data of the office-free person i and the payment data of the office-free person i according to the order of the number S of the office in the federation from 0 to n-1, and storing the absolute values in a sorted manner according to the order of the number S of the office in the federation without the office-free person i, where the sorted manner is represented as: t0, T1,.... T (n-1);

step S4, calculating the arithmetic mean value of the numerical values in each category one by one according to the sequence of the categories T0-T (n-1) to obtain results A0, A1, A.

Step S5, judging that a Shapley value or a Banzhaf value needs to be calculated; if the Shapley value needs to be calculated, the procedure goes to step S6; if the Banzhaf value needs to be calculated, the step is switched to step S7;

step S6, Shapley value isAfter decomposition, becomes:wherein N represents a set of all federation components; v represents the corresponding payment data; s is a subset in N and represents a union; summing the mean values A0, A1 and the added value of the payment data obtained in the step S4, and dividing the sum by n to obtain the payment obtained by the person i in the bureau under the Shapley value distribution; repeating the steps S2-S6 until the payment obtained by all the persons in the bureau under the Shapley value distribution is calculated, so as to obtain the corresponding Shapley value result;

at step S7, the Banzhaf value isAfter decomposition, becomes:multiplying the mean value a0, a1, a (n-1) of the payment data added value obtained in step S4 by S corresponding to SThe weighted sum is calculated to obtain the payment obtained by the person i in the bureau under the distribution of the Banzhaf value; and repeating the steps S2-S7 until the payment obtained by all the people in the bureau under the Banzhaf value distribution is calculated, so as to obtain the corresponding Banzhaf value result.

The technical scheme provided by the invention can be seen that the problem of coefficient calculation in the process of calculating the Shapley value and the Banzhaf value is solved, wherein the Shapley value completely avoids the problem of coefficient calculation and is calculated by using an arithmetic mean value; and the Banzhaf value is not calculated by using an index any more, and a coefficient of binomial distribution is used as a substitute, so that the unification with the calculation of the Shapley value is achieved, and the calculation efficiency of the solution of the cooperative game can be well improved.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.

Fig. 1 is a flowchart of a method for efficiently calculating cooperative game values based on probability distribution according to an embodiment of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.

Fig. 1 is a flowchart of a method for efficiently calculating cooperative game values based on probability distribution according to an embodiment of the present invention. As shown in fig. 1, it mainly includes the following steps:

and 11, acquiring the number of players in the game and corresponding alliance payment data of the cooperative game under each alliance combination condition.

And 12, distinguishing alliance types according to the number of people in the station under each alliance combination condition, and calculating the value of the cooperative game step by step in the angle of conditional probability by combining corresponding alliance payment data and using probability distribution, so that the efficient calculation of the value of the cooperative game is realized.

The specific calculation steps are as follows:

step S1, distinguishing the alliance types according to the number S of people in each alliance central office; the alliance with s being set to be 0 exists only, and the payment data of the alliance is 0; when s is equal to n, the coalition is the only big coalition, and n represents the total number of people in the cooperative game bureau;

step S2, determining a person i in the bureau needing to calculate the payment condition;

step S3, calculating an absolute value of a difference between the payment data of the office-free person i and the payment data of the office-free person i according to the order of the number S of the office in the federation from 0 to n-1, and storing the absolute values in a sorted manner according to the order of the number S of the office in the federation without the office-free person i, where the sorted manner is represented as: t0, T1,.... T (n-1);

step S4, calculating the arithmetic mean value of the numerical values in each category one by one according to the sequence of the categories T0-T (n-1) to obtain results A0, A1, A.

Step S5, judging that a Shapley value or a Banzhaf value needs to be calculated; if the Shapley value needs to be calculated, the procedure goes to step S6; if the Banzhaf value needs to be calculated, the step is switched to step S7;

step S6, Shapley value isAfter decomposition, becomes:wherein N represents a set of all federation components; v represents the corresponding payment data; s is a subset in N and represents a union; summing the mean values A0, A1 and the added value of the payment data obtained in the step S4, and dividing the sum by n to obtain the payment obtained by the person i in the bureau under the Shapley value distribution; repeating the steps S2-S6 until the payment obtained by all the persons in the bureau under the Shapley value distribution is calculated, so as to obtain the corresponding Shapley value result;

at step S7, the Banzhaf value isAfter decomposition, becomes:multiplying the mean value a0, a1, a (n-1) of the payment data added value obtained in step S4 by S corresponding to SCoefficient of binomial distribution (i.e.) Then, the weighted sum is calculated to obtain the payment obtained by the person i in the bureau under the distribution of the Banzhaf value; and repeating the steps S2-S7 until the payment obtained by all the people in the bureau under the Banzhaf value distribution is calculated, so as to obtain the corresponding Banzhaf value result.

In the embodiment of the present invention, if it is not necessary to calculate the payments obtained by all the persons in the bureau, only the required persons in the bureau may be determined in step S2, and the number of cycles may be changed in step S6) and step 7).

The scheme of the embodiment of the invention avoids the problem of coefficient calculation in the process of calculating the Shapley value and the Banzhaf value, wherein the Shapley value completely avoids the problem of coefficient calculation and all uses the arithmetic mean value to calculate; and the Banzhaf value is not calculated by using an index any more, and a coefficient of binomial distribution is used as a substitute, so that the unification with the calculation of the Shapley value is achieved, and the calculation efficiency of the solution of the cooperative game can be well improved.

For ease of understanding, the following description is made in conjunction with a specific example.

It should be emphasized that the specific numerical values of the total number of people in the office and the payment data, etc. used in the following examples are only illustrative and not limiting. In practical application, a user can set a corresponding numerical value according to practical conditions.

In this example, it is assumed that there are 4 players in the cooperative game, i.e., n is 4, and the numbers of the 4 players are 1,2,3, and 4. The payment data for the 4 parties in the bureau and the payment data for the coalition they form are as follows:

$\begin{array}{c}v\left(1\right)=10,v\left(2\right)=25,v\left(3\right)=30,v\left(4\right)=25,v\left(\right\{1,2\left\}\right)=35,v\left(\right\{1,3\left\}\right)=35,v\left(\right\{1,4\left\}\right)=35,v\left(\right\{2,4\left\}\right)=40,\\ v\left(\right\{3,4\left\}\right)=10,v\left(\right\{1,2,3\left\}\right)=50,v\left(\right\{1,2,4\left\}\right)=50,v\left(\right\{1,3,4\left\}\right)=50,v\left(\right\{2,3,4\left\}\right)=50,v\left(\right\{1,2,3,4\left\}\right)=100\end{array}.$

the present example also uses the calculation step in the aforementioned step 12:

step S1, distinguishing the alliance types according to the number S of people in each alliance central office; the alliance with s being set to be 0 exists only, and the payment data of the alliance is 0; when s is 4, the coalition is the only big coalition.

In this example, S ═ 4 means that the federation S ═ {1,2,3,4 }; its payment data is large league payment v ({1,2,3,4}) ═ 100.

And step S2, determining the person i in the bureau needing to calculate the payment condition.

In this example, assume that the person in the office, i, who needs to calculate the payment situation is 1.

Step S3, calculating absolute values of differences between the payment data of the office-free person i and the payment data of the office-free person i according to the sequence of the number S of the office-free persons in the federation from 0 to 3, and storing the absolute values in a sorted manner according to the sequence of the number S of the office-free persons in the federation, where the sorted order is: t0, T1,.... T (n-1), table 1 below:

table 1 absolute value of payment data difference for a person in a hand i-1 under a given category

Wherein,for example, when s is 0,then there isIf S is 1, the union S is {2}, S is {3}, and S is {4} which does not include the person in the station i is 1, and the union S is calculated from the above equations

Step S4, calculating an arithmetic mean value of the values in each category one by one according to the sequence of categories T0 to T (n-1), to obtain results a0, a1, a.

TABLE 2 arithmetic mean of contributions in categories of 1 for person i in office

Step S5, judging that a Shapley value or a Banzhaf value needs to be calculated; if the Shapley value needs to be calculated, the procedure goes to step S6; if the Banzhaf value needs to be calculated, the process proceeds to step S7.

Step S6, Shapley value isAfter decomposition, becomes:wherein N represents a set of all federation components; v represents the corresponding payment data; s is a subset in N and represents a union; summing the mean values a0, a1, a.... a (n-1) of the payment data added value obtained in step S4, and dividing by 4 to obtain the payment obtained by the person in office i ═ 1 under the sharley value distribution; that is, the person in the office i is paid as 1

Repeating the above steps S2-S6 until all the payouts of the bureaus under the sharley value allocation are calculated, thereby obtaining the corresponding sharley value results, as shown in table 3:

person in office i	Shapley value
		i＝1	19.583
i＝2	26.25
		i＝3	27.917
i＝4	26.25
		Total up to	100

TABLE 3 Shapley values for all people in the office

At step S7, the Banzhaf value isAfter decomposition, becomes:multiplying the mean value a0, a1, a (n-1) of the payment data added value obtained in step S4 by S corresponding to SCoefficient of binomial distribution (i.e.) Then, the weighted sum is calculated to obtain the payment obtained by the person i in the bureau under the distribution of the Banzhaf value; that is, the person in the office i is paid as 1

Repeating the steps S2-S7 until the payment obtained by all the people in the bureau under the Banzhaf value distribution is calculated, thereby obtaining the corresponding Banzhaf value result; as in table 4 below:

TABLE 4 Banzhaf values of all people in the office

Through the above description of the embodiments, it is clear to those skilled in the art that the above embodiments can be implemented by software, and can also be implemented by software plus a necessary general hardware platform. With this understanding, the technical solutions of the embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a usb disk, a removable hard disk, etc.), and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods according to the embodiments of the present invention.

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (2)

1. An efficient calculation method of cooperative game values based on probability distribution is characterized by comprising the following steps:

acquiring the number of players in the game and corresponding alliance payment data of the cooperative game under each alliance combination condition;

and distinguishing the alliance types according to the number of people in the station under the condition of each alliance combination, and calculating the value of the cooperative game step by step at the angle of conditional probability by combining corresponding alliance payment data and using probability distribution, thereby realizing the high-efficiency calculation of the value of the cooperative game.

2. The method of claim 1, wherein the step of distinguishing the league types according to the number of people in the game in each league combination and calculating the value of the cooperative game in steps with conditional probability by using probability distribution in combination with corresponding league payment data comprises:

step S1, distinguishing the alliance types according to the number S of people in each alliance central office; the alliance with s being set to be 0 exists only, and the payment data of the alliance is 0; when s is equal to n, the coalition is the only big coalition, and n represents the total number of people in the cooperative game bureau;

step S2, determining a person i in the bureau needing to calculate the payment condition;

step S3, calculating an absolute value of a difference between the payment data of the office-free person i and the payment data of the office-free person i according to the order of the number S of the office in the federation from 0 to n-1, and storing the absolute values in a sorted manner according to the order of the number S of the office in the federation without the office-free person i, where the sorted manner is represented as: t0, T1,.... T (n-1);

step S4, calculating the arithmetic mean value of the numerical values in each category one by one according to the sequence of the categories T0-T (n-1) to obtain results A0, A1, A.

Step S5, judging that a Shapley value or a Banzhaf value needs to be calculated; if the Shapley value needs to be calculated, the procedure goes to step S6; if the Banzhaf value needs to be calculated, the step is switched to step S7;

step S6, Shapley value isAfter decomposition, becomes:wherein N represents a set of all federation components; v represents the corresponding payment data; s is a subset in N and represents a union; summing the mean values A0, A1 and the added value of the payment data obtained in the step S4, and dividing the sum by n to obtain the payment obtained by the person i in the bureau under the Shapley value distribution; repeating the steps S2-S6 untilCalculating the payment obtained by all the people in the bureau under the Shapley value distribution, thereby obtaining the corresponding Shapley value result;

at step S7, the Banzhaf value isAfter decomposition, becomes:multiplying the mean value a0, a1, a (n-1) of the payment data added value obtained in step S4 by S corresponding to SThe weighted sum is calculated to obtain the payment obtained by the person i in the bureau under the distribution of the Banzhaf value; and repeating the steps S2-S7 until the payment obtained by all the people in the bureau under the Banzhaf value distribution is calculated, so as to obtain the corresponding Banzhaf value result.