JP6789554B2 - Matching program, matching method and matching device - Google Patents

Description

Embodiments of the present invention relate to matching programs, matching methods and matching devices.

Conventionally, a serial dictatorship mechanism (hereinafter referred to as SD mechanism) is known in a matching process in which many applicants (for example, children of parents who wish to have childcare) are assigned to application targets (for example, childcare institutions). In the SD mechanism, applicants are prioritized, and the applicants with the highest priority are assigned to the remaining application targets at that time. This SD mechanism guarantees that priority inversion does not occur.

Svensson, Lars-Gunnar. "Strategy-proof allocation of indivisible goods." Social Choice and Welfare 16.4 (1999): 557-567.

However, in the above-mentioned conventional technique, there is a problem that it is difficult to appropriately assign to the application target when the applicant includes an applicant who requests coupling.

For example, when applying for multiple nursery schools, parents may request the coupling of siblings (brothers, siblings, siblings, sisters). Since the SD mechanism does not consider applicants with sibling coupling requests, appropriate matching results (assignments) may not be obtained when including applicants with sibling coupling requests. .. For example, in matching, any of the following problems 1 to 3 may occur.

Problem 1: The nursery school I want to enter has a person with a lower priority than me (regardless of only child / sibling).
Problem 2: As a sibling, a person (not necessarily a sibling) who has a lower priority than himself / herself is in the nursery school of his / her choice.
Problem 3: Even if the nursery school has a lower preference, it is better for the siblings to enter the same nursery school than to enter different nursery schools according to their individual priorities, but the siblings enter different nursery schools. ing.

14 to 16 are explanatory views for explaining the first to third cases. In the examples of FIGS. 14 to 16, the applicant 202a is matched with the application target 201a based on the same application target information 201 and the applicant information 202.

The application target information 201 is information about the application target 201a in which the number of people accepted in the application target 201a (nursery school in the illustrated example) is set in advance. In the illustrated example, the acceptance of two people is set at each nursery school of "S1" to "S3".

The applicant information 202 is information preset for the applicant 202a (child in the illustrated example) for each parental application. Specifically, the applicant information 202 is a score for determining the priority for each child ID that identifies the child to apply for in the application ID indicating the application, and a desired order indicating the order of the desired application target 201a. And are set. For example, the applicant 202a is given a priority in descending order of the score in the applicant information 202. When a plurality of child IDs are included in the same application ID, it is assumed that the children have a sibling relationship and there is a coupling request between the children.

As shown in FIG. 14, in the first case C1, the sibling relationship (coupling request) is ignored, and the applicant 202a is applied by the SD mechanism based on the application target information 201 and the applicant information 202. Assign to. Specifically, the application target 201a desired by the applicant 202a is assigned in order from the applicant 202a having the highest priority (in the order of I1, J1, K1, K2, L1, I2 in the illustrated example) (S201 to S206). ).

As described above, in the first case C1 in which the coupling request is ignored and the allocation is performed by the SD mechanism, the problem 3 occurs. Specifically, even in a nursery school with a low order of preference (for example, S2), K1 and K2 siblings do not enter the same nursery school but enter different nursery schools.

As shown in FIG. 15, in the second case C2, allocation is performed in a form summarized by a sibling relationship (coupling request) (S211 to S214). In the second case C2, when summarized in a sibling relationship, the scores of the coupled children are matched to the higher score.

As shown in FIG. 16, the third case C3 is also assigned in a form summarized by a sibling relationship (coupling request) (S221 to S224). In the third case C3, when summarized in a sibling relationship, the scores of the coupled children are matched to the lower score.

As described above, in the second case C2 and the third case C3 in which the allocation is performed in a form summarized according to the coupling request, the individual prioritization is distorted, which causes a problem 1. Specifically, in the second case C2, the applicant 202a of I2, which has a lower priority than L1, is assigned to the desired application target 201a (S1 in the illustrated example), and the priority is reversed. .. Further, in the third case C3, the applicants 202a of K1 and K2 having a lower priority than I1 are assigned to the desired application target 201a (S1 in the illustrated example), and the priority is reversed.

In this way, when the sibling relationship (coupling request) is ignored and the SD mechanism is used for allocation, problem 3 frequently occurs. In addition, when the siblings are assigned in a grouped form (according to the coupling request), problem 1 frequently occurs.

In order to minimize these problems, if you try to search for matching in the form of siblings, if the preconditions for matching change, such as the number of applicants for each class by age is fixed. , It becomes difficult to obtain stable matching. In addition, the amount of calculation is enormous.

In one aspect, it is an object of the present invention to provide a matching program, a matching method, and a matching device that can reduce the amount of calculation and request an appropriate allocation to an application target.

In the first proposal, the matching program causes a computer to perform matching between a plurality of applicants each having a priority and a plurality of application targets. The matching program causes a computer to execute a process of performing matching and a process of determining. The matching process is an extensive game that supports matching, and the priority is associated with the order of play for a plurality of independent players having gains corresponding to the preferences of each of the plurality of applicants. Multiple players each know the gains of all of the multiple players. Find the subgame perfect equilibrium of an extensive game. In addition, the matching process performs matching based on the result of subgame perfect equilibrium. The gain of the player corresponding to the coupling request applicant having the coupling request requesting matching in the form of a pair with a specific other applicant is set according to whether or not the coupling request is satisfied. The process of deciding is to determine whether or not to prun the options in the player's turn corresponding to the coupling request applicant for the game tree options corresponding to the partial game of the extensive game. Coupling request The applicant's coupling request content. Refer to and decide.

According to one embodiment of the present invention, it is possible to obtain an appropriate allocation to an application target while suppressing the amount of calculation.

FIG. 1 is a block diagram showing a functional configuration example of the matching device according to the embodiment. FIG. 2 is an explanatory diagram for explaining the application target information and the applicant information. FIG. 3 is an explanatory diagram for explaining the result data. FIG. 4 is an explanatory diagram illustrating a gain table. FIG. 5 is an explanatory diagram illustrating a game tree. FIG. 6 is an explanatory diagram illustrating subgame perfect equilibrium. FIG. 7 is a flowchart showing an example of the matching process. FIG. 8 is an explanatory diagram illustrating a specific example of the matching process. FIG. 9 is an explanatory diagram illustrating a specific example of the matching process. FIG. 10 is an explanatory diagram illustrating a specific example of the matching process. FIG. 11 is an explanatory diagram illustrating an example of the look-ahead process. FIG. 12 is an explanatory diagram illustrating a specific example of the matching process after the look-ahead process. FIG. 13 is an explanatory diagram illustrating a hardware configuration example of the matching device according to the embodiment. FIG. 14 is an explanatory diagram illustrating the first case. FIG. 15 is an explanatory diagram illustrating the second case. FIG. 16 is an explanatory diagram illustrating a third case.

Hereinafter, the matching program, the matching method, and the matching apparatus according to the embodiment will be described with reference to the drawings. Configurations having the same function in the embodiment are designated by the same reference numerals, and duplicate description will be omitted. The matching program, matching method, and matching device described in the following embodiments are merely examples, and the embodiments are not limited. In addition, the following embodiments may be appropriately combined within a consistent range.

FIG. 1 is a block diagram showing a functional configuration example of the matching device according to the embodiment. The matching device 1 shown in FIG. 1 is an information processing device such as a PC (personal computer). The matching device 1 performs matching processing between a plurality of applicants each given a priority and a plurality of application targets based on the input information, and outputs the obtained matching result. Based on this matching result, the user assigns the applicant to the application target.

In this embodiment, the application target is a nursery school, and the applicant is a child of a guardian who wishes to have childcare at the nursery school, but the application target and the applicant are not limited to the example of the embodiment. For example, the applicant may be a guest and the application target may be a guest room, which may be applied to the room allocation of the guest at the inn.

As shown in FIG. 1, the matching device 1 includes a storage unit 10, an input unit 20, a matching processing unit 30, a selection determination unit 40, and an output unit 50.

The storage unit 10 stores various types of information in a storage device such as a RAM (Random Access Memory) or an HDD (Hard Disk Drive). Specifically, the storage unit 10 contains input information such as application target information 11 and applicant information 12 input from the input unit 20, calculation data 13 at the time of calculation by the matching processing unit 30 and the option determination unit 40, and matching processing. The result data 14 indicating the matching result calculated by the unit 30 is stored.

The application target information 11 is information about the application target input and preset by the input unit 20. The applicant information 12 is information about the applicant that is input and preset by the input unit 20.

FIG. 2 is an explanatory diagram for explaining the application target information 11 and the applicant information 12. As shown in FIG. 2, in the application target information 11, the number of people accepted for each nursery school (application target) identified by the nursery school ID is set. At each nursery school, the number of students accepted is set for each age-specific class (0-year-old class, 1-year-old class).

In the applicant information 12, a preference list showing the order of the desired nursery school, an age, and a priority for assignment are set for each child (applicant) identified by the child ID.

If the same application ID includes a plurality of child IDs in the applicant information 12, for example, the children have a sibling (brother, brother / sister, sibling, sister) relationship, and the coupling request between the children. Suppose there is. The coupling request is a request for allocation (matching) to the application target (nursery school) in a combined form.

For example, it is assumed that a1 and a0 and b1 and b0 are applicants who have a sibling relationship with each other and request each other's coupling (coupling request applicant). A1 and a0 and b1 and b0 are requested by the guardian who is the applicant to be assigned (matched) to the application target (nursery school) in a combined form.

Returning to FIG. 1, the calculation data 13 is data at the time of calculation of matching processing between a plurality of applicants and a plurality of application targets by the matching processing unit 30 and the option determination unit 40. For example, the calculation data 13 includes a gain table, data related to a search for a game tree (details will be described later), and the like.

The result data 14 is data showing the allocation result of the applicant (child) to the application target (nursery school) calculated by the matching process by the matching processing unit 30 and the option determination unit 40.

FIG. 3 is an explanatory diagram illustrating the result data 14. As shown in FIG. 3, in the result data 14, the child ID indicating the child and the nursery school ID indicating the nursery school to which the child is assigned are associated with each other.

Returning to FIG. 1, the input unit 20 receives input information related to matching processing such as application target information 11 and applicant information 12 from an input device such as a mouse or a keyboard. The input unit 20 stores the received application target information 11 and the applicant information 12 in the storage unit 10.

The matching processing unit 30 performs matching processing between a plurality of applicants and a plurality of application targets, each of which has a priority, based on the application target information 11 and the applicant information 12. In this matching process, the matching processing unit 30 virtualizes an extensive game corresponding to matching between a plurality of applicants and a plurality of application targets. Then, the matching processing unit 30 obtains the subgame perfect equilibrium of the expanded game that knows the gains of all the plurality of players, and performs matching based on the result of the subgame perfect equilibrium.

Extensive-form games are one of the game expression formats in game theory, and the sequence of each player's turn is expressed by a tree structure called a game tree. A game tree is represented by nodes (nodes), branches (branches), and leaves (leafs (nodes)). The node indicates the turn (phase of the game) for each player. The branches indicate the player's choices (strategies). The leaves are the end of the game. In extensive games, each player's choice from the top node to the end of the branch through the branches gives each player a gain.

A subgame is an entire or part of the original extensive game, and is itself an extensive game. Subgame perfect equilibrium is a situation in which options are selected that provide Nash equilibrium in all subgames (every player chooses the best strategy for the strategies of other players).

The matching processing unit 30 makes each of the plurality of applicants (children) in the applicant information 12 into a plurality of independent players having a gain corresponding to their own preferences, and plays once in order (selection of a nursery school). Virtualize an information game. A perfect information game is an extensive game in which all the states and options up to that point are given at all nodes. That is, all players know all the information about the game (assignment) (mutual priorities, ages, sibling relationships (whether or not there is a coupling request), preference list and the number of people accepted in each nursery / age class). It is assumed that

First, the matching processing unit 30 sets a gain table according to the strategy for each player (child) corresponding to the applicant based on the applicant information 12. This gain table is set according to the preference list in the applicant information 12 and the presence / absence of a coupling request.

Specifically, for each player's strategy (option), the gain is set higher in the order of the preference list. Further, for a coupling request applicant having a coupling request requesting matching in a paired form, a high gain is set when the coupling request is satisfied.

FIG. 4 is an explanatory diagram illustrating a gain table. As shown in FIG. 4, for applicants (c0, d1) who do not have a coupling request, gain tables 15B and 15C with higher gains are set in the order of preference list. In addition, N / A indicates the case where the nursery school in the preference list could not be reserved.

Further, for the coupling request applicants (a1, a0, b1, b0), the gain table 15A in which the gain is increased in the order according to the following cases 1 to 3 is set.
1. 1. If the children select the same nursery school (in addition, the selected nursery school will be ranked higher in the preference list)
2. 2. If different nursery schools are selected (in addition, the selected nursery school will be ranked higher in the preference list).
3. 3. If you could not book a nursery school in your preference list

For example, when the same nursery school is selected, the gain values are set to "6", "5", and "4" in the order of the preference list (s → t → u). Next, when nursery schools with different scholarships are selected, the gain values are set to "3", "2", and "1" in the order of preference list (s → t → u). Next, when the nursery school in the preference list cannot be reserved (N / A), the gain value is set to "0".

Next, the matching processing unit 30 plays each player (selection of options) in the same order as the priority of the children (in the order of a1, b1, c0, b0, a0, d1 in the example of FIG. 4). The strategy of each player is that the number of nursery schools in the application target information 11 has not reached the capacity from the nursery schools in their preference list (the number of selected players in the higher order has not reached the accepted number). Is to choose. However, no action shall be taken when any desired nursery school (all nursery schools included in the preference list) has reached capacity.

At this time, the matching processing unit 30 shall select an option having the highest gain value and a Nash equilibrium in each player's play based on the gain tables 15A to 15C. As a result, the matching processing unit 30 is the first path to reach the leaves (end phase) along the tree structure of the game tree, and searches for a path that is in Nash equilibrium (hereinafter, equilibrium path), that is, subgame perfect equilibrium Find the equilibrium.

FIG. 5 is an explanatory diagram illustrating a game tree. As shown in FIG. 5, the game tree 16 uses the aspects of each player (a1, b1, c0, b0, a0, d1) as nodes in the same order as the priority of the children, and each player's choices (s, t). , U) is a tree structure with branches. That is, the game tree 16 corresponds to a partial game of an extensive game corresponding to matching between a plurality of applicants (a1, b1, c0, b0, a0, d1) and a plurality of application targets (s, t, u). It is a game tree.

FIG. 6 is an explanatory diagram illustrating subgame perfect equilibrium. As shown in FIG. 6, the matching processing unit 30 searches for an equilibrium path (thick line) that is a Nash equilibrium among the paths from the top node (a1) in the game tree 16 to the leaves (d1). Find the subgame perfect equilibrium.

Here, playing in the same order as the child's priority corresponds to assigning the nursery school from the child with the highest priority in the SD mechanism. Then, for children without a sibling (no coupling requirement), the choice to maximize the gain is always made (matching the operation of the SD mechanism). In addition, for children with siblings (coupling request applicants), the preference regarding coupling is reflected as the gain value of the game by the gain table 15A in which the gain value corresponding to whether or not the coupling is satisfied is set. Then, the selection for maximum gain is made.

In this way, the selection that maximizes the gain of each player contributes to the stable matching between a plurality of applicants and a plurality of application targets. Then, the matching processing unit 30 searches for an equilibrium path (thick line) that becomes the Nash equilibrium and obtains the subgame perfect equilibrium, which is appropriate according to the preferences of a plurality of applicants (preference list, presence / absence of coupling). The result (result data 14) of assigning applicants to the application target can be obtained.

Returning to FIG. 1, the option determination unit 40 determines whether or not to prun the options in the turn of the player corresponding to the coupling request applicant for the game tree options of the extensive game in the matching process of the matching processing unit 30. Ring request Determined by referring to the applicant's coupling request. That is, the option determination unit 40 is an example of the determination unit.

For example, the final gain determined for one strategy (option) selected by the applicant for the coupling request is whether or not the coupling request is satisfied (for example, when the sibling strategies are the same / different). There are two ways. Therefore, the other can be classified according to whether or not the gain is expected to satisfy the coupling requirement. After the case classification, the gain is determined in one way. Utilizing this, the option determination unit 40 selects an option having a gain expected to satisfy the coupling requirement on the other side. Then, the option determination unit 40 backtracks and removes the disappointing option when the expected gain is not obtained and the expectation is disappointing. In this way, the option determination unit 40 determines that the option is pruned in the player's turn corresponding to the coupling request applicant after the gain is determined in one way.

For example, the option determination unit 40 initially determines the option with the maximum gain that is expected to satisfy the coupling request in the turn of the player corresponding to the coupling request applicant. Next, in the turn of the player corresponding to the other low-priority coupling request applicant, there may be no option to satisfy the coupling request depending on conditions such as the number of people accepted by the nursery school.

In such a case, it turns out that the option selected in the turn of the player corresponding to the high-priority coupling request applicant in anticipation of satisfying the coupling request is disappointing. Therefore, if the option determination unit 40 cannot select an option that satisfies the coupling request in the turn of the player corresponding to the other coupling request applicant having a low priority, the option determination unit 40 responds to the coupling request applicant having a high priority. Backtrack to the player's turn and remove the disappointing options.

In this way, the option determination unit 40 prunes the options in the game tree 16. Since the number of paths to be searched can be reduced by pruning, the matching processing unit 30 can reduce the calculation cost for obtaining the subgame perfect equilibrium.

Here, the details of the matching process will be described by the matching processing unit 30 and the option determination unit 40. FIG. 7 is a flowchart showing an example of the matching process.

As shown in FIG. 7, when the processing is started, the matching processing unit 30 initializes the variable (i) corresponding to the player order of the matching processing (i ← 1) (S1).

Next, the matching processing unit 30 selects a strategy in which the player i may bring the maximum gain to himself / herself based on the gain tables 15A to 15C (S2). Here, in the turn of the player corresponding to the coupling request applicant, the other side also selects a strategy with the expected gain that satisfies the coupling request.

Next, the option determination unit 40 determines whether or not it is determined that the player j (j <i) having a higher priority than the player i cannot achieve the expected gain (S3). For example, if the player i's turn corresponding to the other low-priority coupling request applicant cannot select an option that satisfies the coupling request, the player j corresponding to the high-priority coupling request applicant is expected. It is determined that the obtained gain cannot be achieved.

When it is determined that the expected gain cannot be achieved by the player j (S3: YES), the option determination unit 40 backtracks the matching process in the matching processing unit 30 to the node of the player j (S7). Then, the option determination unit 40 removes the strategy (option) determined that the expected gain cannot be achieved, sets i ← j (S8), and returns the process to S2. As a result, the matching processing unit 30 selects the strategy after removing the disappointing strategy from the turn of the player who backtracked and returned the turn.

When it is not determined that the expected gain cannot be achieved by the player j (S3: NO), the matching processing unit 30 determines whether or not the player i is the last player (applicant with the lowest priority). Judgment (S4).

In the case of the last player (S4: YES), the matching processing unit 30 ends the processing because it finds the equilibrium path leading to the leaves (end phase) along the tree structure of the game tree.

If it is not the last player (S4: NO), the matching processing unit 30 creates a node of the player (i + 1) whose priority corresponds to the next applicant (S5), sets i ← i + 1 (S6), and goes to S2. Return the process.

Here, a specific example of the above matching process will be described. In addition, the sample data of the specific example described below shall conform to the values of the application target information 11 and the applicant information 12 in FIG. The game tree and subgame perfect equilibrium in the sample data shall be in accordance with FIGS. 5 and 6.

8 to 10 are explanatory views for explaining a specific example of the matching process. In addition, in the application target information 11 corresponding to each step (S10 to S14, S20 to S23, S30 to S35) in FIGS. 8 to 10, 0-year-old class and 1-year-old class in each nursery school (s, t, u) The number of acceptances shall be reduced by the player selecting.

As shown in FIG. 8, the matching processing unit 30 is based on the gain tables 15A to 15C in order from the player corresponding to the applicant with the highest priority (in the order of a1, b1, c0, b0, a0). , The player selects a strategy that may bring the maximum gain to himself (S10-S13).

Specifically, in the turn of the player of a1, aiming for a maximum gain of 6 (selection of s) in the expectation of selecting a strategy that satisfies the coupling requirement in the turn of a0, which is related to the sibling (S10). .. Next, in the turn of the player of b1, the player aims for a maximum gain of 5 (selection of t) in anticipation of selecting a strategy that satisfies the coupling requirement with the turn of b0, which is related to the sibling (S11).

Next, in the turn of the player of c0, the optimum strategy (selection of s) is determined on the spot because there is no sibling relationship (S12). Then, in the turn of the player of b0, the strategy (selection of t) as expected of b1 can be performed. Therefore, it is determined that b1 can obtain the gain "5". Further, up to this point, it is confirmed that the subgames in the order of b1 or less are equilibrium paths (S13).

Next, in the turn of a0, the strategy (selection of s) as expected of a1 cannot be performed. In this case, it is determined that the player of a1 cannot obtain the gain "6". Therefore, the option determination unit 40 excludes the strategy of acquiring the gain “6” (selection of s) from the strategy of the player of a1, and backtracks to the turn of the player of a1 (S14).

As shown in FIG. 9, the matching processing unit 30 selects a strategy in which the player may bring the maximum gain to himself / herself from the turn of the player a1 after the backtrack (S20 to S22). However, in the turn of the player of a1, the strategy of acquiring the gain "6" (selection of s) is excluded.

Specifically, in the turn of the player of a1, aiming for a maximum gain of 5 (selection of t) in the expectation of selecting a strategy that satisfies the coupling requirement in the turn of a0, which is related to the sibling (S20). .. Next, in the turn of the player of b1, the player aims for a maximum gain of 6 (selection of s) in anticipation of selecting a strategy that satisfies the coupling requirement with the turn of b0, which is related to the sibling (S21).

Next, in the turn of the player of c0, the optimum strategy (selection of s) is determined on the spot because there is no sibling relationship (S22).

Next, in the turn of the player of b0, the strategy (selection of s) as expected of b1 cannot be performed. In this case, it is determined that the player of b1 cannot obtain the gain "6". Therefore, the option determination unit 40 excludes the strategy of acquiring the gain “6” (selection of s) from the strategy of the player of b1 and backtracks to the turn of the player of b1 (S23).

As shown in FIG. 10, the matching processing unit 30 selects a strategy in which the player may bring the maximum gain to himself / herself from the turn of the player in b1 after the backtrack (S30 to S35). However, in the turn of the player of b1, the strategy of acquiring the gain "6" (selection of s) is excluded.

Specifically, in the turn of the player of b1, aiming for a maximum gain of 4 (selection of u) in the expectation of selecting a strategy that satisfies the coupling requirement with the turn of b0, which is related to the sibling (S30). .. Next, in the turn of the player of c0, the optimum strategy (selection of s) is determined on the spot because there is no sibling relationship (S31). In the turn of the player of b0, the strategy (selection of u) as expected of b1 can be performed. Therefore, it is determined that b1 can obtain the gain "4". Further, up to this point, it is determined that the subgames in the order of b1 or less are equilibrium paths (S32).

Next, in the turn of the player of a0, the strategy (selection of t) as expected of a1 can be performed. Therefore, it is determined that a1 can obtain the gain "5". Further, up to this point, it is determined that the subgames in the order of a1 or less are equilibrium paths (S33).

Next, in the turn of the player of d1, the optimum strategy (selection of s) is determined on the spot because there is no sibling relationship (S34). Since d1 is the last player, the equilibrium path of the entire game is determined (S35).

The option determination unit 40 may perform a look-ahead process of pre-reading the behavior of a player whose optimal strategy is clear, and pruning the options in the game tree 16 based on the action result of the pre-read player. This look-ahead process may be executed prior to the search for the balanced path in the matching processing unit 30, or may be executed during the search for the balanced path.

For example, applicants other than coupling request applicants can simply seek their own gain, so that the optimal strategy becomes clear. Therefore, the option determination unit 40 executes the turn of the player corresponding to the applicant other than the coupling request applicant before the player corresponding to the coupling request applicant. Then, the option determination unit 40 excludes the strategy that the coupling request applicant cannot select due to the player's strategy corresponding to the applicant other than the coupling request applicant.

FIG. 11 is an explanatory diagram illustrating an example of the look-ahead process. FIG. 12 is an explanatory diagram illustrating a specific example of the matching process after the look-ahead process.

In the example of the pre-reading process and the matching process after the pre-reading process described below, the values of the application target information 11 and the applicant information 12 in FIG. 4 are used as samples. The game tree and subgame perfect equilibrium shall be in accordance with FIGS. 5 and 6. Further, in the application target information 11 corresponding to each step (S40 to S43, S50 to S56) in FIGS. 11 and 12, the player selects a 0-year-old class and a 1-year-old class at each nursery school (s, t, u). By doing so, the number of acceptances shall be reduced.

As shown in FIG. 11, the option determination unit 40 is the turn of the player corresponding to the applicant (c0, d1) other than the coupling request applicant than the player (a1, b1) corresponding to the coupling request applicant. Is executed first (S40 to S43).

Specifically, the option determination unit 40 skips the turn of the player (a1, b1) corresponding to the coupling request applicant (S40). Next, the option determination unit 40 executes the turn of c0. Here, c0 should be selected if there is a vacancy in the 0-year-old frame of the strategy (s), so when the upper bound (acceptance number) of the 0-year-old class of the nursery school (s) is 1 or more. Decreases by 1 (S41).

From the execution result of the turn of c0, it is certain that the strategy (s) cannot be selected in the turns of b0 and a0 (S42). Therefore, the option determination unit 40 excludes the selection of the strategy (s) in the turns of b0 and a0 based on the execution result of the turn of c0.

Then, the option determination unit 40 executes the turn of d1. Here, d1 should select if there is a vacancy in the 1-year-old frame of the strategy (s), so when the upper bound (acceptance number) of the 1-year-old class of the nursery school (s) is 1 or more. Decreases by 1 (S43).

As shown in FIG. 12, the above-mentioned look-ahead process prunes the options in the game tree 16. Specifically, the selection of the strategy (s) in the turn of b0 and a0 is excluded. Due to this exclusion, in the gain table 15Aa of a1 and b1, s is not included in the strategy of siblings (b0, a0). Further, in the gain table 15Ab of b0 and a0, s is not included in one's strategy.

Therefore, in the matching process after the look-ahead process, the process is started in a state where s is excluded from the strategies of b0 and a0. Specifically, the matching processing unit 30 also includes the gain tables 15Aa, 15ab, 15B, and 15C in order from the player corresponding to the applicant with the highest priority (in the order of a1, b1, c0, b0, a0). In addition, the player selects a strategy that may bring the maximum gain to himself (S50-S56).

In the turn of the player of a1, the player aims for a maximum gain of 5 (selection of t) in anticipation of selecting a strategy that satisfies the coupling requirement with the turn of a0, which is related to the sibling (S50). Next, in the turn of the player of b1, the player aims for a maximum gain of 4 (selection of u) in anticipation of selecting a strategy that satisfies the coupling requirement with the turn of b0, which is related to the sibling (S51).

Next, in the turn of the player of c0, the optimum strategy (selection of s) is determined on the spot because there is no sibling relationship (S52). Then, in the turn of the player of b0, the strategy (selection of u) as expected of b1 can be performed. Therefore, it is determined that b1 can obtain the gain "4". Further, up to this point, it is determined that the subgames in the order of b1 or less are equilibrium paths (S53).

Next, in the turn of the player of a0, the strategy (selection of t) as expected of a1 can be performed. Therefore, it is determined that a1 can obtain the gain "5". Further, up to this point, it is confirmed that the subgames in the order of a1 or less are equilibrium paths (S54).

Next, in the turn of the player of d1, the optimum strategy (selection of s) is determined on the spot because there is no sibling relationship (S55). Since d1 is the last player, the equilibrium path of the entire game is determined (S56).

In this way, when the option determination unit 40 performs the look-ahead processing, the number of passes to be searched for when obtaining the subgame perfect equilibrium can be further reduced, and the amount of calculation can be suppressed.

Returning to FIG. 1, the output unit 50 uses the result data 14 stored in the storage unit 10 as a matching result by the matching processing unit 30 and the option determination unit 40, that is, a plurality of applicants to a plurality of application targets. The allocation result of is output by display on the display device, printing on the printing device, file output, etc. For example, the output unit 50 displays the nursery school assigned to each child based on the result data 14. This allows the user to assign the child to the nursery school.

As described above, the matching device 1 is a device that executes matching between a plurality of applicants each having a priority and a plurality of application targets, and has a matching processing unit 30 and an option determination unit 40. The matching processing unit 30 is an extensive game corresponding to matching, and the priority is associated with the order of play with respect to a plurality of independent players having gains corresponding to the preferences of each of the plurality of applicants. Multiple players each know the gains of all of the multiple players. Find the subgame perfect equilibrium of an extensive game. Then, the matching processing unit 30 performs matching based on the result of the subgame perfect equilibrium, and obtains the result data 14. Further, the matching processing unit 30 has a coupling request requesting matching in the form of a pair with another specific applicant. The gain of the player corresponding to the coupling request applicant is whether or not the coupling request is satisfied. Set according to. The option determination unit 40 determines whether or not to prun the options in the player's turn corresponding to the coupling request applicant for the game tree options corresponding to the partial game of the extensive game in the matching processing unit 30. Determined by referring to the content of the coupling request.

In this way, the matching device 1 applies for an appropriate application target according to the preferences of a plurality of applicants (preference list, presence / absence of coupling) by obtaining the subgame perfect equilibrium of the expanded game corresponding to matching. The result of assigning the person (result data 14) can be obtained. Further, the matching device 1 can reduce the number of paths to be searched when obtaining the subgame perfect equilibrium by pruning the options of the game tree, and can obtain the subgame perfect equilibrium while suppressing the amount of calculation.

Here, the experimental results under the following setting conditions in the matching device 1 of the present embodiment are shown in the table.
[Setting conditions]
・ Number of nursery schools: 2 to 10 facilities ・ Number of classes by age at each nursery school: 6 classes ・ Number of children accepted by each nursery school: 4 ・ Number of children: 48-240 ・ Children with a sibling relationship Ratio: 0.4
・ Preference list length: 2-10
-For each of the above parameter settings, calculate the average of the experimental results for 100 random problems.

As shown in the table of experimental results, in the matching quality of the present embodiment, it is possible to obtain a stable matching result in which the occurrence of problems 2 and 3 is suppressed as much as possible without causing the above-mentioned problem 1. Moreover, even if the game tree becomes large, it is possible to prevent a long calculation time. Further, when the pre-reading process is performed, the calculation time can be suppressed to be shorter even when the game tree becomes larger than when the pre-reading process is not performed.

It should be noted that each component of each of the illustrated devices does not necessarily have to be physically configured as shown in the figure. That is, the specific form of distribution / integration of each device is not limited to the one shown in the figure, and all or part of the device is functionally or physically distributed / physically in arbitrary units according to various loads and usage conditions. It can be integrated and configured.

The various processing functions performed by the matching device 1 may be executed in whole or in any part on the CPU (or a microcomputer such as an MPU or an MCU (Micro Controller Unit)). In addition, various processing functions may be executed in whole or in any part on a program analyzed and executed by a CPU (or a microcomputer such as an MPU or MCU) or on hardware by wired logic. Needless to say, it's good. Further, various processing functions performed by the matching device 1 may be executed by a plurality of computers in cooperation by cloud computing.

By the way, various processes described in the above-described embodiment can be realized by executing a program prepared in advance on a computer. Therefore, an example of a computer (hardware) that executes a program having the same function as that of the above embodiment will be described below. FIG. 13 is an explanatory diagram illustrating a hardware configuration example of the matching device 1 according to the embodiment.

As shown in FIG. 13, the matching device 1 includes a CPU 101 that executes various arithmetic processes, an input device 102 that accepts data input, a monitor 103, and a speaker 104. Further, the matching device 1 includes a medium reading device 105 for reading a program or the like from a storage medium, an interface device 106 for connecting to various devices, and a communication device 107 for communicating with an external device by wire or wirelessly. .. Further, the matching device 1 has a RAM 108 for temporarily storing various information and a hard disk device 109. Further, each part (101 to 109) in the matching device 1 is connected to the bus 110.

The hard disk device 109 stores a program 111 for executing various processes described in the above embodiment. Further, the hard disk device 109 stores various data 112 referred to by the program 111. The input device 102 receives, for example, input of operation information from the operator of the matching device 1. The monitor 103 displays, for example, various screens operated by the operator. For example, a printing device or the like is connected to the interface device 106. The communication device 107 is connected to a communication network such as a LAN (Local Area Network), and exchanges various information with an external device via the communication network.

The CPU 101 reads the program 111 stored in the hard disk device 109, expands it in the RAM 108, and executes it to perform various processes. The program 111 does not have to be stored in the hard disk device 109. For example, the matching device 1 may read and execute the program 111 stored in the storage medium that can be read by the matching device 1. The storage medium that can be read by the matching device 1 includes, for example, a CD-ROM, a DVD disk, a portable recording medium such as a USB (Universal Serial Bus) memory, a semiconductor memory such as a flash memory, a hard disk drive, or the like. Further, the program may be stored in a device connected to a public line, the Internet, a LAN, or the like, and the matching device 1 may read the program from these and execute the program.

Regarding the above embodiments, the following additional notes will be further disclosed.

(Appendix 1) A matching program that causes a computer to match multiple applicants with priorities and multiple application targets.
With respect to a plurality of independent players having a gain corresponding to the preference of each of the plurality of applicants, which is an extensive game corresponding to the matching, the priority is associated with the order of play, and the plurality of players are described. Each player knows the gains of all of the multiple players, and seeks the subgame perfect equilibrium of the extensive game.
Matching based on the result of the subgame perfect equilibrium is performed.
The gain of the player corresponding to the coupling request applicant having the coupling request requesting matching in the form of a pair with a specific other applicant is set according to whether or not the coupling request is satisfied.
Regarding the game tree options corresponding to the partial games of the expansion type game, refer to the coupling request contents of the coupling request applicant for the presence or absence of pruning of the options in the turn of the player corresponding to the coupling request applicant. To decide,
A matching program characterized by having a computer execute processing.

(Appendix 2) The determination process is based on the result of executing the turn of the player corresponding to the applicant other than the coupling request applicant earlier than the player corresponding to the coupling request applicant. The matching program according to Appendix 1, characterized in that it determines whether or not to prun the options in the player's turn corresponding to the coupling request applicant.

(Appendix 3) A plurality of coupling request applicants associated with the coupling request are applicants who have a sibling relationship with each other.
The matching program according to Appendix 1 or 2, characterized in that.

(Appendix 4) The matching is a matching between a plurality of prioritized children and a plurality of nursery schools.
The matching program according to any one of Supplementary note 1 to 3, wherein the matching program is characterized in that.

(Appendix 5) A matching method in which a computer executes matching between a plurality of applicants each having a priority and a plurality of application targets.
With respect to a plurality of independent players having gains corresponding to the preferences of each of the plurality of applicants, which is an extensive game corresponding to the matching, the priority is associated with the order of play, and the plurality of players are described. Each player knows the gains of all of the multiple players, and seeks the subgame perfect equilibrium of the extensive game.
Matching based on the result of the subgame perfect equilibrium is performed.
The gain of the player corresponding to the coupling request applicant who has the coupling request requesting matching in the form of a pair with a specific other applicant is set according to whether or not the coupling request is satisfied.
Regarding the game tree options corresponding to the partial games of the expansion type game, refer to the coupling request contents of the coupling request applicant for the presence or absence of pruning of the options in the turn of the player corresponding to the coupling request applicant. To decide,
A matching method characterized in that the processing is performed by a computer.

(Appendix 6) The determination process is based on the result of executing the turn of the player corresponding to the applicant other than the coupling request applicant before the player corresponding to the coupling request applicant. The matching method according to Appendix 5, wherein the presence or absence of pruning of options in the turn of the player corresponding to the coupling request applicant is determined.

(Appendix 7) A plurality of coupling request applicants associated with the coupling request are applicants who have a sibling relationship with each other.
The matching method according to Appendix 5 or 6, characterized in that.

(Appendix 8) The matching is a matching between a plurality of prioritized children and a plurality of nursery schools.
The matching method according to any one of Supplementary Provisions 5 to 7, characterized in that.

(Appendix 9) A matching device that executes matching between a plurality of applicants each having a priority and a plurality of application targets.
With respect to a plurality of independent players having gains corresponding to the preferences of each of the plurality of applicants, which is an extensive game corresponding to the matching, the priority is associated with the order of play, and the plurality of players are described. A matching processing unit that obtains the subgame perfect equilibrium of the extensive game in which each player knows the gains of all the plurality of players and performs matching based on the result of the subgame perfect equilibrium.
The gain of the player corresponding to the coupling request applicant having the coupling request requesting matching in the form of a pair with a specific other applicant is set according to whether or not the coupling request is satisfied.
Regarding the game tree options corresponding to the partial games of the expansion type game, refer to the coupling request contents of the coupling request applicant for the presence or absence of pruning of the options in the turn of the player corresponding to the coupling request applicant. And the decision-making part to decide
A matching device characterized by having.

(Appendix 10) The determination unit is based on the result of executing the turn of the player corresponding to the applicant other than the coupling request applicant before the player corresponding to the coupling request applicant. Coupling Request The matching device according to Appendix 9, characterized in that it determines whether or not to prun the options in the player's turn corresponding to the applicant.

(Appendix 11) A plurality of coupling request applicants associated with the coupling request are applicants who have a sibling relationship with each other.
The matching device according to Appendix 9 or 10, wherein the matching device is characterized in that.

(Appendix 12) The matching is a matching between a plurality of prioritized children and a plurality of nursery schools.
The matching apparatus according to any one of Supplementary note 9 to 11, wherein the matching apparatus is characterized in that.

1 ... Matching device 10 ... Storage unit 11, 201 ... Application target information 12, 202 ... Applicant information 13 ... Calculation data 14 ... Result data 15A, 15Aa, 15Ab, 15B, 15C ... Gain table 16 ... Game tree 20 ... Input unit 30 ... Matching processing unit 40 ... Choice determination unit 50 ... Output unit 101 ... CPU
102 ... Input device 103 ... Monitor 104 ... Speaker 105 ... Media reader 106 ... Interface device 107 ... Communication device 108 ... RAM
109 ... Hard disk device 110 ... Bus 111 ... Program 112 ... Various data C1 to C3 ... First to third cases

Claims (6)

It is a matching program that causes a computer to match multiple applicants with priorities and multiple applicants.
With respect to a plurality of independent players having a gain corresponding to the preference of each of the plurality of applicants, which is an extensive game corresponding to the matching, the priority is associated with the order of play, and the plurality of players are described. Each player knows the gains of all of the multiple players, and seeks the subgame perfect equilibrium of the extensive game.
Matching based on the result of the subgame perfect equilibrium is performed.
The gain of the player corresponding to the coupling request applicant having the coupling request requesting matching in the form of a pair with a specific other applicant is set according to whether or not the coupling request is satisfied.
Regarding the game tree options corresponding to the partial games of the expansion type game, refer to the coupling request contents of the coupling request applicant for the presence or absence of pruning of the options in the turn of the player corresponding to the coupling request applicant. To decide,
A matching program characterized by having a computer execute processing. The process of determining the coupling request is based on the result of executing the turn of the player corresponding to the applicant other than the coupling request applicant before the player corresponding to the coupling request applicant. The matching program according to claim 1, wherein the player determines whether or not to prun the options in the player's turn corresponding to the applicant. The plurality of coupling request applicants associated with the coupling request are applicants who have a sibling relationship with each other.
The matching program according to claim 1 or 2. The matching is a matching between a plurality of prioritized children and a plurality of nursery schools.
The matching program according to any one of claims 1 to 3, wherein the matching program is characterized in that. It is a matching method in which a computer executes matching between multiple applicants with priorities and multiple application targets.
With respect to a plurality of independent players having gains corresponding to the preferences of each of the plurality of applicants, which is an extensive game corresponding to the matching, the priority is associated with the order of play, and the plurality of players are described. Each player knows the gains of all of the multiple players, and seeks the subgame perfect equilibrium of the extensive game.
Matching based on the result of the subgame perfect equilibrium is performed.
The gain of the player corresponding to the coupling request applicant having the coupling request requesting matching in the form of a pair with a specific other applicant is set according to whether or not the coupling request is satisfied.
Regarding the game tree options corresponding to the partial games of the expansion type game, refer to the coupling request contents of the coupling request applicant for the presence or absence of pruning of the options in the turn of the player corresponding to the coupling request applicant. To decide,
A matching method characterized in that the processing is performed by a computer. It is a matching device that executes matching between multiple applicants with priorities and multiple application targets.
With respect to a plurality of independent players having gains corresponding to the preferences of each of the plurality of applicants, which is an extensive game corresponding to the matching, the priority is associated with the order of play, and the plurality of players are described. A matching processing unit that obtains the subgame perfect equilibrium of the extensive game in which each player knows the gains of all the plurality of players and performs matching based on the result of the subgame perfect equilibrium.
The gain of the player corresponding to the coupling request applicant having the coupling request requesting matching in the form of a pair with a specific other applicant is set according to whether or not the coupling request is satisfied.
Regarding the game tree options corresponding to the partial games of the expansion type game, refer to the coupling request contents of the coupling request applicant for the presence or absence of pruning of the options in the turn of the player corresponding to the coupling request applicant. And the decision-making part to decide
A matching device characterized by having.

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