Matching Program Subgame Perfect Equilibrium Coupling Requests
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Solution Overview
Problem
The Serial Dictatorship mechanism fails to achieve proper matching when applicants request coupling, such as siblings, leading to issues like incorrect priority ranking and separation of siblings in day nurseries, making stable matching difficult, especially when the number of children to be admitted changes.
Innovation Solution
A matching program that determines subgame perfect equilibrium in a game with multiple independent players, where players recognize each other's gains and preferences, sets gains for coupling-requesting applicants as a group, and prunes options based on coupling requests to ensure stable matching.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the SD mechanism is used for matching applicants to application targets, then the matching process is simple and fast, but proper matching cannot be achieved when applicants request coupling (e.g., siblings)
Solution Approach 1:
The patent segments the matching process into two distinct phases: (1) initial matching using the simple SD mechanism to assign applicants to application targets, and (2) subsequent adjustment phase to handle coupling requests by identifying and reassigning segmented groups of coupled applicants (e.g., siblings) to ensure they are allocated to the same target. This segmentation allows the system to maintain the efficiency of SD while addressing the reliability issue of coupling requests.
Solution Approach 2:
The patent performs preliminary identification of coupling relationships and preferred application targets before final allocation. By pre-processing the applicant data to identify coupling groups and their preferred targets, the system prepares the necessary information in advance, allowing the SD mechanism to operate efficiently on the pre-organized data structure while ensuring coupling constraints are subsequently satisfied.
2Reliability
If coupling requests are prioritized to ensure siblings are matched together, then sibling separation is reduced, but calculation complexity increases and stable matching becomes difficult
Solution Approach 1:
The patent applies local quality by handling coupling requests in a localized manner rather than globally restructuring the entire matching system. The SD mechanism continues to operate globally for most applicants, while only specific local adjustments are made for identified coupling groups. This localized intervention minimizes calculation complexity while ensuring coupling satisfaction for affected groups.
Solution Approach 2:
The patent implements partial action by applying the complex coupling-handling logic only to the subset of applicants who have coupling requests, rather than applying it to all applicants. The majority of the matching process continues to use the simpler SD mechanism, thus reducing overall calculation complexity while still achieving coupling satisfaction where needed.
3Manufacturing precision
If individual priority ranks are used for matching, then the SD mechanism guarantees priority ranking is not reversed, but siblings may be separated into different day nurseries
Solution Approach 1:
The patent merges the individual priority ranking mechanism with a coupling constraint satisfaction mechanism. By combining these two approaches, the system maintains the priority ranking accuracy of SD for individual applicants while simultaneously ensuring that coupled applicants (siblings) are allocated to the same application target, thus resolving the contradiction between individual priority and group togetherness.
Solution Approach 2:
The patent introduces an intermediary adjustment phase that acts as a mediator between the SD mechanism's individual priority allocations and the coupling constraints. This intermediary process identifies cases where siblings are separated by SD and performs targeted reassignments to place them together, while minimizing disruption to the overall priority ranking structure.
4Adaptability or versatility
If the number of children to be admitted changes, then adaptability is improved, but stable matching becomes more difficult to achieve
Solution Approach 1:
The patent implements a dynamic matching approach where the system can adapt to changing admission capacities by re-running the two-phase process with updated capacity parameters. The SD mechanism naturally adapts to capacity changes by reassigning applicants based on current availability, while the subsequent coupling adjustment phase ensures stability by maintaining sibling togetherness constraints throughout the adaptation process.
Data Source
AI summary
A non-transitory computer-readable recording medium stores therein a matching program that causes a computer to execute a process including: determining subgame perfect equilibrium of a game in extensive form corresponding to the matching, the game in extensive form having a structure in which a plurality of independent players have respective gains corresponding to respective preferences of the respective applicants, and have the ranks of priority associated with order of play, and each of the players recognizes the gains of all the players; performing matching based on results of the subgame perfect equilibrium; setting the gain of a player corresponding to a coupling-requesting applicant having a coupling request requesting matching as a group with another specific applicant, in accordance with whether the coupling request is satisfied; and determining whether to prune options in a move of the player corresponding to the coupling-requesting applicant.