Gale-Shapley Model Research Articles

The Marriage Problem with Interdependent Preferences

This paper considers the Gale–Shapley model with interdependent preferences. Women’s preferences over men are common knowledge but whether or not a man is acceptable depends on the preferences of men which are private information. It is shown that no ex-post incentive-compatible and ex-post stable matching rules exist. A characterization of ex-post incentive-compatible, ex-post individually rational and ex-post nonbossy matching rules in terms of modified priority rules is provided.

A game theory model based on Gale-Shapley for dual-resource constrained (DRC) flexible job shop scheduling

Most job shops in practice are constrained by both machine and labor availability. Worker assignment in these so-called Dual Resource Constrained (DRC) job shops is typically solved in the literature via the use of meta-heuristics, i.e. “when” and “where” rules, or heuristic assignment rules. While the former does not necessarily lead to optimal results, the latter suffers from high computational time and complexity, especially when there is a large number of workstations. This paper uses game theory to propose a new worker assignment rule for DRC job shops. The Gale-Shapley model (also known as the stable marriage problem) forms a ‘couple’ made up of a worker and machine following a periodic review strategy. Simulation is used to evaluate and compare the proposed model to “when” and “where” rules previously proposed in the literature. Simulation experiments under different conditions demonstrate that the Gale-Shapley model provides better results for worker assignments in complex DRC systems, particularly when the workers have different efficiency levels. The implications of the findings for research and practice are outlined.

A Two Layer Cooperative Game theoretic Approach for Optimal Operation of Fast Charging Stations

Abstract This paper presents a two layer energy trading framework for energy exchange among electric vehicles (EVs) and charging stations (CSs). The first layer includes peer to peer energy trading among EVs which is achieved by using assignment theoretic game model. The second layer is energy exchange among CSs which is achieved via buyer driven modified Gale Shapley model. A two layer cooperative energy trading model aims to reduce the grid dependency, power losses and ensures the optimal performance of the charging station.

Decision-making method of reconfigurable manufacturing systems’ reconfiguration by a Gale-Shapley model

The companies need to rapid response to new product introduction, mix and demand changes to stay competitive. A reconfigurable manufacturing system can quickly react to changes in products and market. The control method to reconfigure the machines of a reconfigurable manufacturing system is crucial for the performance level. This paper proposes a reconfiguration decision-making method based on a Game-Theory algorithm, and in particular the Gale-Shapley model. A periodic review strategy is used to create two sets: one set of machine over-loaded and one set under-loaded. The Gale-Shapley model forms a coupled of over-loaded and under-loaded machines. The reconfiguration concerns the under-loaded machine of the coupled adding also the task performed by the over-loaded machine. This paper presents a simulation environment developed to evaluate the proposed method and highlight the main topics. The simulation results highlight how the game-theory approach developed improves all the performance measures with controlled number of machines’ reconfigurations.

Analysis of ground state in random bipartite matching

Bipartite matching problems emerge in many human social phenomena. In this paper, we study the ground state of the Gale–Shapley model, which is the most popular bipartite matching model. We apply the Kuhn–Munkres algorithm to compute the numerical ground state of the model. For the first time, we obtain the number of blocking pairs which is a measure of the system instability. We also show that the number of blocking pairs formed by each person follows a geometric distribution. Furthermore, we study how the connectivity in the bipartite matching problems influences the instability of the ground state.

Assortative mating without assortative preference

Assortative mating--marriage of a man and a woman with similar social characteristics--is a commonly observed phenomenon. In the existing literature in both sociology and economics, this phenomenon has mainly been attributed to individuals' conscious preferences for assortative mating. In this paper, we show that patterns of assortative mating may arise from another structural source even if individuals do not have assortative preferences or possess complementary attributes: dynamic processes of marriages in a closed system. For a given cohort of youth in a finite population, as the percentage of married persons increases, unmarried persons who newly enter marriage are systematically different from those who married earlier, giving rise to the phenomenon of assortative mating. We use microsimulation methods to illustrate this dynamic process, using first the conventional deterministic Gale-Shapley model, then a probabilistic Gale-Shapley model, and then two versions of the encounter mating model.

Supporting capacity sharing in the cloud manufacturing environment based on game theory and fuzzy logic

This paper proposes a Framework for Capacity Sharing in Cloud Manufacturing (FCSCM) able to support the capacity sharing issue among independent firms. The success of geographical distributed plants depends strongly on the use of opportune tools to integrate their resources and demand forecast in order to gather a specific production objective. The framework proposed is based on two different tools: a cooperative game algorithm, based on the Gale–Shapley model, and a fuzzy engine. The capacity allocation policy takes into account the utility functions of the involved firms. It is shown how the capacity allocation policy proposed induces all firms to report truthfully their information about their requirements. A discrete event simulation environment has been developed to test the proposed FCSCM. The numerical results show the drastic reduction of unsatisfied capacity obtained by the model of cooperation implemented in this work.

Capacity sharing in a network of enterprises using the Gale–Shapley model

In this paper, we analyze a model of capacity sharing for a set of independent firms, geographically distributed, that often have to implement an opportune tool to integrate their resources and demand forecasts in order to gather a specific production objective. We formulate the problem as a cooperative game and identify a capacity sharing solution using the Gale–Shapley model. The allocation rule takes into account the utility functions of the involved firms, and we show how the capacity allocation rule can be designed to induce all firms to report truthfully their information. Moreover, we show that, under this allocation rule, truth telling is a dominant strategy, with each firm reporting truthfully its private information, regardless of the reporting decisions of other firms. Moreover, the proposed research develops a distributed approach able to facilitate the capacity sharing process by using a multi-agent architecture; then a discrete simulation environment has been developed to compare the proposed approach with a centralized one. Several simulation scenarios were conducted to analyze the performances' trends in various environment conditions.

Równowagi na rynkach z dwustronnymi preferencjami

In the paper we have introduced a concept of market equilibrium in the model of market with twosided preferences (the model is based on the well-known Gale-Shapley model of college admissions from 1962). We have investigated relationships between our concept of equilibrium and the concept of stable matching as defined by Gale and Shapley.

Matching and Sorting in Online Dating

This paper studies the economics of match formation using a novel data set obtained from a major online dating service. Using detailed information on the users' attributes and interactions, we estimate a model of mate preferences. Based on the estimated preferences, we use the Gale-Shapley algorithm to predict the stable matches among the users of the dating site. Comparing the predicted and observed matching patterns, we find that the Gale-Shapley model explains the matches achieved by the online dating market well, and that the matches are approximately efficient (within the class of stable matches). We then explore whether the estimated mate preferences, in conjunction with the Gale-Shapley algorithm, can explain the matching patterns in offline, real-world marriages. We find that we can predict assortative mating patterns that are similar to those observed in marriages. As the Gale-Shapley algorithm predicts match outcomes in the absence of search costs, we conclude that mate preferences, not search frictions, explain much of the strong degree of sorting along various attributes in marriages.