The Nucleolus, the Kernel, and the Bargaining Set: An Update

One of David Schmeidler’s many important contributions in his distinguished career was the introduction of the nucleolus, one of the central single-valued solution concepts in cooperative game theory. This paper is an updated survey on the nucleolus and its two related supersolutions, i.e., the kernel and the bargaining set. As a first approach to these concepts, we refer the reader to the great survey by Maschler (1992); see also the relevant chapters in Peleg and Sudholter (2003). Building on the notes of four lectures on the nucleolus and the kernel delivered by one of the authors at the Hebrew University of Jerusalem in 1999, we have updated Maschler’s survey by adding more recent contributions to the literature. Following a similar structure, we have also added a new section that covers the bargaining set. The nucleolus has a number of desirable properties, including nonemptiness, uniqueness, core selection, and consistency. The first way to understand it is based on an egalitarian principle among coalitions. However, by going over the axioms that characterize it, what comes across as important is its connection with coalitional stability, as formalized in the notion of the core. Indeed, if one likes a single-valued version of core stability that always yields a prediction, one should consider the nucleolus as a recommendation. The kernel, which contains the nucleolus, is based on the idea of “bilateral equilibrium” for every pair of players. And the bargaining set, which contains the kernel, checks for the credibility of objections coming from coalitions. In this paper, section 2 presents preliminaries, section 3 is devoted to the nucleolus, section 4 to the kernel, and section 5 to the bargaining set.Iñarra acknowledges research support from the Spanish Government grant ECO2015-67519-P, and Shimomura from Grant-in-Aid for Scientific Research (A)18H03641 and (C)19K01558

Fairness in online vehicle-cargo matching: An intuitionistic fuzzy set theory and tripartite evolutionary game approach

This paper explores the concept of fairness and equitable matching in an on-line vehicle-cargo matching setting, addressing the varying degrees of satisfaction experienced by shippers and carriers. Relevant indicators for shippers and carriers in the on-line matching process are categorized as attributes, expectations, and reliability, which are subsequent quantified to form satisfaction indicators. Employing the intuitionistic fuzzy set theory, we devise a transformed vehicle-cargo matching optimization model by combining the fuzzy set's membership, non-membership, and uncertainty information. Through an adaptive interactive algorithm, the matching scheme with fairness concerns is solved using CPLEX. The effectiveness of the proposed matching mechanism in securing high levels of satisfaction is established by comparison with three benchmark methods. To further investigate the impact of considering fairness in vehicle-cargo matching, a shipper-carrier-platform tripartite evolutionary game framework is developed under the waiting response time cost (WRTC) sharing mechanism. Simulation results show that with fairness concerns in vehicle-cargo matching, all stakeholders are better off: The platform achieves positive revenue growth, and shippers and carriers receive positive subsidy. This study offers both theoretical insights and practical guidance for the long-term and stable operation of the on-line freight stowage industry.Comment: 36 pages, 15 figure

Strategic decision modeling in Brownfield redevelopment

De ruimtelijke planning en het herstructureringsproces van bedrijventerreinen zijn onlangs aan enkele belangrijke veranderingen onderhevig geweest. Ten eerste is de omvang van de ruimtelijke herstructureringsprojecten toegenomen. Ten tweede zijn de traditionele lineaire planningsprocessen vervangen door publiek-private samenwerkingen waarbinnen de rollen en de onderlinge afhankelijkheid van ontwikkelaars en overheidsorganen gewijzigd zijn. Binnen deze nieuwe kaders is de herstructurering van brownfields veelal problematisch; er treden veel conflicten op tijdens planprocessen. In dit onderzoek wordt beargumenteerd dat het gebrek aan consensus onder betrokken stakeholders een belangrijke oorzaak is van de optredende stagnatie binnen brownfield herstructureringsprocessen. Het uiteindelijke doel van dit onderzoek is het voorspellen en analyseren van het optreden van conflicten in herstructureringsprocessen, alsmede het doen van aanbevelingen over optimale publiek-private samenwerkingsovereenkomsten voor de herstructurering van brownfields. Om dit doel te verwezenlijken is er een onderzoekskader opgesteld, welke is gericht op het specificeren en analyseren van: (1) de attributen van een brownfield; (2) de voorkeuren van de groepen van actoren; en (3) de kenmerken in het onderhandelingsproces tussen de twee groepen van actoren. Voor het verzamelen van noodzakelijke data zijn er twee online enquêtes gehouden. In beide gevallen waren de geënquêteerden experts binnen een specifieke tak van gebiedsontwikkeling. Voor dit onderzoek zijn verschillende methoden gebruikt. Ten eerste is de Fuzzy Delphi methode gebruikt om brownfield attributen te structureren en te prioriteren. Stated Choice experimenten verschaffen vervolgens het inzicht in de individuele voorkeuren van verschillende actor-groepen. Deze resulterende nutsfuncties zijn uiteindelijk gebruikt als de input voor de analyse van multi-actor besluitvorming, waarvoor de methode Game Theory is gebruikt. De resultaten van het besluitvormingsproces hangen niet alleen af van een individuele keuze maar ze bevatten ook de invloed van de keuzes van een tegenspeler. Het vinden van mogelijke consensusrijke strategieën in de onderhandelingen over de herstructurering van brownfields is het doel van deze laatste stap. Tot op heden is er weinig onderzoek verricht naar de ontwikkeling van besluitvormingsmodellen waarin systematisch de kenmerken van de brownfieldterreinen en de herstructureringsplannen verbonden wordt met het gedrag van de betrokken actoren; een dergelijke verbinding kan inzicht geven in mogelijke bronnen van conflicten. Dit onderzoek draagt bij aan de ontwikkeling van modellen waarin de interactie tussen verschillende actoren binnen een complex probleemgebied wordt geanalyseerd. De resultaten van dit onderzoek ondersteunen besluitvormers en procesmanagers bij het vinden van een optimale overeenkomst in de publiek-private onderhandelingen omtrent de herstructurering van brownfields

On bargaining sets for finite economies

We define a bargaining set for finite economies using Aubin’s veto mechanism and show its coincidence with the set of Walrasian allocations. Then, we rewrite our notion in terms of replicated economies showing that, in contrast with Anderson, Trockel and Zhou’s (1997) non-convergence result, this Edgeworth bargaining set shrinks to the set of Walrasian allocations

Strategic Trip Planning: Striking a Balance Between Competition and Cooperation

In intelligent transportation systems, cooperative mobility planning is considered to be one of the challenging problems. Mobility planning as it stands today is an in- dividual decision-making effort that takes place in an environment governed by the collective actions of various competing travellers. Despite the extensive research on mobility planning, a situation in which multiple behavioural-driven travellers partic- ipate in a cooperative endeavour to help each other optimize their objectives has not been investigated. Furthermore, due to the inherent multi-participant nature of the mobility problem, the existing solutions fail to produce ground truth optimal mobil- ity plans in the practical sense - despite their claimed and well proven theoretical optimality. This thesis proposes a multi-module team mobility planning framework to address the team trip planning problem with a particular emphasis on modelling the inter- action between behaviour-driven rational travellers. The framework accommodates the travellers’ individual behaviours, preferences, and goals in cooperative and com- petitive scenarios. The individual behaviours of the travellers and their interaction processes are viewed as a team trip planning game. For this game, a theoretical anal- ysis is presented, which includes an analysis of the existence and the balancedness of the final solution. The proposed framework is composed of three principal modules: cooperative trip planning, team formation, and traveller-centric trip planning (TCTP). The cooper- ative trip planning module deploys a bargaining model to manage conflicts between the travellers that could occur in their endeavour to discover a general, satisfactory solution. The number of players and their interaction process is controlled by the team formation module. The TCTP module adopts an alternative perspective to the individualized trip-planning problem in the sense that it is being behavioural driven problem. This allows for multitudes of traveler centric objectives and constraints, as well as aspects of the environment as they pertain to the traveller’s preferences, to be incorporated in the process. Within the scope of the team mobility planning frame- work, the TCTP is utilized to supply the travellers with personalized strategies that are incorporated in the cooperative game. The concentration problem is used in this thesis to demonstrate the effectiveness of the TCTP module as a behavioural-driven trip planner. Finally, to validate the theoretical set-up of the team trip planning game, we introduce the territory sharing problem for social taxis. We use the team mobility framework as a basis to solve the problem. Furthermore, we present an argument for the convergence and the efficiency of a coarse correlated equilibrium. In addition to the validation of a variety of theoretical concepts, the territory sharing problem is used to demonstrate the applicability of the proposed framework in dealing with cooperative mobility planning problems

Supply Chain

Traditionally supply chain management has meant factories, assembly lines, warehouses, transportation vehicles, and time sheets. Modern supply chain management is a highly complex, multidimensional problem set with virtually endless number of variables for optimization. An Internet enabled supply chain may have just-in-time delivery, precise inventory visibility, and up-to-the-minute distribution-tracking capabilities. Technology advances have enabled supply chains to become strategic weapons that can help avoid disasters, lower costs, and make money. From internal enterprise processes to external business transactions with suppliers, transporters, channels and end-users marks the wide range of challenges researchers have to handle. The aim of this book is at revealing and illustrating this diversity in terms of scientific and theoretical fundamentals, prevailing concepts as well as current practical applications

Cooperative Autonomous Vehicle Speed Optimization near Signalized Intersections

Road congestion in urban environments, especially near signalized intersections, has been a major cause of significant fuel and time waste. Various solutions have been proposed to solve the problem of increasing idling times and number of stops of vehicles at signalized intersections, ranging from infrastructure-based techniques, such as dynamic traffic light control systems, to vehicle-based techniques that rely on optimal speed computation. However, all of the vehicle-based solutions introduced to solve the problem have approached the problem from a single vehicle point of view. Speed optimization for vehicles approaching a traffic light is an individual decision-making process governed by the actions/decisions of the other vehicles sharing the same traffic light. Since the optimization of other vehicles’ speed decisions is not taken into consideration, vehicles selfishly compete over the available green light; as a result, some of them experience unnecessary delay which may lead to increasing congestion. In addition, the integration of dynamic traffic light control system with vehicle speed optimization such that coordination and cooperation between the traffic light and vehicles themselves has not yet been addressed. As a step toward technological solutions to popularize the use of autonomous vehicles, this thesis introduces a game theoretic-based cooperative speed optimization framework to minimize the idling times and number of stops of vehicles at signalized intersections. This framework consists of three modules to cover issues of autonomous vehicle individual speed optimization, information acquisition and conflict recognition, and cooperative speed decision making. It relies on a linear programming optimization technique and game theory to allow autonomous vehicles heading toward a traffic light cooperate and agree on certain speed actions such that the average idling times and number of stops are minimized. In addition, the concept of bargaining in game theory is introduced to allow autonomous vehicles trade their right of passing the traffic light with less or without any stops. Furthermore, a dynamic traffic light control system is introduced to allow the cooperative autonomous vehicles cooperate and coordinate with the traffic light to further minimize their idling times and number of stops. Simulation has been conducted in MATLAB to test and validate the proposed framework under various traffic conditions and results are reported showing significant reductions of average idling times and number of stops for vehicles using the proposed framework as compared to a non-cooperative speed optimization algorithm. Moreover, a platoon-based autonomous vehicle speed optimization scheme is posed to minimize the average idling times and number of stops for autonomous vehicles connected in platoons. This platoon-based scheme consists of a linear programming optimization technique and intelligent vehicle decision-making algorithm to allow vehicles connected in a platoon and approaching a signalized intersection decide in a decentralized manner whether it is efficient to be part of the platoon or not. Simulation has been conducted in MATLAB to investigate the performance of this platoon-based scheme under various traffic conditions and results are reported, showing that vehicles using the proposed scheme achieve lower average values of idling times and number of stops as compared to two other platoon scenarios

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy