Rationalizable Strategies in Games With Incomplete Preferences

Games with incomplete preferences are normal-form games where the preferences of the players are defined as partial orders over the outcomes of the game. We define rationality in these games as follows. A rational player forms a set-valued belief of possible strategies selected by the opponent(s) and selects a strategy that is not dominated with respect to this belief. Here, we say a strategy is dominated with respect to the set-valued belief if the player has another strategy that would yield a better outcome according to the player's preference relation, no matter which strategy combination the opponent(s) play among those contained in the belief. We define rationalizable strategies as the logical implication of common knowledge of this rationality. We show that the sets of rationalizable strategies are the maximal mutually nondominated sets, i.e., the maximal sets that contain no dominated strategies with respect to each other. We show that no new rationalizable strategies appear when additional preference information is included. We consider multicriteria games as a special case of games with incomplete preferences and introduce a way of representing incomplete preference information in multicriteria games by sets of feasible weights of the criteria

Rationalizable Strategies in Games With Incomplete Preferences

Games with incomplete preferences are normal-form games where the preferences of the players are defined as partial orders over the outcomes of the game. We define rationality in these games as follows. A rational player forms a set-valued belief of possible strategies selected by the opponent(s) and selects a strategy that is not dominated with respect to this belief. Here, we say a strategy is dominated with respect to the set-valued belief if the player has another strategy that would yield a better outcome according to the player's preference relation, no matter which strategy combination the opponent(s) play among those contained in the belief. We define rationalizable strategies as the logical implication of common knowledge of this rationality. We show that the sets of rationalizable strategies are the maximal mutually nondominated sets, i.e., the maximal sets that contain no dominated strategies with respect to each other. We show that no new rationalizable strategies appear when additional preference information is included. We consider multicriteria games as a special case of games with incomplete preferences and introduce a way of representing incomplete preference information in multicriteria games by sets of feasible weights of the criteria

Design optimisation of complex space systems under epistemic uncertainty

This thesis presents an innovative methodology for System Design Optimisation (SDO) through the framework of Model-Based System Engineering (MBSE) that bridges system modelling, Constrained Global Optimisation (CGO), Uncertainty Quantification (UQ), System Dynamics (SD) and other mathematical tools for the design of Complex Engineered and Engineering Systems (CEdgSs) under epistemic uncertainty. The problem under analysis has analogies with what is nowadays studied as Generative Design under Uncertainty. The method is finally applied to the design of Space Systems which are Complex Engineered Systems (CEdSs) composed of multiple interconnected sub-systems. A critical aspect in the design of Space Systems is the uncertainty involved. Much of the uncertainty is epistemic and is here modelled with Dempster Shafer Theory (DST). Designing space systems is a complex task that involves the coordination of different disciplines and problems. The thesis then proposes a set of building blocks, that is a toolbox of methodologies for the solution of problems which are of interest also if considered independently. It proposes then a holistic framework that couples these building blocks to form a SDO procedure. With regard to the building blocks, the thesis includes a network-based modelling procedure for CEdSs and a generalisation for CEdgSs where the system and the whole design process are both taken into account. Then, it presents a constraint min-max solver as an algorithmic procedures for the solution of the general Optimisation Under Uncertainty (OUU) problem. An extension of the method for the Multi-Objective Problems (MOP) is also proposed in Appendix as a minor result. A side contribution for the optimisation part refers to the extension of the global optimiser Multi Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA) with the introduction of constraint handling and multiple objective functions. The Constraint Multi-Objective Problem (CMOP) solver is however a preliminary result and it is reported in Appendix. Furthermore, the thesis proposes a decomposition methodology for the computational reduction of UQ with DST. As a partial contribution, a second approach based on a Binary Tree decomposition is also reported in Appendix. With regard to the holistic approach, instead, the thesis gives a new dentition and proposes a framework for system network robustness and for system network resilience. It finally presents the framework for the optimisation of the whole design process through the use of a multi-layer network model.This thesis presents an innovative methodology for System Design Optimisation (SDO) through the framework of Model-Based System Engineering (MBSE) that bridges system modelling, Constrained Global Optimisation (CGO), Uncertainty Quantification (UQ), System Dynamics (SD) and other mathematical tools for the design of Complex Engineered and Engineering Systems (CEdgSs) under epistemic uncertainty. The problem under analysis has analogies with what is nowadays studied as Generative Design under Uncertainty. The method is finally applied to the design of Space Systems which are Complex Engineered Systems (CEdSs) composed of multiple interconnected sub-systems. A critical aspect in the design of Space Systems is the uncertainty involved. Much of the uncertainty is epistemic and is here modelled with Dempster Shafer Theory (DST). Designing space systems is a complex task that involves the coordination of different disciplines and problems. The thesis then proposes a set of building blocks, that is a toolbox of methodologies for the solution of problems which are of interest also if considered independently. It proposes then a holistic framework that couples these building blocks to form a SDO procedure. With regard to the building blocks, the thesis includes a network-based modelling procedure for CEdSs and a generalisation for CEdgSs where the system and the whole design process are both taken into account. Then, it presents a constraint min-max solver as an algorithmic procedures for the solution of the general Optimisation Under Uncertainty (OUU) problem. An extension of the method for the Multi-Objective Problems (MOP) is also proposed in Appendix as a minor result. A side contribution for the optimisation part refers to the extension of the global optimiser Multi Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA) with the introduction of constraint handling and multiple objective functions. The Constraint Multi-Objective Problem (CMOP) solver is however a preliminary result and it is reported in Appendix. Furthermore, the thesis proposes a decomposition methodology for the computational reduction of UQ with DST. As a partial contribution, a second approach based on a Binary Tree decomposition is also reported in Appendix. With regard to the holistic approach, instead, the thesis gives a new dentition and proposes a framework for system network robustness and for system network resilience. It finally presents the framework for the optimisation of the whole design process through the use of a multi-layer network model

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios

A Refinement Concept for Equilibria in Multicriteria Games via Stable Scalarizations

In a finite multicriteria game, one or more systems of weights might be implicitly used by the agents by playing a Nash equilibrium of the corresponding trade-off scalar games. In this paper, we present a refinement concept for equilibria in finite multicriteria games, called scalarization-stable equilibrium, that selects equilibria stable with respect to perturbations on the scalarization. An existence theorem is provided together with some illustrative examples and connections with some other refinement concepts are investigated

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

A REFINEMENT CONCEPT FOR EQUILIBRIA IN MULTICRITERIA GAMES VIA STABLE SCALARIZATIONS

In a finite multicriteria game, one or more systems of weights might be implicitly used by the agents by playing a Nash equilibrium of the corresponding trade-off scalar games. In this paper, we present a refinement concept for equilibria in finite multicriteria games, called scalarization-stable equilibrium, that selects equilibria stable with respect to perturbations on the scalarization. An existence theorem is provided together with some illustrative examples and connections with some other refinement concepts are investigated.Multicriteria game, Pareto Nash equilibrium, refinement, perturbation, scalarization-stable equilibrium