João Pedro Pedroso

Abstract
We study the strategical behaviour of firms facing a lot-sizing problem with Cournot competition. Each player is a firm with her own production facility, modeled as an uncapacitated lot-sizing problem (Le., production incurs set-up and variable costs and inventories are allowed). A Cournot competition is played in each time period (market) with each player deciding the quantity of product to place on it. The market price of that product in each time period depends on the total quantity placed in the market. We show that this is a potential game with possibly multiple pure Nash equilibria. We then investigate the plausibility of these equilibria to predict the game outcome by evaluating the difficulty of computing them. If the game has a single period, we prove that an equilibrium can be found in polynomial time, but it is weakly NP hard to find an optimal pure Nash equilibrium (with respect to a given equilibrium refinement). If the game has no variable production and inventory costs, we prove that a pure Nash equilibrium can be computed in polynomial time.

Abstract
For the predicted growth of e-commerce, supply chains need to adapt to new conditions, so that delivery can be fast, cheap and reliable. The key to success is the last-mile product delivery (LMD) - the last stage of the supply chain, where the ordered product is delivered to the final consumer's location. One innovative proposal puts foundations in a new delivery model where a professional delivery fleet (PF) is supplemented partially or fully with crowdshipping. The main idea of crowdshipping is to involve ordinary people - in our case in-store shoppers - in the delivery of packages to other customers. In return, occasional couriers (OC) are offered a small compensation. In hitherto formulated problems it was assumed that OCs always accept delivery tasks assigned to them. In this paper we consider OCs as independent agents, which are free to reject assignments. The main contribution of the paper is an original bi-level methodology for matching and routing problem in LMD with OCs and the PF. The goal is to use crowdshipping to reduce the total delivery cost in a same-day last-mile delivery system with respect to occasional couriers' freedom to accept or reject the assigned delivery. We introduce probability to represent each OC's willingness to perform the delivery to a given final customer. We study the OCs' willingness to accept or reject delivery tasks assigned to them and the influence of their decision on the total delivery cost associated to both the OCs' compensation fees and the delivery cost generated by the PF used for the delivery of remaining parcels. © 2018 The Author(s).

Abstract
We aim to investigate a new class of games, where each player's set of strategies is a union of polyhedra. These are called integer programming games. To motivate our work, we describe some practical examples suitable to be modeled under this paradigm. We analyze the problem of determining whether or not a Nash equilibria exists for an integer programming game, and demonstrate that it is complete for the second level of the polynomial hierarchy.

Abstract
Kidney exchange programs have been set in several countries within national, regional or hospital frameworks, to increase the possibility of kidney patients being transplanted. For the case of hospital programs, it has been claimed that hospitals would benefit if they collaborated with each other, sharing their internal pools and allowing transplants involving patients of different hospitals. This claim led to the study of multi-hospital exchange markets. We propose a novel direction in this setting by modeling the exchange market as an integer programming game. The analysis of the strategic behavior of the entities participating in the kidney exchange game allowed us to prove that the most rational game outcome maximizes the social welfare and that it can be computed in polynomial time.

Abstract
One of the challenges in a kidney exchange program (KEP) is to choose policies that ensure an effective and fair management of all participating patients. In order to understand the implications of different policies of patient allocation and pool management, decision makers should be supported by a simulation tool capable of tackling realistic exchange pools and modeling their dynamic behavior. In this paper, we propose a KEP simulator that takes into consideration the wide typology of actors found in practice (incompatible pairs, altruistic donors, and compatible pairs) and handles different matching policies. Additionally, it includes the possibility of evaluating the impact of positive crossmatch of a selected transplant, and of dropouts, in a dynamic environment. Results are compared to those obtained with a complete information model, with knowledge of future events, which provides an upper bound to the objective values. Final results show that shorter time intervals between matches lead to higher number of effective transplants and to shorter waiting times for patients. Furthermore, the inclusion of compatible pairs is essential to match pairs of specific patient-donor blood type. In particular, O-blood type patients benefit greatly from this inclusion.