Competitive uncapacitated lot-sizing game

Carvalho, Margarida; Pedroso, João Pedro; Telha, Claudio; Vyve, Mathieu Van

doi:10.1016/j.ijpe.2018.07.026

Cited by 9 publications

(7 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Through dynamic programming, a player p's best reaction (25) for a fixed (y −p , x −p , q −p , h −p ) can be computed in polynomial time if there are no production capacities, neither inventory costs (Carvalho et al, 2018b). For this reason, we decided to concentrate on these simpler instances.…”

Section: Competitive Lot-sizing Gamementioning

confidence: 99%

“…The competitive lot-sizing game (Carvalho et al, 2018b) is a Cournot competition played through T periods by a set of firms (players) that produce the same good. Each firm has to plan its production as in the lot-sizing problems (see Pochet and Wolsey (2006)) but, instead of satisfying a known demand in each period of the time horizon, the demand depends on the total quantity of the produced good that exists in the market.…”

Section: Competitive Lot-sizing Gamementioning

confidence: 99%

“…In Carvalho et al (2018b), it was proven that there is a function that is potential for this game; a maximum of this function is a (pure) equilibrium (recall Lemma 8). This is an additional motivation to analyze our framework in this problem: it can be compared with the maximization of the associated potential function.…”

Section: Competitive Lot-sizing Gamementioning

confidence: 99%

See 2 more Smart Citations

Existence of Nash Equilibria on Integer Programming Games

Carvalho

Lodi

Pedroso

2018

Springer Proceedings in Mathematics &Amp; Statistics

Self Cite

View full text Add to dashboard Cite

The recently defined class of integer programming games (IPG) models situations where multiple self-interested decision makers interact, with their strategy sets represented by a finite set of linear constraints together with integer requirements. Many real-world problems can suitably be fit in this class, and hence anticipating IPG outcomes is of crucial value for policy makers and regulators. Nash equilibria have been widely accepted as the solution concept of a game. Consequently, their computation provides a reasonable prediction of games outcome. In this paper, we start by showing the computational complexity of deciding the existence of a Nash equilibrium for an IPG. Then, using sufficient conditions for their existence, we develop two general algorithmic approaches that are guaranteed to approximate an equilibrium under mild conditions. We also showcase how our methodology can be changed to determine other equilibria definitions. The performance of our methods is analysed through computational experiments in a knapsack game, a competitive lot-sizing game and a kidney exchange game. To the best of our knowledge, this is the first time that equilibria computation methods for general integer programming games have been designed and computationally tested.

show abstract

Section: Competitive Lot-sizing Gamementioning

confidence: 99%

Section: Competitive Lot-sizing Gamementioning

confidence: 99%

See 1 more Smart Citation

Existence of Nash Equilibria on Integer Programming Games

Carvalho

Lodi

Pedroso

2018

Springer Proceedings in Mathematics &Amp; Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The fact that the outcomes from the agents' decisions partly depend on the decisions of other independent agents makes game theory a natural approach to modeling those decisions. In practice, the agents may behave either cooperatively or noncooperatively, and the recent literature contains two comprehensive general reviews, by [4] for both cooperative and noncooperative planning and scheduling games, and by [5,6] for non cooperative lotsizing games, with and without capacity restrictions, respectively. However, our focus is specifically on cooperative lot-sizing models with backlogging, but without capacity restrictions.…”

Section: Introductionmentioning

confidence: 99%

Unitary Owen Points in Cooperative Lot-Sizing Models with Backlogging

2021

View full text Add to dashboard Cite

This paper analyzes cost sharing in uncapacitated lot-sizing models with backlogging and heterogeneous costs. It is assumed that several firms participate in a consortium aiming at satisfying their demand over the planning horizon with minimal operating cost. Each individual firm has its own ordering channel and holding technology, but cooperation with other firms consists in sharing that information. Therefore, the firms that cooperate can use the best ordering channels and holding technology among members of the consortium. This mode of cooperation is stable. in that allocations of the overall operating cost exist, so that no group of agents benefit from leaving the consortium. Our contribution in the current paper is to present a new family of cost sharing allocations with good properties for enforcing cooperation: the unitary Owen points. Necessary and sufficient conditions are provided for the unitary Owen points to belong to the core of the cooperative game. In addition, we provide empirical evidence, through simulation, showing that, in randomly-generated situations, the above condition is fulfilled in 99% of the cases. Additionally, a relationship between lot-sizing games and a certain family of production-inventory games, through Owen’s points of the latter, is described. This interesting relationship enables easily constructing a variety of coalitionally stable allocations for cooperative lot-sizing models.

show abstract

“…For instance, [13,14,18,19,24,38,41] focus on the gas market, where each player solves a convex optimization problem parametrized in other players variables. The cross-border kidney exchange program model [9], the competitive lot-sizing models [10,31], and the fixed charge transportation models [42] feature players solving non-convex problems.…”

Section: Introductionmentioning

confidence: 99%

When Nash Meets Stackelberg

Carvalho¹,

Dragotto²,

Feijoo³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

We analyze Nash games played among leaders of Stackelberg games (NASP ), and prove it is both Σ p 2 -hard to decide if the game has a pure-strategy (PNE ) or mixed-strategy Nash equilibrium (MNE ). We then provide a finite algorithm that computes exact MNE s for NASP when there is at least one, or returns a certificate if no MNE exists. We introduce an inner approximation hierarchy that increasingly grows the description of each Stackelberg leader feasible region. Furthermore, we extend the algorithmic framework to specifically retrieve a pure-strategy Nash Equilibrium if one exists. Finally, we provide computational tests on a range of NASP s instances inspired by international energy trades.

show abstract

Competitive uncapacitated lot-sizing game

Cited by 9 publications

References 21 publications

Existence of Nash Equilibria on Integer Programming Games

Existence of Nash Equilibria on Integer Programming Games

Unitary Owen Points in Cooperative Lot-Sizing Models with Backlogging

When Nash Meets Stackelberg

Contact Info

Product

Resources

About