Search results for "OPTIMIZATION"
showing 10 items of 2824 documents
Convex semi-infinite games
1986
This paper introduces a generalization of semi-infinite games. The pure strategies for player I involve choosing one function from an infinite family of convex functions, while the set of mixed strategies for player II is a closed convex setC inRn. The minimax theorem applies under a condition which limits the directions of recession ofC. Player II always has optimal strategies. These are shown to exist for player I also if a certain infinite system verifies the property of Farkas-Minkowski. The paper also studies certain conditions that guarantee the finiteness of the value of the game and the existence of optimal pure strategies for player I.
Existence and Optimality of Nash Equilibria in Inventory Games
2005
Abstract This paper studies the stability and optimality of a distributed consensus protocol for n -player repeated non cooperative games under incomplete information. At each stage, the players choose binary strategies and incur in a payoff monotonically decreasing with the number of active players. The game is specialized to an inventory application, where fixed costs are shared among all retailers, interested in whether reordering or not from a common warehouse. The authors focus on Pareto optimality as a measure of coordination of reordering strategies, proving that there exists a unique Pareto optimal Nash equilibrium that verifies certain stability conditions.
Noncooperative dynamic games for inventory applications: A consensus approach
2008
We focus on a finite horizon noncooperative dynamic game where the stage cost of a single player associated to a decision is a monotonically nonincreasing function of the total number of players making the same decision. For the single-stage version of the game, we characterize Nash equilibria and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multi-stage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately not necessarily Pareto optimal. The algorithm returns a seque…
Bounded Computational Capacity Equilibrium
2010
We study repeated games played by players with bounded computational power, where, in contrast to Abreu and Rubisntein (1988), the memory is costly. We prove a folk theorem: the limit set of equilibrium payoffs in mixed strategies, as the cost of memory goes to 0, includes the set of feasible and individually rational payoffs. This result stands in sharp contrast to Abreu and Rubisntein (1988), who proved that when memory is free, the set of equilibrium payoffs in repeated games played by players with bounded computational power is a strict subset of the set of feasible and individually rational payoffs. Our result emphasizes the role of memory cost and of mixing when players have bounded c…
Competitive versus efficient extraction of a common property resource: The groundwater case
2001
Abstract In this paper socially optimal and private extraction of a common property aquifer are compared. Open-loop equilibrium and feedback equilibrium in linear strategies have been computed to characterize private extraction. The use of these two equilibrium concepts allows us to distinguish between cost and strategic externalities as long as the open-loop solution captures only the cost externality, and the feedback solution captures both. The results show that strategic behaviour increases the overexploitation of the aquifer compared to the open-loop solution. However, if the groundwater storage capacity is large, the difference between the socially optimal and private extraction, the …
Multiobjective GRASP with Path Relinking
2015
In this paper we review and propose different adaptations of the GRASP metaheuristic to solve multiobjective combinatorial optimization problems. In particular, we describe several alternatives to specialize the construction and improvement components of GRASP when two or more objectives are considered. GRASP has been successfully coupled with Path Relinking for single-objective optimization. Moreover, we propose different hybridizations of GRASP and Path Relinking for multiobjective optimization. We apply the proposed GRASP with Path Relinking variants to two combinatorial optimization problems, the biobjective orienteering problem and the biobjective path dissimilarity problem. We report …
Mean Field Linear Quadratic Games with Set Up Costs
2013
This paper studies linear quadratic games with set up costs monotonic on the number of active players, namely, players whose action is non-null. Such games arise naturally in joint replenishment inventory systems. Building upon a preliminary analysis of the properties of the best response strategies and Nash equilibria for the given game, the main contribution is the study of the same game under large population. We also analyze the influence of an additional disturbance in the spirit of the literature on H∞ control. Numerical illustrations are provided. © 2012 Springer Science+Business Media New York.
Introspection and equilibrium selection in 2 � 2 matrix games
1994
Game theory lacks an explanation of how players' beliefs are formed and why they are in equilibrium. This is the reason why it has failed to make significant advances with the problem of equilibrium selection even for quite siniple games, as 2x2 games with two strict Nash equilibria. Our paper models the introspection process by which the selected equilibrium is achieved in this class of games. Players begin their analysis with imprecise priors, obtained under weak restrictions formulated as Axioms. For a large class of reasoning dynamics we obtain as the solution the risk dominant Nash equilibrium.
An overview of semi-infinite programming theory and related topics through a generalization of the alternative theorems
1984
We propose new alternative theorems for convex infinite systems which constitute the generalization of the corresponding toGale, Farkas, Gordan andMotzkin. By means of these powerful results we establish new approaches to the Theory of Infinite Linear Inequality Systems, Perfect Duality, Semi-infinite Games and Optimality Theory for non-differentiable convex Semi-Infinite Programming Problem.
Preliminary thermal optimization and investigation of the overall structural behaviour of the EU-DEMO water-cooled lead lithium left outboard blanket…
2022
The conceptual design phase of the EU-DEMO reactor has been recently launched, with the aim of evolving the DEMO pre-conceptual layout towards a more robust and articulated geometric configuration able to cope with most of the design requirements and to show further margins for the passing of the current potential show-stoppers. Hence, the achievement of the conceptual design of the Water-Cooled Lead Lithium Breeding Blanket (WCLL BB) is one of the milestones the EUROfusion consortium aims to achieve in the close future. To this purpose, within the framework of the research activities promoted by EUROfusion, a research campaign has been launched at the University of Palermo, in close cooper…