Sharif Digital Repository

We study the connection between biobjective mixed integer linear programming and normal form games with two players. We first investigate computing Nash equilibria of normal form games with two players using single-objective mixed integer linear programming. Then, we define the concept of efficient (Pareto optimal) Nash equilibria. This concept is precisely equivalent to the concept of efficient solutions in multi-objective optimization, where the solutions are Nash equilibria. We prove that the set of all points in the payoff (or objective) space of a normal form game with two players corresponding to the utilities of players in an efficient Nash equilibrium, the so-called nondominated Nash... 

We study the connection between biobjective mixed integer linear programming and normal form games with two players. We first investigate computing Nash equilibria of normal form games with two players using single-objective mixed integer linear programming. Then, we define the concept of efficient (Pareto optimal) Nash equilibria. This concept is precisely equivalent to the concept of efficient solutions in multi-objective optimization, where the solutions are Nash equilibria. We prove that the set of all points in the payoff (or objective) space of a normal form game with two players corresponding to the utilities of players in an efficient Nash equilibrium, the so-called nondominated Nash... 

Supply function equilibrium (SFE) is often used to describe the behavior of generating companies in electricity markets. However, comprehensive analytical description of supply function models is rarely available in the literature. In this paper, using some analytical calculations, a novel direct approach is proposed to compute the Nash equilibrium (NE) of the supply function model under uniform marginal pricing mechanism. An explicit mathematical proof for its existence and uniqueness is also presented. The proposed methodology is then generalized to accommodate practical market constraints. In addition, a new concept of robust NE is introduced and calculated based on this approach.... 

In transportation literature, User Equilibrium (UE) has been widely studied since early 1950's, many studies of which define equilibrium flow of traffic for uncapacitated networks based on Wardrop's first principle, implying also a Nash Equilibrium (NE). Although, in general, the two equilibria (UE and NE) are not explicitly the same, they are shown to be equivalent under special conditions for uncapacitated UE, when volume delay functions are separable, continuous, non-decreasing and non-negative. A good deal of research is devoted to explain UE in capacitated networks based on Wardrop's first principle and the concept of generalized costs. However, UE for capacitated networks, even under... 

In transportation literature, User Equilibrium (UE) has been widely studied since early 1950's, many studies of which define equilibrium flow of traffic for uncapacitated networks based on Wardrop's first principle, implying also a Nash Equilibrium (NE). Although, in general, the two equilibria (UE and NE) are not explicitly the same, they are shown to be equivalent under special conditions for uncapacitated UE, when volume delay functions are separable, continuous, non-decreasing and non-negative. A good deal of research is devoted to explain UE in capacitated networks based on Wardrop's first principle and the concept of generalized costs. However, UE for capacitated networks, even under... 

In this paper we study a two-echelon decentralized supply chain consists of one retailer and several manufacturers in competitive environment. The manufacturers compete on their price and lead time. To model the interactions between the retailer and manufacturers, we use Stackelberg game in which the manufacturers decide on their wholesale price and lead time as leader and the retailer decides on retail price and its order quantity to each manufacturer as follower. Besides, we use the Nash Equilibrium analysis to investigate the horizontal competition between manufacturers to model their simultaneous decision making on their price and lead time. In this problem, the customers' demand is a... 

We study Nash equilibria in the setting of network creation games introduced recently by Fabrikant, Luthra, Maneva, Papadimitriou, and Shenker. In this game we have a set of selfish node players, each creating some incident links, and the goal is to minimize α times the cost of the created links plus sum of the distances to all other players. Fabrikant et al. proved an upper bound O(√α) on the price of anarchy: the relative cost of the lack of coordination. Albers, Eilts, Even-Dar, Mansour, and Roditty show that the price of anarchy is constant for α = O(√n) and for α ≥ 12n[lgn], and that the price of anarchy is 15(1 + (min{α/n, n 2/alpha;}) 1/3) for any α. The latter bound shows the first... 

Water allocation is a process of identifying the stakeholders, assessing the amount of water they need, and estimating the volume of renewable water resources. This study investigates the coalition possibilities among the riparian in the Aras River as a transboundary basin over-allocating the environmental flow share. To this end, first, the environmental flow is estimated downstream of the basin based on the annual potential runoff. Then, to estimate the agricultural production function in each country, the relationship between the agriculture value-added and the variables like annual potential runoff and capital in the agricultural sector is derived using the seemingly unrelated regression... 

The presence of energy hubs and the advancement in smart grid technologies have motivated system planners to deploy intelligent multicarrier energy systems entitled "smart energy hub" (S.E. Hub). In this paper, we model S.E. Hub, and propose a modern energy management technique in electricity and natural gas networks based on integrated demand side management (IDSM). In conventional studies, energy consumption is optimized from the perspective of each individual user without considering the interactions with each other. Here, the interaction among S.E. Hubs in IDSM program is formulated as a noncooperative game. The existence and uniqueness of a pure strategy Nash equilibrium (NE) is proved.... 

With increasing the presence of co-and tri-generating units, energy hub operators are encouraged to optimally schedule the available energy resources in an economic way. This scheduling needs to be run in an online manner due to the uncertainties in energy prices and demands. In this paper, the real-time scheduling problem of energy hubs is formulated in a dynamic pricing market. The energy hubs interaction is modeled as an exact potential game to optimize each energy hub’s payments to the electricity and gas utilities, as well as the customers’ satisfaction from energy consumption. The potential game approach enables us to study the existence and uniqueness of the Nash equilibrium (NE) and... 

With increasing the presence of co- and tri-generating units, energy hub operators are encouraged to optimally schedule the available energy resources in an economic way. This scheduling needs to be run in an online manner due to the uncertainties in energy prices and demands. In this paper, the real-time scheduling problem of energy hubs is formulated in a dynamic pricing market. The energy hubs interaction is modeled as an exact potential game to optimize each energy hub's payments to the electricity and gas utilities, as well as the customers' satisfaction from energy consumption. The potential game approach enables us to study the existence and uniqueness of the Nash equilibrium and to... 

In this paper, the problem of frequency-constrained electricity market (FCEM) is modeled in the presence of renewable energy sources (RESs) and price-maker players by using equilibrium problem with equilibrium constraints formulation. It is worth mentioning that due to the intermittency of RESs, the FCEM problem in the presence of price-maker players becomes more imperative as stability of power system frequency is a public good and the free-rider problem arises. Moreover, as players of FCEM do not know their rivals' objective functions, the problem is modeled based on Bayesian game theory. The FCEM problem is converted into a game of complete but imperfect information under the common prior... 

The development of technologies such as micro turbines and gas furnaces has been the major driving force towards integration of electricity and natural gas networks in the EH (energy hubs). Besides, the existing power grids are getting smarter by implementing the new generation of information technologies and communication systems. In smart grid, the electricity suppliers can modify the customers' electrical load consumption by employing appropriate scheduling schemes such as DR (demand response) programs. In this paper, we consider the S. E. Hubs (smart energy hubs) framework, in which the customers can use EMS (energy management system) to access to the electricity and natural gas prices...