Multi-leader Multi-follower Game Research Articles

Development of a multi-leader multi-follower game to design industrial symbioses

The implementation of industrial symbioses all over the world has been proven to be a significant lever to decarbonize production facilities. By enhancing cooperation and exchanging resources, important decrease of emissions can be achieved while reducing operating costs. In the light of our previous work, a game theory model is developed to design resources exchanges in eco-industrial parks (EIP). This new model allows to take into account each authority of an industrial park as an independent player, thus becoming a multi-leader-multi-follower game (MLMFG) model. Water and energy networks are generated simultaneously in the model through a well-known case study. The bi-level model is designed with the water and energy managers as leaders and the plants as followers. In this way, the plants play a Nash game with each other and so do the EIP managers. These managers choose a solution from among the equilibria of the followers before reaching their own equilibrium. The results obtained are then compared with those of the previous article, demonstrating that the MLMFG model provides fairly interesting conclusions for the factories and also for the authorities. The relative gain for the companies is around 30 % for all the factories, which constitutes a strong argument of fairness to convince them to participate in the symbiosis. The result obtained after solving the MLMFG problem is very different from that obtained using the AHP method on the set of feasible solutions. To demonstrate the decision-making aspect of the MLMFG method, the coefficients of the AHP method were identified to find the solution to the MLMFG problem among all the feasible points. It is shown that the coefficients are difficult to determine for an expert, despite the relevance of the solution found.

Local energy communities with strategic behavior of multi-energy players for peer-to-peer trading: A techno-economic assessment

Peer-to-peer (P2P) energy trading for profit-driven communities in distribution networks (DNs) has become increasingly critical in terms of economic view especially in the absence of supportive subsidies for renewable generation. However, the risk behavior of local energy communities (LECs), as well as their inherent flexibility options, can affect the profit achieved through local energy trading. This paper seeks to carefully examine to what extent the aforementioned factors contribute to the economic value of P2P energy trading for LECs. To do this, a mathematical model is developed as a multi-leader–multi-follower game which is formulated as equilibrium problems with equilibrium constraints (EPEC). In this game, operators of different LECs are leaders while the market operator who is in charge of clearing the local community market and the distribution system operator (DSO) who is responsible for addressing security constraints of the grid are deemed as followers. In addition, the conditional value at risk (CVaR) technique is utilized to model the risk-averse behavior of communities’ operators. Finally, the model is implemented into a typical DN modified by three different types of LECs. The findings of the simulation highlight that P2P energy trading can bring financial gains for a typical community under certain conditions. Flexibility originated from distributed energy resources (DERs) and sector coupling within a community provide more profit in local energy trading for the community, but risk-averse strategies have the opposite effect.

Strategizing Sustainability and Profitability in Electric Mobility-as-A-Service (E-Maas) Ecosystems with Carbon Incentives: A Multi-Leader Multi-Follower Game Model

Strategizing Sustainability and Profitability in Electric Mobility-as-A-Service (E-Maas) Ecosystems with Carbon Incentives: A Multi-Leader Multi-Follower Game Model

Shared-constraint approach for multi-leader multi-follower game of generation companies participating in electricity markets with carbon emission trading mechanism

There is a high degree of overlap between market entities covered by the carbon emission trading (CET) market and electricity market, and the two markets are closely related. Therefore, it is of great significance to analyze the impact of the CET market mechanism on the bidding strategy of generation companies (GENCOs) and electricity market clearing results. In this paper, the problem of GENCOs participating in both the day-ahead and real-time balancing electricity market within the CET mechanism is studied as a multi-leader multi-follower (MFML) Stackelberg game problem. The GENCOs are considered as leaders in the game who decide on the submitted bid and offer in terms of price and quantity to maximize their expected profit in the market, while both the clearing problems of day-ahead and real-time markets are considered as followers on the lower level. In order to expand the Nash equilibrium of the considered MFML game, the shared-constraint approach is applied to modify this problem. Two typical Nash equilibria of the proposed MLMF game are analyzed and discussed. Finally, the results of the simulations conducted on a modified IEEE 39-bus system and a real 2778-bus system indicate that GENCOs tend to submit bids with a higher price in the market under the global Nash equilibrium solution. Within the CET mechanism, the overall market clearing share of the gas-fired units increases from 21.76% to 18.1%–32.33% and 19.51%, at valley and peak loads, respectively. Thus, the operation of the CET market will make low-emission units more competitive in the electricity market.

Competitive scheduling in a hybrid flow shop problem using multi-leader–multi-follower game - A case study from Iran

It is logical that organizations pay more attention to their major customers which have more impacts on their abilities or benefits. In many real cases, decision makers in scheduling system must prioritize the sequence of processing orders according to the agent of orders while the classic production scheduling do not have the ability to consider the relationships between agents. These problems can be modeled by the Stackelberg problems in the field of game theory. In this study, an agent-based hybrid flow shop problem is formulated by using the multi-leader multi-follower mathematical model. Each level is evaluated by Nash equilibrium and Nash bargaining with the new co-evolutionary and genetic algorithm. The proposed model is validated in a real case problem in the tire manufacturing industry. The results show that Nash equilibrium is superior to Nash bargaining for all agents.

A Real-Time Pricing Scheme with Advertisement Competition Based on Multi-Leader–Multi-Follower Game in Smart Community

In this paper, an advertising differential game model is proposed to describe the competition among different power retailers for attracting users in continuous time. After the equilibrium of advertising differential game is obtained, a multi-leader–multi-follower game model is developed to study the real-time pricing scheme in smart community. The power retailers calculate the optimal prices in response to the users’ power consumption and obtain the non-cooperation Nash equilibrium, and then the multi-leader–multi-follower game equilibrium is found. The numerical simulation is performed to discuss the influence of different factors on the payoff of power retailers and users and to verify the rationality of the proposed pricing scheme. The results show that both advertising efficiency and user scale have positive effects on the revenues of the power retailers. Besides, the rise of electricity price has negative effect on users’ utilities, meanwhile it makes the revenues of power retailers increase at first and then decrease. Moreover, power retailers will not transfer advertising costs to the users in the form of incremental electricity price.

Transactive Energy Based Aggregation of Prosumers as a Retailer

The rapid growth of distributed energy resources results in the proliferation of prosumers at the distribution level, who can both produce and consume energy. In order to harvest benefits of aggregation to obtain revenues in wholesale market and encourage direct interactions among prosumers and other flexible players at the same time, this paper proposes an aggregation framework for prosumers based on transactive energy, in which prosumers aggregate and trade in an independent, proactive and privacy-preserved manner without relying on a real central entity, while other flexible players could be benefited equally. The aggregation of prosumers as a whole behaves as a retailer that trades in wholesale market and towards end-users in retail market. Therefore, the problem is generalized as a bi-level multi-leader multi-follower game in which prosumers are leaders and end-users are followers. To realize the transactive energy based trading framework, an inner-outer iteration approach is proposed, where the outer iteration involves interactions among prosumers and end-users, and achieves final results including the retail price and optimal behaviors of all players. The inner iteration is conducted during each time of the outer iteration to solve end-users' optimal consuming profiles. The whole iteration process involves the independent decision makings of players, and only relies on exchange of information of retail price and prosumers' offers instead of players' private information. Case studies are then carried out demonstrating the proposed transactive energy based aggregation framework for prosumers could decrease the retail price, increase revenues for both prosumers and end-users, and reduce the peak load.

A trilevel model for best response in energy demand-side management

Demand-side management (DSM) is a powerful tool to efficiently manage the consumption of energy. DSM relies on various techniques and means. In this work, we propose a trilevel energy market model for load shifting induced by time-of-use pricing. Four kinds of actors are involved: electricity suppliers (sell energy), local agents (buy, sell and consume), aggregators (buy and sell) and end users (consume). The interactions among these actors lead to a trilevel multi-leader–multi-follower game. Solving such games is known to be hard, thus we assume that the decision variables of all electricity suppliers but one are known and optimize the decisions of the remaining supplier. This leads to a single-leader–multi-follower game, which aims to compute the leader’s best response to the decisions of his competitors.The trilevel model is first formulated as a bilevel problem using an explicit formula for the lowest optimization level. Solution algorithms are developed in the optimistic case and in a variant named “semi-optimistic” approach leading to more robust solutions. Finally, numerical results highlight the efficiency of the methods and the sensitivity of the solutions with respect to the model parameters.

Mobile Data Offloading in FiWi Enhanced LTE-A Heterogeneous Networks

This paper proposes to empower capacity- and coverage-centric fiber-wireless (FiWi) enhanced 4G Long-Term Evolution Advanced (LTE-A) heterogeneous networks (HetNets) with computation- and storage-centric mobile cloud computing to cope with the unprecedented growth of mobile data traffic. Minimizing energy consumption and maximizing revenue while offloading mobile data in such highly converged and hierarchical networks is not trivial, where multiple players (i.e., cloud service providers, macrocell and small cells, users) with multiple objectives coexist. This paper proposes a mobile data offloading framework using a noncooperative multi-level game-theoretic approach from an end-to-end perspective in the envisioned network. More specifically, we design three-level Stackelberg games, in which a single-leader multi-follower game, a multi-leader multi-follower game, and a single-leader multi-follower game are modeled in the introduced network such that individual players selfishly optimize their local payoff functions and collectively solve the large complex network-wide optimization problem. Further, we develop distributed mobile data offloading algorithms to reduce the complexity of the hierarchical games and to achieve a unique Nash equilibrium condition in each subgame. Simulation results show that by reaching the Nash equilibrium condition, the proposed solution helps minimize energy consumption, interference price, and processing cost, while maximizing revenues of the players in the envisioned network. In addition, the efficiency of the equilibria in terms of price of anarchy and price of stability is quantified for the best/worst case of the Nash equilibrium.

A Shared-Constraint Approach to Multi-Leader Multi-Follower Games

Multi-leader multi-follower games are a class of hierarchical games in which a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium problem with equilibrium constraints is complicated by nonconvex agent problems and therefore providing tractable conditions for existence of global or even local equilibria for it has proved challenging. Consequently, much of the extant research on this topic is either model specific or relies on weaker notions of equilibria. We consider a modified formulation in which every leader is cognizant of the equilibrium constraints of all leaders. Equilibria of this modified game contain the equilibria, if any, of the original game. The new formulation has a constraint structure called shared constraints, and our main result shows that if the leader objectives admit a potential function, the global minimizers of the potential function over the shared constraint are equilibria of the modified formulation. We provide another existence result using fixed point theory that does not require potentiality. Additionally, local minima, B-stationary, and strong-stationary points of this minimization are shown to be local Nash equilibria, Nash B-stationary, and Nash strong-stationary points of the corresponding multi-leader multi-follower game. We demonstrate the relationship between variational equilibria associated with this modified shared-constraint game and equilibria of the original game from the standpoint of the multiplier sets and show how equilibria of the original formulation may be recovered. We note through several examples that such potential multi-leader multi-follower games capture a breadth of application problems of interest and demonstrate our findings on a multi-leader multi-follower Cournot game.

A Complementarity Framework for Forward Contracting Under Uncertainty

We consider a particular instance of a stochastic multi-leader multi-follower equilibrium problem in which players compete in the forward and spot markets in successive periods. Proving the existence of such equilibria has proved difficult, as has the construction of globally convergent algorithms for obtaining such points. By conjecturing a relationship between forward and spot decisions, we consider a variant of the original game and relate the equilibria of this game to a related simultaneous stochastic Nash game where forward and spot decisions are made simultaneously. We characterize the complementarity problem corresponding to the simultaneous Nash game and prove that it is indeed solvable. Moreover, we show that an equilibrium to this Nash game is a local Nash equilibrium of the conjectured variant of the multi-leader multi-follower game of interest. Numerical tests reveal that the difference between equilibrium profits between the original and constrained games are small. Under uncertainty, the equilibrium point of interest is obtainable as the solution to a stochastic mixed-complementarity problem. Based on matrix-splitting methods, a globally convergent decomposition method is suggested for such a class of problems. Computational tests show that the effort grows linearly with the number of scenarios. Further tests show that the method can address larger networks as well. Finally, some policy-based insights are drawn from utilizing the framework to model a two-settlement six-node electricity market.