A Multi-Microgrid Thermal Game Model Based on Quantum Blockchain

The electricity transactions of microgrids face several problems: the high platform management cost, the low security, and the untimely consumption of scattered electricity. To solve these problems, this paper presents a multi-microgrid thermal game model based on quantum blockchain. Specifically, a dynamic model was established for the noncooperative game between aggregators, microgrids, and large users to maximize the benefit of each party, and to realize the timely consumption of scattered electricity. Next, a transaction platform was constructed based on the two-round password based authenticated key exchange (PAKE) protocol, which eliminates non-interactive zero-knowledge (NIZK), aiming to substantially enhance the post-quantum security of transactions. Then, the quantum signature using two-particle entangled Bell states was adopted to safeguard the quantum communication of electricity transactions, and authenticate the nodes. Example analysis shows that our model can realize the timely consumption of scattered electricity and thermal energy, improve the security of transaction data and users, and achieve Pareto optimality. The research provides theoretical support and decision-making basis for electricity transactions in the post-quantum age.

Asynchronous Horizons Durable-Strategies Dynamic Games and Tragedy of Cross-Generational Environmental Commons

Different entry and exit times and overlapping generations of players are common in real-life game situations. In addition, durable strategies which have effects over a period of time are no less common than nondurable strategies which have only one-shot effects. This paper develops a new class of dynamic games which contains durable strategies with asynchronous players’ horizons. The optimization techniques for solving asynchronous horizons durable strategies control are derived. Noncooperative game equilibria and cooperative optimal solution are presented. An asynchronous horizons durable strategies dynamic environmental game is provided to analyze the seemingly catastrophe-bound environmental degradation problem. The Price of Anarchy (PoA) in cross-generational exploitation of environmental commons is calibrated. A cooperative solution with a dynamically stable compensatory scheme is presented to alleviate the problem.

The Spontaneous Pricing Order in the Noncooperative Game of Monopolistic Manufacturer and Many Retailers

We consider the collective pricing orders in a minimum supply chain that is composed of a monopolistic manufacturer and many retailers that belong to the same chain store firm. The retailers have the freedom to raise or lower the local price. The chain store firm sets up the commercial rules for local retail stores to maximize its total payoff. The monopolistic manufacturer firm controls the total quantity supplied for the market to achieve maximum benefits. We applied the two dimensional Ising model in statistical physics to map the collective distribution of microscopic strategy of local retailers into the macroscopic total payoff of the chain store firm. The local stores choose to raise the price or lower the price based their own mind when the supply in market surpasses the demand. When the supply in market is far less than the demand, the stores synchronously raise prices, even though a local store only have the incomplete information of their nearest neighboring supermarket. We find the critical equation for the balance point between the action of supplier and the action of chain store management based on game theory and statistical physics. The critical equation can identify the Nash equilibrium point of the non-cooperative game between the manufacturer and the chain-store seller, and reveal different levels of collective operations. This statistical physics method also holds for more complicate supply chains and economic systems.

Applying the noncooperative game model for compensation concept in contractor selection process for large-scale projects

Nowadays, the scale of construction projects has been larger and more complex, the tender preparation is often costly to the bidder thus. It is becoming one of the primary barriers for attracting bidder’s involvement, as well as contractor's encouraging high effort. Bid compensation concept is proposed as a reward to foster the bidder participating in a higher endeavor. Game theory is ideal for modeling the dynamics and deriving high-effort strategies for bid compensation. The experiment results have demonstrated the owner can gain benefit by using rational compensation. The sensitivity analysis also shows the interest correlation between the owner and bidders. By choosing a proper strategy based on Nash Equilibrium solutions, both the owner and bidders can reach to win-win situation.

Acceptable-and-attractive Approximate Solution of a Continuous Non-Cooperative Game on a Product of Sinusoidal Strategy Functional Spaces

A problem of solving a continuous noncooperative game is considered, where the player’s pure strategies are sinusoidal functions of time. In order to reduce issues of practical computability, certainty, and realizability, a method of solving the game approximately is presented. The method is based on mapping the product of the functional spaces into a hyperparallelepiped of the players’ phase lags. The hyperparallelepiped is then substituted with a hypercubic grid due to a uniform sampling. Thus, the initial game is mapped into a finite one, in which the players’ payoff matrices are hypercubic. The approximation is an iterative procedure. The number of intervals along the player’s phase lag is gradually increased, and the respective finite games are solved until an acceptable solution of the finite game becomes sufficiently close to the same-type solutions at the preceding iterations. The sufficient closeness implies that the player’s strategies at the succeeding iterations should be not farther from each other than at the preceding iterations. In a more feasible form, it implies that the respective distance polylines are required to be decreasing on average once they are smoothed with respective polynomials of degree 2, where the parabolas must be having positive coefficients at the squared variable.

A Building-Material Supply Chain Sustainable Operations under Fairness Concerns and Reference Price Benefits

This paper incorporates fairness concerns and consumer reference price effects into a two-echelon building-material closed-loop supply chain consisting of a manufacturer and a retailer. By establishing four differential game models, we investigate the sustainable operations and cooperation of this supply chain. The four game models are a Nash noncooperative game, Stackelberg game with cost sharing, Stackelberg game with fairness concerns and cost sharing, and centralized decision model. By using dynamic models and optimal control theory, we obtain the two members’ optimal equilibrium strategies in the supply chain. Analytical results show that the consumer reference price effect has a positive impact on the manufacturer’s effort level, retailer’s publicity level, and product brand goodwill, which can improve the supply chain performance. The retailer’s partial commitment to cost sharing can enhance the production enthusiasm of the manufacturer, improve the brand reputation of the product, and enhance the two members’ individual profitability. The distributional fairness concerns of the manufacturer not only prevent the manufacturer and retailer from achieving Pareto improvement but also lead to the decline of the manufacturer’s effort level and profitability. The research conclusions of this paper can provide some insights into the cooperation and sustainable development of the supply chain.

High-Order Sliding Mode Control for Networked Control System with Dynamic Noncooperative Game Scheduling

Specific to the NCSs where sensor signals can be processed centrally, a collaborative design scheme of dynamic game scheduling and advanced control theory was proposed in the present study. Firstly, by using the Jordan standard state space equation of the research object, the three elements of state noncooperative game were built, and the existence and uniqueness of Nash equilibrium solution were verified. In addition, the iterative equation of the scheduling matrix was derived by complying with the designed utility function. Secondly, refer to the number of restricted states the order of sliding mode was determined. And based on it, the corresponding sliding surface was designed. Subsequently, the quadratic optimization theory was adopted to regulate the control value following the implementation of the scheduling strategy to ensure that the control quality was further enhanced in the limited network service. Lastly, a TrueTime simulation example is established to verify the effectiveness of the proposed scheme.

Store-Brand Introduction and Multilateral Contracting

Problem definition: We explore the impacts of store-brand (SB) introduction on multilateral contracting in vertical supply relationships that involve two upstream national-brand manufacturers (NBMs) selling through a common retailer. Two different information structures are scrutinized: simultaneous (secret offers) versus sequential contracting (public offers), essentially different timing by which the NBMs contract with the retailer. Academic/practical relevance: SB products are prevalent nowadays; however, the market shares in different categories vary substantially, from negligible sales (e.g., alcoholic beverages) to more than half of the total sales (e.g., milk). As retailers encroach on the NBMs’ product market, their relationships are reshaped accordingly. Thus, investigating whether SB introduction would overturn the conventional wisdom about multilateral contracting is pertinent. Methodology: The methodology is noncooperative game theory. Results: We identify a boundary equilibrium where the sale of the SB is negligible, but its presence enables the retailer to intensify the upstream competition and elicits better wholesale contracts. We show that this equilibrium tends to occur in a wider region under sequential contracting than under simultaneous contracting. In the boundary equilibrium of sequential contracting, the NBM could entail a first-mover advantage, a stark contrast to the second-mover advantage in the nonboundary equilibrium. Further, as opposed to the uniqueness of sequential contracting, we characterize a continuum of boundary equilibria under simultaneous contracting such that symmetric NBMs may even set asymmetric wholesale prices so as to drive the SB out of the market. Managerial implications: We provide a rationale for the observed negligible sales of certain SBs and further shed light on the choice between public and secret offers. Public offers could perform better for the retailer who, in turn, benefits from information leakage. With public offers, the NBMs’ preference for the leadership could also be reversed for SBs with negligible sales. Because of the intricate impact of SBs on contracting sequence, these two instruments should be jointly analyzed.