Equilibrium Of Game Research Articles

A multi-timescale and chance-constrained energy dispatching strategy of integrated heat-power community with shared hybrid energy storage

The community in the future may develop into an integrated heat-power system, which includes a high proportion of renewable energy, power generator units, heat generator units, and shared hybrid energy storage. In the integrated heat-power system with coupling heat-power generators and demands, the key challenges lie in the interaction between heat and power, the inherent uncertainty of renewable energy and consumers’ demands, and the multi-timescale scheduling of heat and power. In this paper, we propose a game theoretic model of the integrated heat-power system. For the welfare-maximizing community operator, its energy dispatch strategy is under chance constraints, where the day-ahead scheduling determines the scheduled energy dispatching strategies, and the real-time dispatch considers the adjustment of generators. For utility-maximizing consumers, their demands are sensitive to the preference parameters. Taking into account the uncertainty in both renewable energy and consumer demand, we prove the existence and uniqueness of the Stackelberg game equilibrium and develop a fixed-point algorithm to find the market equilibrium between the community operator and community consumers. Numerical simulations on integrated heat-power community show that the proposed solution outperforms the constant curtailment strategy with the daily cost reduced by 14.38%.

Distributed Computing Column 87 Distributed and Algorithmic Thinking across Domains

Overview. One of the goals of the column is to stimulate and publicise results by the younger generation of Distributed Computing researchers. In this spirit, this month we go into more depth into one of the two theses highlighted by the Doctoral Dissertation Award, by Dr. Siddartha Jayanti. (Unfortunately, the other 2023 recipient, Dr. Dean Leitersdorf, could not contribute this time, due to outside constraints.) Dr. Siddartha Jayanti's thesis comprises novel results in the scope of distributed and concurrent synchronization. The thesis, and Siddartha's work in general, is remarkable for both its depth and breadth: as you can see in the overview, the work incorporates technical results spanning from multi-processor synchronization to finding equilibria in multiplayer games! Another remarkable aspect is Siddartha's commitment to broadening participation in STEM, specifically to expanding science availability by writing what appears to be the first research paper in the Telugu language. It is also worth noting that Siddartha is part of the second generation of Distributed Computing researchers from his family. (As readers probably know, his father is Prof. Prasad Jayanti.) The strength and diversity of the 2023 awarded theses, together with the fact that PODC has received a record number of submissions this year, suggest that the future is bright for our area.

Risk-dominant Equilibrium in Chicken and Stag-hunt Games with Different Dilemma Strengths

Objective: This study investigates how the strength of risk-averting and gamble-intending dilemmas can affect the risk-dominant equilibrium in chicken and stag-hunt games. The focus is on deriving conditions under which the risk-dominant equilibrium can maximize group benefit. Methods: Basic concepts of game theory were used to determine the Nash equilibria of each game.The Harsanyi-Selten theory was applied to determine the risk-dominant equilibrium. By manipulating the parameters related to risk-averting and gamble-intending dilemmas, different game scenarios are sim-ulated to observe the resulting equilibria. Results: The study found that for a given strength of the risk-averting dilemma, the risk-dominant equilibrium in the chicken game continuously shifts towards mutual cooperation as the strength of the gamble-intending dilemma decreases. In the SH game, the degree of cooperation of the risk-dominant equilibrium for a given strength of the gamble-intending dilemma decreases with increasing strength of the risk-averting dilemma and takes the discrete values: 1, 0.5 and 0. The results show the importance of understanding individual risk preferences to predict strategic decisions and equilibrium outcomes in these game settings. Conclusion: The risk-dominant equilibrium in chicken and stag-hunt games depends on the relative strength of the risk-averting and gamble-intending dilemmas. By taking these factors into account, researchers and policy makers can better predict the likely outcomes of strategic interactions in scenarios with conflicting interests and different risk tolerances. The risk-dominant equilibrium can provide reasonable solutions to real-world conflict situations, such as the Iran-Iraq conflict over shared oil and gas resources.

Distributed Algorithm for Continuous-Type Bayesian Nash Equilibrium in Subnetwork Zero-Sum Games

Distributed Algorithm for Continuous-Type Bayesian Nash Equilibrium in Subnetwork Zero-Sum Games

Green subsidies as strategic trade policy tools

In a third-country market model in which two export countries adopt environmental policies (taxes and subsidies), this article analyses how an abatement (“green”) subsidy can become a potential strategic trade policy tool. When governments set the optimal policy considering their local environmental damages, a rich set of equilibria arises. In contrast to the standard result, it is shown that subsidising pollution abatement can 1) emerge as the unique Pareto-efficient Nash equilibrium of the policy game, 2) be the only feasible environmental policy when environmental awareness is low, irrespective of the efficiency of the cleaning technology, and 3) emerge as the unique Pareto-inefficient Nash equilibrium of the policy game at the end of the ecological transition. The article also tackles some dynamic issues that the policy game implies.

Invariant Equilibrium in Discontinuous Bayesian Games

We provide sufficient conditions on the primitives of a class of discontinuous Bayesian games such that all games in the class share equilibria. If a Bayesian game in the class also satisfies a weak efficiency condition, then we show its normal form is better-reply secure. The invariance property then provides an existence result for all Bayesian games in the class. Results are shown for both pure strategy and behavioral strategy equilibrium. We illustrate the application of the results with an example of a class of contests with bid caps.

Enhancing renewable energy certificate transactions through reinforcement learning and smart contracts integration

Given the complexity of issuing, verifying, and trading green power certificates in China, along with the challenges posed by policy changes, ensuring that China’s green certificate market trading system receives proper mechanisms and technical support is crucial. This study presents a green power certificate trading (GC-TS) architecture based on an equilibrium strategy, which enhances the quoting efficiency and multi-party collaboration capability of green certificate trading by introducing Q-learning, smart contracts, and effectively integrating a multi-agent trading Nash strategy. Firstly, we integrate green certificate trading with electricity and carbon asset trading, constructing pricing strategies for the green certificate, carbon, and electricity trading markets; secondly, we design a certificate-electricity-carbon efficiency model based on ensuring the consistency of green certificates, green electricity, and carbon markets; then, to achieve diversified green certificate trading, we establish a multi-agent reinforcement learning game equilibrium model. Additionally, we propose an integrated Nash Q-learning offer with a smart contract dynamic trading joint clearing mechanism. Experiments show that trading prices have increased by 20%, and the transaction success rate by 30 times, with an analysis of trading performance from groups of 3, 5, 7, and 9 trading agents exhibiting high consistency and redundancy. Compared with models integrating smart contracts, it possesses a higher convergence efficiency of trading quotes.

An adaptive differential evolution algorithm based on relaxation strategy to realize the Nash equilibrium of multi-oligopoly game

. Inspired by the idea of game learning, this paper studies the Cournot game model of the multi-oligopoly market and studies the realization of the Nash equilibrium by using adaptive differential evolution algorithm based on relaxation strategies. The realization path of Nash equilibrium is attained through an adaptive differential evolution based on a relaxation strategy procedure applied to an objective function with best response dynamics. Among them, the objective function is derived from the sum of the payoff changes of each oligopoly under best response decisions. And theoretically proved that the Nash equilibrium is the optimal solution of the objective function.

Coalitional Pareto optimal solution of one differential game

This paper is devoted to the differential positional coalitional games with non-transferable payoffs (games without side payments). We believe that the researches of the objection and counter-objection equilibrium for non-cooperative differential games that have been carried out over the last years allow to cover some aspects of non-transferable payoff coalitional games. In this paper we consider the issues of the internal and external stability of coalitions in the class of positional differential games. For a differential positional linear-quadratic six-player game with a two-coalitional structure, the coefficient constraints are obtained which provide an internal and external stability of the coalitional structure.

Low-carbon economic operation strategy for multi-agent integrated energy system considering uncertainty of renewable energy power generation

The uncertainty of renewable energy output threatens the operation safety of multi-agent integrated energy system (MAIES), which makes it difficult to balance the low-carbon economic operation demands of various stakeholders. However, the existing research solely focuses on the operational strategy of multi-agent game involving integrated energy suppliers and users in deterministic scenarios, overlooking the complementary supporting role and game interaction of shared energy storage and wind farm as independent entities of interest under the instability of renewable energy power generation. Hence, this paper first establishes the optimal operation models for integrated energy system operator (IESO), user aggregator (UA), shared energy storage operator (SESO), and wind farm operator (WFO) considering the stepped carbon trading. Second, in the face of the actual situation of uncertainty of photovoltaic and wind power output, fuzzy chance-constrained programming is adopted for processing. Then, a bi-layer game equilibrium model with IESO as a leader and UA, SESO, and WFO as followers is proposed, and the existence and uniqueness of Stackelberg equilibrium solution are proved. Finally, simulation calculation is carried out based on the YALMIP toolbox in the Matlab R2023a software, and the improved particle swarm optimization algorithm and CPLEX solver are used to solve the model. The results demonstrate that the participation of SESO and WFO as independent stakeholders in the game interaction can improve the economic and environmental benefits of MAIES. The iterative optimization of demand response subsidy prices can effectively motivate users to participate in demand response, improve the ability of MAIES to cope with the uncertain risks of renewable energy generation and load, and reduce the power grid dispatch pressure.

Resource Allocation and Pricing in Energy Harvesting Serverless Computing Internet of Things Networks

This paper considers a resource allocation problem involving servers and mobile users (MUs) operating in a serverless edge computing (SEC)-enabled Internet of Things (IoT) network. Each MU has a fixed budget, and each server is powered by the grid and has energy harvesting (EH) capability. Our objective is to maximize the revenue of the operator that operates the said servers and the number of resources purchased by the MUs. We propose a Stackelberg game approach, where servers and MUs act as leaders and followers, respectively. We prove the existence of a Stackelberg game equilibrium and develop an iterative algorithm to determine the final game equilibrium price. Simulation results show that the proposed scheme is efficient in terms of the SEC’s profit and MU’s demand. Moreover, both MUs and SECs gain benefits from renewable energy.

Low-carbon energy transition multi-agent network evolutionary under carbon trading scheme.

Transitioning to low-carbon energy is key for reaching carbon neutrality and modernizing our energy systems, but it presents significant cost-related challenges for energy businesses. To foster optimal outcomes, this paper develops a game model including power generators, high-energy businesses, and consumers in the carbon trading framework. The model explores how different entities evolve their low-carbon strategies under social learning influence to optimize utility. Stability analysis of strategy and simulation experiments reveal the following findings: (1) Greater carbon quotas reduce power generators' low-carbon transition willingness while high-energy-consuming enterprises and consumers remain unchanged. (2) Higher prices for low-carbon products offered by high-energy-consuming enterprises boost low-carbon transition motivation across all parties. (3) Increased green premiums enhance revenue for all parties but are constrained by policy and carbon pricing. (4) Both direct and indirect increases in carbon emissions negatively impact the revenue and utility for all stakeholders. (5) Increasing social learning effect fosters a shift towards low-carbon strategies, accelerating the attainment of game equilibrium, and enhancing market stability and sustainability. This research provides decision support for carbon trading policy design and low-carbon transition of energy enterprises.

Helping behavior in networked organizations

This article studies a networked organization in which agents work to directly increase the team’s output and help neighbors to reduce the disutility of working. I build a tractable framework to analyze the complexity of mutual help that cannot be simply characterized as strategic complements or substitutes, and the relationship between the structure of social networks within an organization and its efficiency. I establish the existence and uniqueness of the equilibrium of a two-stage game in which agents first decide how much helping effort to give to each neighbor, and, then, how much effort to expend to directly benefit the team. I show that denser networks might not necessarily sustain a higher level of help, because links might be redundant. If the agents are homogeneous, the network in which they are pairwise connected reaches the highest efficiency with the fewest links.

Closed-loop and open-loop equilibrium of a class time-inconsistent linear-quadratic differential games

Closed-loop and open-loop equilibrium of a class time-inconsistent linear-quadratic differential games

A Game Model Analysis of the International Digital Service Tax in an Asymmetric Market Duopoly

Against the backdrop of the rapidly expanding digital economy, multinational corporations are increasingly exploiting information asymmetry in the market to employ covert and diverse methods of tax avoidance. This poses a significant challenge to tax collection and administration. The proposal of a digital service tax aims to adapt the international tax system to the digitalization of the economy, ensuring fair and reasonable tax payments. To address these challenges, this article assumes an asymmetric international digital economy market and a domestic market characterized by duopoly. It establishes an asymmetric market duopoly game, calculates the digital gains of each country's market using the logistic function, determines the Nash equilibrium of the data service tax game, and analyzes the relationship between the digital service tax rates of strong and weak countries in the digital economy.

Evolutionary game analysis of multiple subjects in the management of major public health emergencies

The frequent occurrence of major public health emergencies (MPHEs) significantly challenges national security, economic stability, social operation and the safety of people's lives and property worldwide. Consequently, enhancing the emergency management of MPHEs is critically urgent. This paper constructs a game model involving local government, social organisations, and the public for MPHE management, exploring strategy combinations and influencing factors across various scenarios. Several results were obtained. (1) Local government, social organisations, and the public each have positive and negative strategy choices based on cost–benefit analysis, leading to eight different strategy combinations. Furthermore, all three take positive strategies as the optimal way to achieve the game equilibrium. (2) The transformation of strategy combinations is primarily influenced by the cost-benefit gap and the strategic decisions of local government. (3) Altering a subject's initial strategy value doesn't change its final choice but impacts the time to achieve a stable strategy equilibrium. The severity of local government punishments on social organisations influences their strategic choices and the time to optimal strategy, whereas rewards to the public or social organisations only affect the time to achieve this strategy. The findings of this study can not only help improve the collaborative governance system of MPHEs but also provide scientific guidance on how governments can manage MPHEs.

Strategic Fertility, Education Choices, and Conflicts in Deeply Divided Societies

Abstract Fertility becomes a strategic choice for minorities when having a larger share of the population helps to increase power. If parents invest resources to educate their children, then raising fertility for strategic reasons might be at the cost of future human capital. We dispel this view using census data from several developing countries. We show that religious and ethnic minorities in Indonesia, China, and Malaysia tend to invest more in both education and fertility compared to larger groups. Solving for the Nash equilibrium of an appropriation game between two groups with education and fertility being prescribed as group-specific behavioral norms, we offer a rationale for the observed patterns provided that human capital is an important input to appropriation.

Computing perfect stationary equilibria in stochastic games

The notion of stationary equilibrium is one of the most crucial solution concepts in stochastic games. However, a stochastic game can have multiple stationary equilibria, some of which may be unstable or counterintuitive. As a refinement of stationary equilibrium, we extend the concept of perfect equilibrium in strategic games to stochastic games and formulate the notion of perfect stationary equilibrium (PeSE). To further promote its applications, we develop a differentiable homotopy method to compute such an equilibrium. We incorporate vanishing logarithmic barrier terms into the payoff functions, thereby constituting a logarithmic-barrier stochastic game. As a result of this barrier game, we attain a continuously differentiable homotopy system. To reduce the number of variables in the homotopy system, we eliminate the Bellman equations through a replacement of variables and derive an equivalent system. We use the equivalent system to establish the existence of a smooth path, which starts from an arbitrary total mixed strategy profile and ends at a PeSE. Extensive numerical experiments, including relevant applications like dynamic oligopoly models and dynamic legislative voting, further affirm the effectiveness and efficiency of the method.

The choice of suppliers and consumers: the evolutionary game equilibrium of platforms

ABSTRACT Platforms competition affects both the structure of the whole industry and the fate of the individual companies within it. The extant studies either simply divide the participants of a platforms war into suppliers and consumers or adopt unbounded rationality assumptions. This paper constructs a game model that includes platforms, suppliers, and the final consumers. We analyze the condition and stability of each equilibrium and the impacts of the characteristics of the core and complementary products on the equilibrium by using the method of evolutionary game. Our results show the following: (1) If the two platforms initially have separate advantages in terms of the number of suppliers or consumers, there will be an equilibrium of the coexistence; otherwise, there will be an equilibrium of single platform dominating. (2) The equilibrium of a single platform dominating is more stable than that of the coexistence of multiple platforms. (3) Incidental shocks to the number of suppliers are more likely to break the coexistence equilibrium than consumers. (4) Platforms with poor core product quality and a high price for core and complementary products can coexist with other superior platforms only if the former has more consumers and suppliers at the beginning of the competition.

On Construction of Subgame Perfect Nash Equilibria in Stackelberg Games

Identifying a Subgame Perfect Nash Equilibrium (SPNE) of a two-player Stackelberg game could be not a manageable task, especially when the players have a continuum of actions and the follower’s best reply correspondence is not single-valued. Aim of the paper is to investigate the issue of construction of SPNEs in Stackelberg games by exploiting perturbations of both the action sets and the payoff functions of the leader and the follower. To achieve the goal, since the limit of SPNEs of perturbed games is not necessarily an SPNE of the original game even for classical perturbations, we prove under nonrestrictive convergence conditions how to produce an SPNE starting from a sequence of SPNEs of general perturbed games. This result allows to describe a procedure to find SPNEs that can accommodate various types of perturbations. More precisely, under mild assumptions on the data of the original game, we show that a large class of perturbed games (including, for example, perturbation approaches relying on the Tikhonov and entropic regularizations or motivated by altruistic and antagonistic behaviors) satisfies the convergence conditions for constructing an SPNE. The specific SPNE selections associated to such a class, together with their possible behavioral interpretations, are discussed and an illustrative example is provided.