Complete Information Game Research Articles

Modeling and optimization of networked evolutionary game based on incomplete information with switched topologies

AbstractIn the realm of evolutionary game theory, the majority of scenarios involve players with incomplete knowledge, specially regarding their opponents' actions and payoffs compounded by the ever‐shifting landscape of players' interactions. These dynamics present formidable challenges in both the analysis and optimization of game evolution. To address this, a novel model named the networked evolutionary game (NEG) is proposed based on incomplete information with switched topologies. This model captures situations where players possess limited insight into their opponents' benefits, yet make decisions based on their own payoffs while adapting to different networks and new players. To bridge the gap between incomplete and complete information games, R. Selten's transformation method is leveraged, a renowned approach that converts an incomplete information game into an interim agent game, thereby establishing the equivalence of pure Nash equilibria (NE) in both scenarios. Employing the semi‐tensor product (STP) of matrices, a powerful tool in logistic system, the evolution of the model is articulated through algebraic relationships. This enables to unravel the patterns of game evolution and identify the corresponding pure Nash equilibria. By introducing control players, strategically positioned within the game, optimized control is facilitated over the evolutionary trajectory, ultimately leading to convergence towards an optimal outcome. Finally, these concepts are illustrated with a practical example within the paper.

Two-Stage Games of Complete but Imperfect Information: Application in International Trade with Tariff

Trade relationships are very complicated especially given the battles between Keynesian and Neo-liberal economic views on the issue. Game theory and its application in international trade can provide a simplistic but important method for quantifying the benefits of trading. In this paper, we intend to use two-stage games of complete but imperfect information in the trading context among two and three countries and compare it with the non-trading country. The purpose of this work is to apply a two-level game model of complete but incomplete information in game theory and apply it to international economics in the context of customs trading. The basic literature for this work is “Game Theory for Applied Economists” by Robert Gibbons. Glenn W. Harrison and E. E. Rustrom on Trade War, Trade Negotiation, and Applied Game Theory. We provide mathematical models and eventually provide the interpretation in a broader context.

Formation mechanism of on-grid power tariff using game model of complete information

The key to the reform of the power system is to design a fair bidding and trading system. Analyzing the transaction process of electricity price competition, suppressing market power and other unfavorable factors, and finding a perfect bidding system are the research goals of this paper. In order to study the competition in the power spot market and power contract market, this paper employs the game model of complete information and the game theory as a tool. The power spot market adopts the Market Clearing Price (MCP) settlement method, in which the power grid determines the maximal real-time price of the generator node as the MCP. The price is based on the three bidding strategy curves of the power plant. As a result, a Nash equilibrium of power plant revenue is formed. According to the Cournot model and Stackelberg model that analyze the power contract market, the long-term equilibrium price of Stackelberg model in the power contract market is higher than that of the perfectly competitive market and less than or equal to the output of perfect monopoly market. The long-term equilibrium price and output in the power contract market are both certain and stable. This paper has analyzed the static game of complete information in the power market and carried out practical application. The results show that the bidding strategies of power plants have a Nash equilibrium and they have an incentive to collude. The MCP mechanism cannot solve the problem of market power influence. The conclusion of the research provides a basis for the design of the power hybrid auction system.

Treatment effect models with strategic interaction in treatment decisions

This study considers treatment effect models in which others’ treatment decisions can affect both one’s own treatment and outcome. Focusing on the case of two-player interactions, we formulate treatment decision behavior as a complete information game with multiple equilibria. Using a latent index framework and assuming a stochastic equilibrium selection, we prove that the marginal treatment effect from one’s own treatment and that from the partner are identifiable on the conditional supports of certain threshold variables determined through the game model. Based on our constructive identification results, we propose a two-step semiparametric procedure for estimating the marginal treatment effects using series approximation. We show that the proposed estimator is uniformly consistent and asymptotically normally distributed. As an empirical illustration, we investigate the impacts of risky behaviors on adolescents’ academic performance.

Strict robustness to incomplete information

We study a strict version of the notion of equilibrium robustness by Kajii and Morris (Econometrica 65:1283–1309, 1997) that allows for a larger class of incomplete information perturbations of a given complete information game, where with high probability, players believe that their payoffs are close to (but may be different from) those of the complete information game. We show that a strict monotone potential maximizer of a complete information game is strictly robust if either the game or the associated strict monotone potential is supermodular, and that the converse also holds in all binary-action supermodular games.

Game Theory Optimization Based on Python: Evidence from Board Game “Go-Moku”

Game theory has been widely used in multiple fields such as economics, computer science, and political science to study the rational behavior of multiple decision makers in different scenarios. In recent years, with the rapid development of artificial intelligence, AI trained using game theory has shown outstanding performance in board games such as Go, chess and backgammon. This study explores the application of game theory optimization in the board game "Go-Moku" using a learning algorithm combining Monte Carlo tree search algorithm and reinforcement learning. The paper discusses recent developments in game theory in Go-Moku and explains the Monte Carlo tree search algorithm in detail. The performance of the algorithm is evaluated through experimental results of the application of Alpha Zero in the Go-Moku domain, demonstrating its effectiveness in improving the gaming capabilities of artificial intelligence. According to the analysis, after 1,100 training sessions, the algorithm combining reinforcement learning and MCTS had a 9:1 win rate compared to a pure MCTS approach with 2,000 self-simulations per step. And playing against the 800-times pure MCTS method, it reached a 10:0 win rate for the first time in the 300th game. In addition, the paper discusses potential applications of game-theoretic optimization in other dynamic games. Overall, these results shed light on further exploration of game theory in the area of complete information games and reinforcement learning.

중학생 R&E 지도 사례

This is a case study of R&E instruction for middle school students in Science Gifted Education Center who explored the winning solution of the NIM game, a type of two-person finite turn-based fixed complete information game, and modified the game. It is not difficult for middle school students to understand the solution of the NIM game and solve the problem while obtaining the logical sum expressed in binary. However, unlike the enrichment course, R&E education for gifted students explores new mathematical properties beyond the given problem-solving method, and experiences the rediscovery of principles, reinvention of forms, and re-creation of games through various transformations (making, development). We should be able to guide them through these methods. As a result of re-creation mathematics through recreational activities, students created a modified NIM game that extended it in addition to several known modified NIM games. The results of this study can be used for the development of modified NIM games and will be helpful for teaching R&E in the secondary school course.

Bargaining game based on psychological cost of electric vehicles and risk assessment of aggregators

AbstractAs electric vehicles (EVs) begin to participate in the peak‐shaving auxiliary service market, the question of how price aggregators can maximize the peak‐shaving capacity provided by EVs and maximize their own profit has become a major problem. This paper proposes a bargaining game pricing method based on the psychological cost of EVs and the risk assessment of aggregators. First, the comprehensive psychological cost of EV users is obtained based on the impact of users’ participation in peak shaving on the battery life of EVs and on users’ original travel plans and time, and the impact of aggregator pricing on users’ psychology. Then, based on users’ psychological cost and the law of gravitation, the evaluation scheme for the peak‐shaving capacity of EVs is obtained. On the basis of conditional value at risk (CVaR), the mixed CVaR is obtained by considering the risk‐chasing behaviour of users. Based on the mixed CVaR, the risk assessment of aggregators’ participation in the peak‐shaving auxiliary service market is carried out. According to the above information, the aggregator and EV groups are engaged in a bargaining game based on the peak‐shaving pricing problem, which is divided into complete information game and incomplete information game. Finally, the feasibility of the proposed method is verified by an example analysis which is run by the MATLAB R2019b. The method proposed in this paper provides aggregators with a complete peak‐shaving electricity pricing scheme, effectively improving the dispatching capacity of EVs. It is helpful to rationalize the pricing of aggregators and maximize their profits. EVs can also obtain satisfactory profits, attracting more EVs to participate in peak shaving, and reduce the pressure on power grid peak shaving.

A jointly optimal design of control and scheduling in networked systems under denial-of-service attacks

We consider the joint design of control and scheduling under stochastic Denial-of-Service (DoS) attacks in the context of networked control systems. A sensor takes measurements of the system output and forwards its dynamic state estimates to a remote controller over a packet-dropping link. The controller determines the optimal control law for the process using the estimates it receives. An attacker aims at degrading the control performance by increasing the packet-dropout rate with a DoS attack on the sensor-controller channel. We assume both the controller and the attacker are rational in a game-theoretic sense and establish a partially observable stochastic game to derive the optimal joint design of scheduling and control. Using dynamic programming we prove that the control and scheduling policies can be designed separately without sacrificing optimality, making the problem equivalent to a complete information game. We employ Nash Q-learning to solve the problem and prove that the solution is guaranteed to constitute an ϵ-Nash equilibrium. Numerical examples are provided to illustrate the interactions between the controller and the attacker.

Multiple treatments with strategic substitutes

We develop an empirical framework to identify and estimate the effects of treatments on outcomes of interest when the treatments are the result of strategic interaction (e.g., bargaining, oligopolistic entry, peer effects). We consider a model where agents play a discrete game of complete information and strategic substitutability, whose equilibrium actions (i.e., binary treatments) determine a post-game outcome in a nonseparable model with endogeneity. Due to the simultaneity in the first stage, the model as a whole is incomplete and the selection process fails to exhibit the conventional monotonicity. Without imposing parametric restrictions or large support assumptions, this poses challenges in recovering treatment parameters. To address these challenges, we establish a monotonic pattern of the equilibria in the first-stage game in terms of the number of treatments selected. Based on this finding, we derive bounds on the average treatment effects (ATE’s) under nonparametric shape restrictions and the existence of excluded exogenous variables. We show that the instrument variation that compensates strategic substitution helps solve the multiple equilibria problem. We apply our method to data on airlines and air pollution in cities in the U.S. We find that (i) the causal effect of each airline on pollution is positive, and (ii) the effect is increasing in the number of firms but at a decreasing rate.

Games of incomplete information: A framework based on belief functions

This paper proposes a model for incomplete-information games where the knowledge of the players is represented by a Dempster-Shafer belief function. Beyond an extension of the classical definitions, it shows such a game can be transformed into an equivalent hypergraphical complete-information game (without uncertainty), thus generalizing Howson and Rosenthal's theorem to the framework of belief functions and to any number of players. The complexity of this transformation is finally studied and shown to be polynomial in the degree of k-additivity of the mass function.

Research on strategy of green electricity acquisition transaction of park-level energy internet by using STP

In order to save resources and reduce air pollution, human beings have begun to pay attention to the production and use of photovoltaic, wind power and other green power. Due to the difficulty of direct transaction between green power producers and power users, a park-level energy Internet has been proposed and used to connect all kinds of green electricity with power users. Then park users can effectively buy and use green electricity. Taking the park-level energy Internet as the scenario, this paper constructs a transaction model between green power operators and green power producers. The model is a dynamic game of complete and perfect information. The dynamic characteristics of this game model are analyzed by using semi-tensor product method, and corresponding strategies are provided for all players. From the results obtained, it is easy to find that in many cases, the strategy profile of all participants are constantly changing to obtain more profits, rather than stable at some traditional Nash equilibrium.

A Hybrid Game Strategy for the Pursuit of Out-of-Control Spacecraft under Incomplete-Information

This paper investigates the pursuit problem of out-of-control spacecraft under incomplete-information, and provides new ideas for the disposal of dangerous spacecraft with obstacle avoidance capability. Throughout the pursuit process, the maneuver strategy of the out-of-control spacecraft is unknown, and its possibly unconventional and irregular maneuvers may endanger the safe operation of any other spacecraft on orbit. Based on the differential game theory, complete information game strategy pairs are derived. Then, considering that the control information of the target is unavailable to the pursuer, the target’s maneuver is regarded as the disturbance item. The incomplete information game strategy is derived from the unilateral optimal cost function. Furthermore, the disturbance estimator is designed to identify the missing information of the target. The optimal hybrid game strategy is proposed as an approach to compensate the target maneuver strategy. Simulation study has been conducted and the results have validated that the missing information can be effectively estimated using the estimator. The designed hybrid game strategy can achieve rapid approach, while saving fuel consumption for on-orbit service.

Characterizing robust solutions in monotone games

In game theory, p-dominance and its set-valued generalizations serve as important robust solution concepts. We show that in monotone games, (which include the broad classes of supermodular games, submodular games, and their combinations) these concepts can be characterized in terms of pure strategy Nash equilibria in an auxiliary game of complete information. The auxiliary game is constructed in a transparent manner that is easy to follow and retains a natural connection to the original game. Our results show explicitly how to map these concepts to corresponding Nash equilibria thereby identifying a new bijection between robust solutions in the original game and equilibrium notions in the auxiliary game. Moreover, our characterizations lead to new results about the structure of entire classes of such solution concepts. In games with strategic complements, these classes are complete lattices. More generally, they are totally unordered. We provide several examples to highlight these results.

Protection and Planning of Historic Districts Based on Internet of Things Perception.

With the development of the Internet of Things era, the Internet of Things technology has been gradually accepted by people and gradually entered the category of block management, but the specific practical application scope is not wide enough. At present, the community management of residents in blocks generally adopts closed management, and there are some problems such as insufficient scope of property management, weak strength, and serious waste of human resources. Incomplete development of the hidden value is of cultural tourism blocks. At the same time, there are still some problems in the traffic management of blocks, such as incomplete monitoring scope and weak supervision. Therefore, this study proposes a bilevel programming model to solve the optimization scheme of block road network, adopts the complete information game model to analyze the imbalance between property and residents, and adopts the AHP fuzzy evaluation method to detect the current life happiness coefficient of urban residents and collect residents' suggestions for the future planning of historical blocks. Because the perception layer of the Internet of Things has the advantages of rapidity, accuracy, and unmanned operation, it can contribute a practical force to the protection and planning of historical blocks quickly and at low cost.

Principal-agent VCG contracts

We study a complete information game with multiple principals and multiple common agents. Each agent takes an action that can affect the payoffs of all principals. Prat and Rustichini (2003) who introduce this model assume classic contracts: each principal offers monetary transfers to each agent conditional on the action taken by the agent. We define VCG contracts in which the monetary transfers to each agent additionally depend on all principals' offers, and study its effect on the existence of efficient pure subgame perfect equilibrium outcomes. Using a necessary and sufficient condition for the existence of a pure subgame perfect equilibrium (pure SPE) with VCG contracts, which we develop, we show that the class of instances that admit an efficient pure SPE with VCG contracts strictly contains the class of instances that admit an efficient pure SPE with classic contracts. In addition, the difference between the former class and the class of instances that admit a ‘weakly truthful’ SPE with classic contracts has positive measure. Although VCG contracts broaden the existence of pure subgame perfect equilibria, we show that the worst case welfare loss in a pure SPE outcome, over all games with any fixed M≥2 number of principals, is the same for both VCG contracts and classic contracts.

Two-Stage Games of Complete but Imperfect Information: Application in International Trade with Tariff

Two-Stage Games of Complete but Imperfect Information: Application in International Trade with Tariff

Game Theory Based Dynamic Adaptive Video Streaming for Multi-Client Over NDN

The performance of Dynamic Adaptive Streaming (DAS) in multi-client scenarios can be improved by taking advantage of the aggregation capability of Named Data Networking (NDN). In this paper, we propose a client-side game theory based (GB) ABR algorithm for NDN that can achieve proactive aggregation of requests among clients as much as possible without requiring coordinating with other clients or scheduling by a central controller. We model the interaction between a DAS client and network as an incomplete information non-cooperative game. Then, this game is transformed into a complete but imperfect information game by Harsanyi transformation, and each client can issue an appropriate bitrate request by solving the Bayesian Nash Equilibrium (BNE) problem respectively. By designing the payoff function pair elaborately, the equilibrium point of the game can correspond to the situation that multiple clients issuing the same video bitrate request, that is, requests aggregation, which will reduce the repeated traffic and also achieve fairness. Compared with the existing solutions, through simulation and real-world experiments in multi-client video distribution scenarios, the GB algorithm outperforms the comparison algorithms in terms of overall Quality of Experience (QoE), fairness, and network bandwidth utilization, etc.

Credit and guarantee insurance: A consistent pricing approach in supply chain finance

Credit insurance is a new loan guarantee contract which can effectively stimulate domestic demand and promote consumption. According to different modes of payment, individual credit loan guarantees mainly include credit insurance and guarantee insurance. In this paper, we apply the Complete Information Game to analyze the strategies of the insured subject and the risk subject under different scenarios of personal loan guarantee, and obtain the influencing factors of each decision-making subject in supply chain finance. The conclusion shows that the credit status of individual loan applicants greatly affects the decision-making of supply chain financial entities such as banks. Based on this, this paper puts forward corresponding suggestions for the credit insurance business management.

A Bayesian Game Approach for Demand Response Management Considering Incomplete Information

Residential flexible resource is attracting much attention in demand response (DR) for peak load shifting. This paper proposes a scenario for multi-stage DR project to schedule energy consumption of residential communities considering the incomplete information. Communities in the scenario can decide whether to participate in DR in each stage, but the decision is the private information that is unknown to other communities. To optimize the energy consumption, a Bayesian game approach is formulated, in which the probability characteristic of the decision-making of residential communities is described with Markov chain considering human behavior of bounded rationality. Simulation results show that the proposed approach can benefit all residential communities and power grid, but the optimization effect is slightly inferior to that in complete information game approach.