Dynamic Bayesian Game Research Articles

Enhancing ecological uncertainty predictions in pollution control games through dynamic Bayesian updating

This study presents a dynamic Bayesian game model designed to improve predictions of ecological uncertainties leading to natural disasters. It incorporates historical signal data on ecological indicators. Participants, acting as decision-makers, receive signals about an unknown parameter-observations of a random variable’s realization values before a specific time, offering insights into ecological uncertainties. The essence of the model lies in its dynamic Bayesian updating, where beliefs about unknown parameters are refined with each new signal, enhancing predictive accuracy. The main focus of our paper is to theoretically validate this approach, by presenting a number of theorems that prove its precision and efficiency in improving uncertainty estimations. Simulation results validate the model’s effectiveness in various scenarios, highlighting its role in refining natural disaster forecasts.

Dynamic Bayesian game optimization method for multi-energy hub systems with incomplete load information

The interconnection of Energy Hub can enhance the energy efficiency and reliability associated with the independent operation of energy systems. However, the traditional optimal scheduling methods are hard to tackle the situation with the incomplete load information and competitive constraints of a multi-Energy Hub. This paper proposes a dynamic Bayesian game optimization scheduling strategy considering incomplete information on users’ load-side demand. First, a load forecast error coefficient is introduced to handle the conditional probability problem caused by incomplete information through the Bayesian rule. The constraint relationship among multi-Energy Hub under the dynamic price mechanism is analyzed to meet the economic and environmental coordination goals under load uncertainty. Second, extending from Nash equilibrium to Bayes Nash equilibrium proves the existence and uniqueness of Nash equilibrium solutions in Bayesian game models. The decision game algorithm is used to optimize the scheduling of the multi-Energy Hub and subsequently ensure the autonomous scheduling of the system and solve the information barriers. Finally, an Integrated Energy System composed of three Energy Hubs was used to validate the effectiveness and superiority of the proposed optimization method. Results show that under the Bayesian game decision, the multi-Energy Hub game model has reduced the total cost of the Integrated Energy System by 0.78 %, which can improve the economic benefit and address the environmental pollution problem.

Interactive influences of ecosystem services and socioeconomic factors on watershed eco-compensation standard “popularization” based on natural based solutions

Watershed eco-compensation is a policy tool to realize watershed environment improvement and regional economic development. It is important to eliminate the influence of economic differences between upstream & downstream regions and realize the fairness of regional social development based on Natural based Solutions (NbS). At present, lack of clarity in coupling and coordination analysis of ecosystem services & socioeconomic based on NbS could hamper watershed eco-compensation standards “popularization” and reduce the ability to successfully ecological governance. To meet the needs of economic development and ecological service value realization, dynamic equilibrium game research based on multidimensional relationship coordination and a multi-objective optimization solution of economic benefit distribution was carried out. To achieve the bargaining Bayesian/Nash equilibrium of the watershed eco-compensation standard in the game, the existence conditions of the equilibrium solution of the eco-compensation standard based on the mixed equilibrium game implementation process were studied. To carry out the complete information dynamic game, the equilibrium solution of the watershed eco-compensation standard based on the dynamic transfer payment was solved, and the rational analysis of the dynamic Bayesian equilibrium game of bargaining based on the incentive compatibility mechanism was also discussed. Water quantity and quality eco-compensation can ensure balanced development between ecological protection and the social economy in the Mihe River Basin. Combined with the variation law of socioeconomic water intake-utilization standards and the water use value, the city of Shouguang City & Qingzhou City should pay Linqu County 4.78 million US$ and 1.29 million US$ as watershed eco-compensation standards per year based on NbS, respectively. To verify the rationality of the results derived from the economically optimal model, two modes of “bargaining” & “perfect competition”, were used to study the characteristics of the protocols generated by the equilibrium game, and the applicable conditions of the nonzero-sum game solution upstream and downstream of the watershed were also explored. Based on the nonzero-sum processing of the survey results, the current relationship between the input value of eco-compensation and the willingness to pay satisfies v≥c+1/4. Based on the dynamic game & Bayesian equilibrium solution of bargaining, the watershed eco-compensation quota of water quantity & quality is 6.07 million US$, the willingness to pay is 65.63 US$/month. These findings contribute to the quantifying process of bargaining & dynamic equilibrium by transforming “ambiguous” information to achieve sustainable ecosystem service management and develop socioeconomic strategies associated with different compensation features based on NbS, thus helping to inform watershed management.

Research on Game Theory of Air Traffic Management Cyber Physical System Security

For the air traffic management cyber physical system, if an attacker successfully obtains authority or data through a cyber attack, combined with physical attacks, it will cause serious consequences. Game theory can be applied to the strategic interaction between two parties, especially if the two parties have different goals. The offensive and defensive game process of the air traffic management cyber physical system is a non-cooperative and incomplete information dynamic game. The attacker can choose to camouflage the type of attack launched. The attack detection device configured in the system has a certain probability that the attack type can be successfully detected. According to the type of attack detected, the defender updates the posterior belief of the attack type and selects the corresponding protective strategies. According to the game process of offense and defense, a dynamic Bayesian game model of the air traffic management cyber physical system is established, the possible perfect Bayesian Nash equilibrium and its existence conditions are solved, and a complete mathematical model is constructed. The analysis shows that the dynamic Bayesian game model of the air traffic management cyber physical system can help the system defender to quickly obtain an equilibrium strategy and reduce the loss of the system as much as possible.

DDoS Defense Method in Software-Defined Space-Air-Ground Network from Dynamic Bayesian Game Perspective

The centralized management of Software-Defined Network (SDN) brings convenience to Space-Air-Ground Integrated Networks (SAGIN), which also makes it vulnerable to Distributed Denial of Service (DDoS). At present, the popular detection methods are based on machine learning, but most of them are fixed detection strategies with high overhead and real-time control, so the efficiency is not high. This paper designs different defense methods for different DDoS attacks and constructs a multitype DDoS defense model based on a dynamic Bayesian game in the Software-Defined Space-Air-Ground Integrated Networks (SD-SAGIN). The proposed game model’s Nash equilibrium is solved based on the different costs and payoffs of each method. We simulated the attack and defense of DDoS in Ryu controller and Mininet. The results show that, under our model, the attacker and defender’s strategies are in a dynamic balance, and the controller can effectively reduce the defense cost while ensuring detection accuracy. Compared with the existing traditional Support Vector Machine (SVM) defense method, the performance of the proposed method is better, and it provides one of the references for DDoS defense in SD-SAGIN.

Protecting Location Privacy by Multiquery: A Dynamic Bayesian Game Theoretic Approach

When using location-based services (LBSs), a user obtains points-of-interest (PoI) information by providing the LBS platform with his current geo-location. Such a search leads to potential privacy leakage if an adversary has access to his geo-data. Traditional <i>k</i>-anonymity mechanisms instruct a user to bear the overhead to report his current location together with <i>k</i> - 1 dummy locations to confuse the adversary, which only work well given a large number <i>k</i>. Aware of the common practices that a user is actually flexible in service requirement (e.g., as long as the searched PoIs are within his walking distance), we propose a novel approach to help the user gain location privacy from service flexibility for the challenging case of a small number <i>k</i>. By analyzing the strategic interaction between the user and the adversary in a dynamic Bayesian game, we prove that the user&#x2019;s equilibrium strategy depends on the adversary&#x2019;s capability of accessing geo-data. Take <i>k</i> = 2 for example, we find that if the adversary is not likely to access both geo-data, the user should report the two dummy locations at two different directions of his real location, and otherwise at the same direction. Perhaps surprisingly, the user may benefit from the adversary&#x2019;s access to more geo-data. Furthermore, we extend the game-theoretic approach for multi-query and arbitrary user location distributions. Numerical results show that our approach obviously outperforms <i>k</i>-anonymity mechanisms especially under a small number <i>k</i>.

Shipper Cooperation in Stochastic Drone Delivery: A Dynamic Bayesian Game Approach

With the recent technological innovation, unmanned aerial vehicles, known as drones, have found numerous applications including package and parcel delivery for shippers. Drone delivery offers benefits over conventional ground-based vehicle delivery in terms of faster speed, lower cost, more environment-friendly, and less manpower needed. However, most of existing studies on drone delivery planning and scheduling focus on a single shipper and ignore uncertainty factors. As such, in this paper, we consider a scenario that multiple shippers can cooperate to minimize their drone delivery cost. We propose the Bayesian Shipper Cooperation in Stochastic Drone Delivery (BCoSDD) framework. The framework is composed of three functions, i.e., package assignment, shipper cooperation formation and cost management. The uncertainties of drone breakdown and misbehavior of cooperative shippers are taken into account by using multistage stochastic programming optimization and dynamic Bayesian coalition formation game. We conduct extensive performance evaluation of the BCoSDD framework by using customer locations from Solomon benchmark suite and a real Singapore logistics industry. As a result, the framework can help the shippers plan and schedule their drone delivery effectively.

Tripartite Coordinated Regulation of New Energy Vehicles Based on Dynamic Bayesian Game

Manufacturers are disseminating false or ambiguous information regarding new energy vehicles (NEVs), which has led to skepticism from consumers about the quality of NEVs. In this research, we simultaneously considered the relationship among manufacturers, consumers, and governments from the perspective of stakeholders, and then we analyzed the tripartite coordinated regulation. In view of the serious information asymmetry of NEVs, we innovatively developed the Bayesian dynamic game model. By solving refined Bayesian equilibrium strategies, this study explores the effects of key influencing factors on strategic choices. On the basis of the conclusion, relevant countermeasures and suggestions are put forward to engender effective regulation by governments.

Warning Against Recurring Risks: An Information Design Approach

The World Health Organization seeks effective ways to alert its member states about global pandemics. Motivated by this challenge, we study a public agency’s problem of designing warning policies to mitigate potential disasters that occur with advance notice. The agency privately receives early information about recurring harmful events and issues warnings to induce an uninformed stakeholder to take preemptive actions. The agency’s decision to issue a warning critically depends on its reputation, which we define as the stakeholder’s belief regarding the accuracy of the agency’s information. The agency faces then a trade-off between eliciting a proper response today and maintaining its reputation to elicit responses to future events. We formulate this problem as a dynamic Bayesian persuasion game, which we solve in closed form. We find that the agency sometimes strategically misrepresents its advance information about a current threat to cultivate its future reputation. When its reputation is sufficiently low, the agency downplays the risk and actually downplays more as its reputation improves. By contrast, when its reputation is high, the agency sometimes exaggerates the threat and exaggerates more as its reputation deteriorates. Only when its reputation is moderate does the agency send warning messages that fully disclose its private information. Our study suggests a plausible and novel rationale for some of the false alarms or omissions observed in practice. We further test the robustness of our findings to imperfect advance information, disasters without advance notice, and heterogeneous receivers. This paper was accepted by Manel Baucells, decision analysis.

Secured transmission using trust strategy-based dynamic Bayesian game in underwater acoustic sensor networks

Cooperation among sensor nodes and the unreliability of acoustic channels are the significant challenges in underwater acoustic sensor networks (UASNs). In UASNs, the unreliability may results in high packet loss due to the high bit-error-rate and packets being dropped due to network congestion. High packet loss decreases the transmission rate in a network. An effective secure transmission mechanism is very much essential among the nodes in UASNs. In this paper, a trust strategy-based dynamic Bayesian game (TSDBG) model is proposed to resolve these problems. In TSDBG, a secure suite is created among the nodes in the network. Trust and Payoff are calculated for each node to evaluate the particular node involved in the packet-dropping and misbehaving activities that occurred during the transmission. Each node updates its trust value using Bayes' rule. Regular nodes are continuously monitored to analyze their neighbor nodes based on trust value. The simulation results reveal that the proposed scheme significantly reduces the packet-dropping attack, misbehaving activities of malicious nodes, propagation delay, and thereby enhancing secure transmission.

The Economics of Cyber Crime

Digital technologies are creating more value and thus becoming more attractive to cyber criminals. Gary Becker provides a philosophy for understanding crimes from an economic perspective, but criminal behavior and potential policies against it differ in the context of a digital economy. Criminals with economic incentives are expected to hack digital systems and ask for a ransom to not disturb those compromised. We model the interactions between attackers and defenders with a dynamic Bayesian game. There are two processes. The first is the attackers' learning about the distribution of the defenders' level of defense, and the second is the attackers' reputation building based on being honest after being paid. The attackers' dynamic decision is captured by a bandit process. The defenders' behavior exerts externalities on themselves by influencing the attackers' behavior. We explore policies that could enhance social welfare through moderating these externalities.

A Bayesian Game-Theoretic Intrusion Detection System for Hypervisor-Based Software Defined Networks in Smart Grids

The future smart grids (SGs) require advanced capabilities in terms of automation, processing, monitoring, and communication. The most crucial component in the successful sustainability of SGs is communication management. In the vSDNs, a hypervisor is implemented between a physical infrastructure and a control plane that abstracts the underlying SDN infrastructure into multiple isolated virtual slices, i.e., we can have multiple vSDNs each with its controller. For that purpose, the virtualized SDNs offer a promising solution as they offer better network management, programmability, and virtualization. However, vSDN-based SGs are prone to many security issues. To disturb operations of the SGs, the security of the vSDN can be compromised by manipulating the jeopardized switches in the DDoS attacks to repress the resources of vSDN controllers. To prevent the exploitation of a vSDN-based SG architecture and preserve its limited resources, this paper formulates the strategic interaction between a hypervisor monitoring its vSDN controllers and the source of new flow requests potentially launching a DDoS attack, via compromised switches, as a non-cooperative dynamic Bayesian game of intrusion detection. Our game model enables a hypervisor to distribute its limited resources to monitor guest vSDN controllers optimally. The performance evaluation via simulations shows that our game model enables a hypervisor not only to increase the probability of detecting distributed attacks and minimize false positives but at the same time, its monitoring costs get reduced as the allocation of resources to monitor vSDN controllers depends upon its belief about the source of the attacks that it forms based on its observation.

Multi-period inventory games with information update

This paper addresses the multi-period inventory game of two substitutable products with learning, in which the demand distribution form in each period is known but one or more parameters are unknown in advance. The retailers update the estimates of the unknown parameters using the historical demand information as the transaction proceeds. At each period, the retailers check the initial inventories and update the forecasts about their demands first. Then they place the orders, which are delivered immediately. Finally the demands are realized and satisfied by the available inventories. The unsatisfied demand of one retailer switches to another and is satisfied by the other׳s left inventory. Unsatisfied demand is lost and the excess inventories incur a holding cost. All the information is common knowledge. The objectives of the two retailers are to make proper ordering decisions to maximize their total expected discount profits respectively. We model the problem as a dynamic Bayesian game with multi-dimension state-space. We give the conditions under which the state-space can be reduced. We prove the existence and uniqueness of Nash equilibrium and show that the equilibrium ordering strategy is the base-stock policy, the computation of the base-stock levels can be reduced to a game with one-dimension state-space. Moreover, for the case with perishable product, the computation of the base-stock levels can be reduced to the Newsboy game.

On the Conditional Success of International Conditionality Policies (With Evidence from Greece and Spain During the Eurozone Crisis)

Does conditionality always work? If, as it appears, the answer is negative, why do certain externally incentivized countries comply while others do not? To answer these questions we rely on cognitive psychology and dynamic Bayesian principal-agent games to develop a theory of downwards-sloping long-run supply curves. More specifically, we explain how, when applied to an intrinsically motivated agent, external incentives imposed by an informed principal carry an informative signal which in the long run crowds out the agent's intrinsic motivation. To probe the plausibility of the ensuing hypotheses we compare the reformist pace of two centre-left governments of financially distressed Southern European countries during the eurozone crisis, namely Greece's Papandreou administration and Spain's Rodriguez Zapatero administration. Based on the analysis of more than 400 newspaper reports and 12 expert interviews we find positive support for our theory: while Papandreou quickly admitted the need for far-reaching and politically costly reforms, Zapatero initially delayed all kinds of measures. But as European incentives kicked in, the strongly incentivized Papandreou went into irreversible reform fatigue, while the softly incentivized Zapatero dedicated his last months in office to bring about unprecedented reforms. We conclude with some indications about future research in this direction.

Development of a secure routing protocol using game theory model in mobile ad hoc networks

In mobile ad-hoc networks (MANETs), nodes are mobile in nature. Collaboration between mobile nodes is more significant in MANETs, which have as their greatest challenges vulnerabilities to various security attacks and an inability to operate securely while preserving its resources and performing secure routing among nodes. Therefore, it is essential to develop an effective secure routing protocol to protect the nodes from anonymous behaviors. Currently, game theory is a tool that analyzes, formulates and solves selfishness issues. It is seldom applied to detect malicious behavior in networks. It deals, instead, with the strategic and rational behavior of each node. In our study, we used the dynamic Bayesian signaling game to analyze the strategy profile for regular and malicious nodes. This game also revealed the best actions of individual strategies for each node. Perfect Bayesian equilibrium (PBE) provides a prominent solution for signaling games to solve incomplete information by combining strategies and payoff of players that constitute equilibrium. Using PBE strategies of nodes are private information of regular and malicious nodes. Regular nodes should be cooperative during routing and update their payoff, while malicious nodes take sophisticated risks by evaluating their risk of being identified to decide when to decline. This approach minimizes the utility of malicious nodes and it motivates better cooperation between nodes by using the reputation system. Regular nodes monitor continuously to evaluate their neighbors using belief updating systems of the Bayes rule.

Truthful Equilibria in Dynamic Bayesian Games

This paper characterizes an equilibrium payoff subset for Markovian games with private information as discounting vanishes. Monitoring might be imperfect, transitions depend on actions, types correlated or not, values private or interdependent. It focuses on equilibria in which players report their information truthfully. This characterization generalizes those for repeated games, and reduces to a collection of one-shot Bayesian games with transfers. With independent private values, the restriction to truthful equilibria is shown to be without loss, except for individual rationality; in the case of correlated types, results from static mechanism design can be applied, resulting in a folk theorem.

Truthful Equilibria in Dynamic Bayesian Games

This paper characterizes an equilibrium payoff subset for Markovian games with private information as discounting vanishes. Monitoring is imperfect, transitions may depend on actions, types be correlated and values interdependent. The focus is on equilibria in which players report truthfully. The characterization generalizes that for repeated games, reducing the analysis to static Bayesian games with transfers. With correlated types, results from mechanism design apply, yielding a folk theorem. With independent private values, the restriction to truthful equilibria is without loss, except for the punishment level; if players withhold their information during punishment-like phases, a “folk” theorem obtains also.

Enhancing secure routing in Mobile Ad Hoc Networks using a Dynamic Bayesian Signalling Game model

Collaboration between mobile nodes is significant in Mobile Ad Hoc Networks (MANETs). The great challenges of MANETs are their vulnerabilities to various security attacks. Because of the lack of centralized administration, secure routing is challenging in MANETs. Effective secure routing is quite essential to protect nodes from anonymous behaviours. Game theory is currently employed as a tool to analyse, formulate and solve selfishness issues in MANETs. This work uses a Dynamic Bayesian Signalling Game to analyse strategy profiles for regular and malicious nodes. We calculate the Payoff to nodes for motivating the particular nodes involved in misbehaviour. Regular nodes monitor continuously to evaluate their neighbours by using the belief evaluation and belief updating system of the Bayes rule. Simulation results show that the proposed scheme could significantly minimize the misbehaving activities of malicious nodes and thereby enhance secure routing.

Study on Dynamic Bayesian Game of Power Grid Crisis Management

Power grid crisis happening at home and abroad warns the necessity of carry out power grid crisis management. Power-grid crisis management game is a zero sum game between power grid crisis manager and crisis event. Power-grid crisis game belongs to the “dynamic game of incomplete information”-“dynamic Bayesian game”. Dynamic Bayesian game process is just analogous to the process of crisis management of power grid, which fully demonstrates that the process of power-grid crisis management is a course of repeated game between crisis manager and power-crisis, also a constantly optimized process. This article mainly studies: the specific characteristics of dynamic Bayesian game of grid crisis management; the Dynamic game model of power grid crisis management; the calculation of refined Bayesian equilibrium principles.

Learning a population distribution

This paper introduces a dynamic Bayesian game with an unknown population distribution. Players do not know the true population distribution and assess it based on their private observations using Bayes׳ rule. First, we show the existence and characterization of an equilibrium in which each player׳s strategy is a function not only of the player׳s type but also of experience. Second, we show that each player׳s initial belief about the population distribution converges almost surely to a “correct” belief.