Bayesian Nash Equilibrium Research Articles

Risk Assessment of UAV Cyber Range Based on Bayesian–Nash Equilibrium

In order to analyze the choice of the optimal strategy of cyber security attack and defense in the unmanned aerial vehicles’ (UAVs) cyber range, a game model-based UAV cyber range risk assessment method is constructed. Through the attack and defense tree model, the risk assessment method is calculated. The model of attack and defense game with incomplete information is established and the Bayesian–Nash equilibrium of mixed strategy is calculated. The model and method focus on the mutual influence of the actions of both sides and the dynamic change in the confrontation process. According to the calculation methods of different benefits of different strategies selected in the offensive and defensive game, the risk assessment and calculation of the UAV cyber range are carried out based on the probability distribution of the defender’s benefits and the attacker’s optimal strategy selection. An example is given to prove the feasibility and effectiveness of this method.

Green Promotion Service Allocation and Information Sharing Strategy in a Dual-Channel Circumstance

Credit purchase enables the manufacturers in the e-commerce environment to provide pre-sales service that consumers can experience first and pay later. This paper considers demand associated with price and green promotion service level and builds four decentralized game models to study two green promotion service allocation strategies and demand forecasting information sharing strategies in a dual-channel environment. The effects of the degree of dual-channel competition and free-riding on the perfect Bayesian Nash equilibrium are studied. The results show that the retailer should actively cooperate with the manufacturer and share private forecasting information if the coefficient of channel substitution is relatively high. Sharing information will aggravate double marginalization and hurt the retailer. In addition, the retailer’s profit is positively influenced by the forecasting accuracy in four models. When the manufacturer invests in the green promotion service, the prediction accuracy hurts the manufacturer’s profit without information sharing and there is a positive impact with information sharing. In particular, when a retailer provides service, we take the consumer’s free-riding behavior into account, and we find that free-riding hurts both parties and the whole supply chain. In addition, the manufacturer’s profit is irrelevant to the prediction accuracy without information sharing and positively influenced by the accuracy with information sharing.

Optimal premium pricing in a competitive stochastic insurance market with incomplete information: A Bayesian game-theoretic approach

This paper examines a stochastic one-period insurance market with incomplete information. The aggregate amount of claims follows a compound Poisson distribution. Insurers are assumed to be exponential utility maximizers, with their degree of risk aversion forming their private information. A premium strategy is defined as a mapping between risk-aversion types and premium rates. The optimal premium strategies are denoted by the pure-strategy Bayesian Nash equilibrium, whose existence and uniqueness are demonstrated under specific conditions on the insurer-specific demand functions. Boundary and monotonicity properties for equilibrium premium strategies are derived.

The Study of the Strategic Consequences of a Scoring Model Disclosure

In this paper, the disclosure of information about the scoring model is investigated. Some of the company’s customers find out their internal rating in the company. Such customers can change their behavior to increase their internal rating. The customers who are aware of the leakage are represented as players who can choose a strategy: whether to increase their internal rating and, if so, how much. The main goal is to find the Bayesian-Nash equilibrium in this game and find out how it depends on various parameters, such as the scale of the leakage, the distribution of ratings.

Asymmetric auctions: Perturbations, ε- equilibrium, and equilibrium

We consider first-price auctions with independent and private valuations that have asymmetric valuation distributions and supports. We first show the existence of equilibrium in these auctions through a perturbation approach, thereby establishing that the limit of Bayesian Nash equilibria (BNE) of such perturbed auctions is indeed the Bayesian Nash equilibrium (BNE) of the limit auction with asymmetric supports. We then characterize this BNE and show that the ε-equilibrium (ε-BNE) of the auction with asymmetric supports is a BNE of “close” auctions with common supports. We then demonstrate some numerical examples.

An Imitation Learning Based Algorithm Enabling Priori Knowledge Transfer in Modern Electricity Markets for Bayesian Nash Equilibrium Estimation

An Imitation Learning Based Algorithm Enabling Priori Knowledge Transfer in Modern Electricity Markets for Bayesian Nash Equilibrium Estimation

The Partial Solution of First Price Sealed Bid Auction in the Scope of Mechanism Design Theory and With Uniformly Distributed Types

In the article the first price sealed bid auction has been analysed within the scope of mechanism design theory and with uniformly distributed types. The sealed bid auction consisting of two of agents has been observed finding the partial solution to the auction. Bayesian Nash equilibrium strategies, the equilibrium state, and the implemented social choice function for the auction have been evaluated. The mechanism has been designed to truthfully implement the social choice function for the auction consisting of two agents. The variables such as the probability of an agent to win, the expected utility of an agent and the expected revenue of the seller have been evaluated.

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

Efficiency of Public Procurement Function in Moroocco

Public procurement, involving the public sector’s purchase of goods, services, or works from the pri-vate sector, accounts for 13-20% of global GDP (The World Bank, 2020). In Morocco, this sector rep-resents 17% of GDP (The World Bank, 2014) and is a crucial source of business for SMEs, which make up 95% of all businesses (Augier, Castel & El Malki, 2019). The efficiency of public procure-ment is a central issue in research due to its strategic, economic, and managerial impact (Kakwezi & Nyeko, 2019). While past research often focused on practical assessments (Flynn & Davis, 2014) and overlooked the market structure (KLEMPERER, 1999), based on a renewal of the game auction model for first price sealed bid auctions, along with both a qualitative and quantitative empirical research , this paper examines Moroccan public procurement efficiency from a market-based, game auction model perspective. It demonstrates that Morocco’s predominant open tender procedure exhibits pat-terns of an efficient game auction model with a Bayesian Nash equilibrium expression , suggesting opportunities for maintaining and improving the open tender meachnism itself and the surrounding procurement mechanisms.

Bayesian Nash equilibrium in all-pay auctions with interdependent types

We prove the existence of a behavioral-strategy Bayesian Nash equilibrium in all-pay auctions with statistically interdependent types (signals) under quite general assumptions on the values, costs and tie-breaking rules. Moreover, the set of equilibria is shown to be the same for any tie-breaking rule used in the auction.

Enhancing Transshipment Decision-making in Transportation Companies through Computational Intelligence: A Bayesian Game Model with Data-Driven Simulations at Guangzhou Port

The challenge of port congestion significantly impedes the efficiency of global trade flows and the economic vitality of hinterland regions. Addressing this issue, our study harnesses computational intelligence to construct a sophisticated Bayesian game model between the government and multiple transportation companies, where the transshipment costs, considered as private information to the companies, play a pivotal role. This research integrates data analytics and machine learning techniques to analyze the strategic decision-making processes of transportation companies, which decide on transshipment based on a critical cost threshold influenced by government subsidies and a probabilistic assessment of transshipment costs. Utilizing backward induction, the study outlines how the government can leverage computational models to devise an optimal subsidy strategy for transshipment, taking into account the anticipated responses of the transportation companies. The Bayesian Nash equilibrium identified through our model suggests that companies with costs below a predefined threshold are incentivized by government subsidies to opt for transshipment. This conclusion is further validated through evolutionary game theory analysis, enriched by data-driven simulations. Employing real-world data from Guangzhou Port, we conducted extensive computational simulations to quantify the impact of transshipment subsidies. The findings reveal a substantial alleviation in port congestion, with a 33.7% reduction in congestion levels and a 35% decrease in congestion-related costs, alongside a notable 1.9% increase in government revenue. These simulations, powered by advanced computational algorithms and data analytics, not only underscore the effectiveness of informed subsidy strategies in mitigating port congestion but also demonstrate the potential of integrating computational approaches in logistical and transportation decision-making. This study contributes a novel computational framework to the logistics and transportation literature, offering practical insights for policymakers to tackle the enduring problem of port congestion through data-driven strategies.

Entry under placement uncertainty

We present a model of firm entry in an industry that operates under an aggregate production quota or cap-and-trade (CAT) regulation. Firms are heterogeneous in their own productivity; each knows its costs of production but is uncertain about where its costs rank among an entrant population. We show the existence of a unique, symmetric, dominance solvable, Bayesian Nash equilibrium in switching strategies in a parameterized game with a continuum of players. Our main result is that uncertainty over one's productivity rank is sufficient to cause socially inefficient over-entry when the average cost in the population of potential entrants is low. We find socially inefficient under-entry when the opposite conditions hold. Within both the class of models on global games with strategic substitutes and the class of models on firm entry, our model offers innovative insights into inefficient over-entry, under-entry, and introduces a novel underlying mechanism that drives entry bias.

AutoFL: A Bayesian Game Approach for Autonomous Client Participation in Federated Edge Learning

Given that devices (i.e., clients) participating in federated edge learning (FEL) are autonomous and resource-constrained in nature, it is critical to design effective incentive mechanisms to encourage client participation so as to improve the performance of FEL. In this paper, we aim to boost the FEL training efficiency by answering how much compute resource should clients autonomously contribute to maximize their utilities. To this end, we develop AutoFL, an autonomous client participation decision framework for federated learning at the network edge without assuming that each client possesses complete information. We first model the problem of autonomous client participation as a Bayesian game with incomplete information, where each player in the game is associated with a set of types according to network conditions. We optimize an individual client's decision based on the dynamics of the population estimated following the Bayes rule. We prove that AutoFL can converge to a unique Bayesian Nash equilibrium point. Empirical results on three real datasets show that AutoFL achieves a higher model accuracy with only 15.5-24.5% model aggregation time per global training round, and its energy cost saving on mobile devices is 82.2-86.8% compared to the state-of-the-art algorithms. Moreover, we can achieve a 2.75-3.2x long-term fairness compared to classical solutions.

A reinforcement-probability Bayesian approach for strategic bidding and market clearing for renewable energy sources with uncertainty

With the participation of renewable energy sources (RESs) in the electricity market, the inherent uncertainty brings new challenges for strategic bidding and market clearing in the electricity market. In this paper, the market structure is formulated as a non-cooperative game among power suppliers, consumers, and the market operator. A reinforcement-probability Bayesian approach is proposed to obtain the optimal bidding strategy of RESs and achieve maximal social welfare at the market clearing, considering uncertain cost types of RESs and incomplete market information. First, a reinforcement-probability model is presented to obtain the optimal agent-type-strategy combination considering the uncertainty of cost type selection. A agent-type-probability algorithm is proposed for the model to update the mean of probability density function of cost types according to the expected profit. Second, an incremental-cost-based distributed algorithm is proposed to solve the market clearing problem, which accelerates the convergence rate without violating the system constraints via feedback from the scheduled power. Finally, a Bayesian probability model is proposed for RESs to learn the hidden information of the market and transform the incomplete information electricity market into a complete one. A Bayesian Nash equilibrium is reached in the model. To coordinate the information among market participants, the output of the Bayesian probability model is calculated by the Hysteretic Q-learning algorithm and used as the reward to update the agent-type-probability in the reinforcement-probability model. An illustrative example is presented to demonstrate the effectiveness of the proposed approach, which shows that the proposed approach has a better convergence performance and has a 2–6 times faster learning speed compared with the policy gradient and deep Q-network.

Slope Takers in Anonymous Markets

We present a learning-based selection argument for Linear Bayesian Nash equilibrium in a Walrasian auction. Endowments vary stochastically; traders model residual supply as linear, estimate its slope from past trade data, and periodically update these estimates. In the standard setting with quadratic preferences, we show that this learning process converges to the unique LBN. Anonymity and statistical learning therefore support this commonly used equilibrium selection rule. (JEL D43, D44, D83)

Impact of information disclosure on global supply chain greenwashing: Is more information transparency always better?

As supply chains become more globalized, retailers outsource the manufacturing of their products to foreign suppliers. Supply chain greenwashing is an immoral practice employed by retailers whereby they selectively disclose information regarding upstream suppliers after exaggerating the environmental benefits of their fake green products to consumers. Using a perfect Bayesian Nash equilibrium approach, this paper examines the conditions under which a retailer who engages in greenwashing will disclose the information of an unethical foreign supplier under pressure from enhanced scrutiny by a non-governmental organization (NGO). The results show that when the increase in the NGO’s utility from targeting the unrevealed upstream supplier is sufficiently large, the greenwashing retailer prefers to disclose the unethical foreign supplier’s information, whereas when the increased utility is low, the greenwashing retailer prefers to hide the unethical foreign supplier. Different from common belief that increased information transparency may be beneficial, we find that it does not necessarily lead to reduced social damage and that it depends on the unethical foreign supplier’s capability for compliance. In particular, when the unethical foreign supplier has a low capacity for compliance, the supply chain’s transparency advantage will lead to more fake green goods being sold, thus causing greater social damage.

Bayesian Nash equilibrium seeking for multi-agent incomplete-information aggregative games

Bayesian Nash equilibrium seeking for multi-agent incomplete-information aggregative games

"Are we in this together?": embedding social identity detection in drones improves emergency coordination.

Autonomous systems, such as drones, are critical for emergency mitigation, management, and recovery. They provide situational awareness and deliver communication services which effectively guide emergency responders' decision making. This combination of technology and people comprises a socio-technical system. Yet, focusing on the use of drone technology as a solely operational tool, underplays its potential to enhance coordination between the different agents involved in mass emergencies, both human and non-human. This paper proposes a new methodological approach that capitalizes on social identity principles to enable this coordination in an evacuation operation. In the proposed approach, an adaptive drone uses sensor data to infer the group membership of the survivors it encounters during the operation. A corpus of 200 interactions of survivors' talk during real-life emergencies was computationally classified as being indicative of a shared identity or personal/no identity. This classification model, then, informed a game-theoretic model of human-robot interactions. Bayesian Nash Equilibrium analysis determined the predicted behavior for the human agent and the strategy that the drone needs to adopt to help with survivor evacuation. Using linguistic and synthetic data, we show that the identity-adaptive architecture outperformed two non-adaptive architectures in the number of successful evacuations. The identity-adaptive drone can infer which victims are likely to be helped by survivors and where help from emergency teams is needed. This facilitates effective coordination and adaptive performance. This study shows decision-making can be an emergent capacity that arises from the interactions of both human and non-human agents in a socio-technical system.

Social Sourcing: Incorporating Social Networks Into Crowdsourcing Contest Design

In a crowdsourcing contest, a principal holding a task posts it to a crowd. People in the crowd then compete with each other to win the rewards. Although in real life, a crowd is usually networked and people influence each other via social ties, existing crowdsourcing contest theories do not aim to answer how interpersonal relationships influence people's incentives and behaviors and thereby affect the crowdsourcing performance. In this work, we novelly take people's social ties as a key factor in the modeling and designing of agents' incentives in crowdsourcing contests. We establish two contest mechanisms by which the principal can impel the agents to invite their neighbors to contribute to the task. The first mechanism has a symmetric Bayesian Nash equilibrium, and it is very simple for agents to play and easy for the principal to predict the contest performance. The second mechanism has an asymmetric Bayesian Nash equilibrium, and agents' behaviors in equilibrium show a vast diversity which is strongly related to their social relations. The Bayesian Nash equilibrium analysis of these new mechanisms reveals that, besides agents' intrinsic abilities, the social relations among them also play a central role in decision-making. Moreover, we design an effective algorithm to automatically compute the Bayesian Nash equilibrium of the invitation crowdsourcing contest and further adapt it to a large graph dataset. Both theoretical and empirical results show that the new invitation crowdsourcing contests can substantially enlarge the number of participants, whereby the principal can obtain significantly better solutions without a large advertisement expenditure.

Eliciting Joint Truthful Answers and Profiles From Strategic Workers in Mobile Crowdsourcing Systems

Due to the openness of mobile crowdsourcing, workers may yield low-quality task answers. To alleviate this problem, substantial efforts have been devoted to eliciting truthful data from workers. On the other hand, to facilitate task assignment, workers are required to upload to the platform their profiles, such as locations and expertise. Therefore, task assignment outcomes and thus mobile crowdsourcing service accuracy are subject to the quality of worker's self-reported profiles. In this paper, we leverage incentive design to motivate workers to honestly reveal both task answers and their profiles. The challenge is to design one incentive payment for truth elicitation in two kinds of submissions. For this, we first derive the sufficient and necessary conditions for answer truthfulness and profile truthfulness separately. We then construct an incentive optimization problem that incorporates these conditions as constraints. Its optimal solution lists the payment to each worker that elicits answers and profiles jointly. Our proposed mechanism, with formally proved bounded approximation ratio, ensures that truth-telling is a Bayesian Nash equilibrium. We prototype the mechanism and conduct a series of experiments that involve 30 volunteers to validate the efficacy and efficiency of the proposed mechanism