Bayesian Game Research Articles

Optimal Network Defense Strategy Selection Based on Incomplete Information Evolutionary Game

The issue of selecting the optimal defense strategy in the dynamic adversarial network is difficult. To solve this problem, we start from the realistic bounded rationality of both the attacker and the defender. First, we build the Bayesian attack-defense evolutionary game model combining with incomplete information game scenario. Specifically, we convert the uncertainty of the strategy payoffs of attackers and defenders to the uncertainty of their related types. Meanwhile, both the set of player types and the set of game strategies can be expanded to n in our model. Furthermore, we improve the replicator dynamics equation by adding the selecting intensity factor to depict the noise effect. This reflects the randomness of decision making for players due to their bounded learning capacities. In this way, the static analysis in the traditional game is extended as a dynamic process. On this basis, we summarize the evolutions of different player types with different strategies. Finally, by calculating the evolutionary stable equilibrium, we give the algorithm of selecting optimal defense strategy and depict the evolutionary track of this strategy selected by the defender with time going by. Our method provides decision support for the network proactive defense toward moderate security. Moreover, the dynamic analysis efficiency of defense decision making is improved, and the predicting ability of the defense situation is enhanced. Experimental results verify the scientificity and availability of the proposed model and method.

A One-Leader Multi-Follower Bayesian-Stackelberg Game for Anti-Jamming Transmission in UAV Communication Networks

This paper focuses on the anti-jamming transmission problem in unmanned aerial vehicle (UAV) communication networks. Considering the incomplete information constraint and the co-channel mutual interference, a Bayesian Stackelberg game is proposed to formulate the competitive relations between UAVs (users) and the jammer. Specifically, the jammer acts as the leader, whereas users act as followers of the proposed game. Based on their utility functions, the jammer and users select their optimal power control strategies respectively. In addition, the observation error is also investigated in this paper. Due to the incomplete information constraint and the existence of co-channel mutual interference, it is challenging to obtain Stackelberg equilibrium (SE) of the proposed game. Thus, a sub-gradient based Bayesian Stackelberg iterative algorithm is proposed to obtain SE. Finally, simulations are conducted to demonstrate the performance of the proposed algorithm, and the impact of incomplete information and observation error on users’ utilities are also presented.

Bayesian Cooperative Coalition Game as a Service for RFID-Based Secure QoS Management in Mobile Cloud

In this paper, the problem of maintaining the quality of service with respect to high communication cost, available bandwidth, and security is investigated in a mobile cloud environment. A Bayesian cooperative coalition game is formulated in which learning automata stationed at Radio frequency identification (RFID) readers are assumed as the players. These players form a coalition among themselves using newly defined payoff value function (PVF) based upon the communication cost, network bandwidth, and storage requirements. Each player in the game makes his best efforts to increase his individual PVF for which it selects one of the strategies from the strategy space using the conditional probability. For each action taken by the players, they may get a reward or a penalty from the environment according to which they update their action probability vector. Tags are arranged in acyclic directed graph, and a secure access control algorithm is proposed, which results a complexity of $O(\log (n))$ in comparison with earlier solutions having the complexity of $O(n)$ . The proposed scheme is evaluated in comparison with other schemes by extensive simulations using various metrics. The results obtained show that the proposed scheme is effective in maintaining the RFID-based secure data dissemination in the mobile cloud environment. In particular, there is a reduction of 20% in computational time, and overhead generated with an increase of more than 30% in packet delivery ratio.

Axiomatic decomposition of a zero-sum game: the penalty shoot-out case

The game of soccer has offered matter of wide scientific analysis about the effective application of the game theory in real-life. The field observations have often detected divergent behaviors from theoretical predictions. The basic problem comes from the fact that it is difficult to build scientific models reflecting reality as closely as possible. Axiomatic Design offers us a powerful tool of rational decomposition of a real and complex issue into elementary components. Independence Axiom guarantees that game decomposition will define a set of elementary actions logically consistent and free of redundancies. At the same time, Information Axiom can allow to select among alternative strategies, those that they predict the actions with a higher probability rate of success. In this paper, it is suggested the use of the Axiomatic Design methodology in the Collectively Exhaustive and Mutually Exclusive (CEME) mode, as a tool of analysis of the penalty shoot-out in extra time. This methodology allows to define the game strategies for goalkeepers and penalty takers. It will be analyzed both, the case when the opponents' behavior is well known and the situation when the statistics about the opponents are unknown. Axiomatic Design allows the process of decomposition to be simplified, enabling the selection of optimal game strategies. These strategies correspond to Nash’s equilibrium solutions when you already know about your opponents' game behavior. On the contrary, when penalty takers whose behavior is unknown, then it is always possible to define a strategy corresponding to the Bayesian equilibrium game solutions.

Direct incentive-compatible mechanism for innovator-investor bargain in an innovation investment system

The functioning of the system of innovation investment, where an objective evaluation of an investment project containing new knowledge is impossible both for the investor and the innovator, currently is a matter of great interest. While for traditional industries, the use of statistical data is a satisfactory approach to the problem of uncertainty, for innovation projects this method isn’t applicable due to the natural absence of a valid statistical base. The practice shows that the empirical mechanisms used for innovation projects are rarely used for investing in traditional industries and vice versa. In this connection, there arises the problem of development an effective mechanism for financing innovation projects. We developed such a mechanism for the innovator-investor system in the form of a Bayesian non-cooperative repeating game with recalculated payments. The equilibrium parameters for any period of the given game are obtained. It is shown that, depending on the a priori estimates of the type of project, four different equilibria are possible in any particular period of that game. Therefore, using the strategy of adjusting a priori estimates of the investor and innovator on the basis of the Regret Matching rule, equilibrium for this finite Bayesian game is obtained.

Optimal Demand-Side Management for Smart Micro Grid with Storage

In this paper, an autonomous and distributive demand-side management based on Bayesian game theory is developed and applied among users in a grid connected micro-grid with storage. To derive that strategy, an energy consumption of shiftable loads belonging to a given user is modelled as a noncooperative three-player game of incomplete information, in which each user plays against the storage unit and an opponent gathering all the other users in the micro-grid. Each player is assumed to be endowed with statistical information about its behavior and that of its opponents so that he can take actions maximizing his expected utility. Results of the proposed strategy evaluated by simulating, under MATLAB environment, a connected micro-grid with storage device evidence its efficacy when employed to manage the charging of electric vehicles.

On the Existence of Monotone Pure-Strategy Perfect Bayesian Equilibrium in Games with Complementarities

Many important economic situations can be modeled as dynamic games of incomplete information with strategic complementarities of actions and types. In this paper, we extend the results of Athey (2001) and Reny (2011) from static Bayesian games to dynamic environments, providing conditions that guarantee the existence of monotone equilibria in types in such games. A feature that distinguishes this environment from those of previous results is the endogeneity of beliefs, which can complicate continuity of payoffs, needed to find a fixed point. To address this, we define an auxiliary static game which pins down beliefs while preserving continuity of payoffs. We also provide conditions which guarantee that there will exist monotone best-replies to monotone strategies of one's opponents in a dynamic environment. Applications are given to signaling games and stopping games such as auctions, wars of attrition, and joint research projects.

Bayesian game model to analyze electric vehicles and smart grid interaction

Bayesian game model to analyze electric vehicles and smart grid interaction

Designing Cost-Sharing Methods for Bayesian Games

We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE). We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players.

On pure-strategy equilibria in games with correlated information

This paper rehabilitates a program initiated in Aumann (1974) by contributing a result to the theory of finite-player Bayesian games in environments that explicitly include correlated information. An equivalence theorem offers conditions under which the set of mixed-strategy equilibrium payoffs in a classical finite-action game of complete information coincides with the set of objective pure-strategy Nash equilibrium (PSNE) expected payoffs in an affiliated Bayesian game with type-independent payoffs. This result is motivated for a non-specialist reader by several examples. An Appendix devoted to an intuitive discussion of the so-called ‘Lebesgue extension’ is added to make the paper self-contained.

MTD-Spamguard: a moving target defense-based spammer detection system in social network

Machine learning classifiers are currently the state of the art for spammer detection tasks in SNSs. Note, however, that these classifiers fail to detect adaptive spammers that dynamically change their spamming strategies or behaviors and attempt to pose as legitimate users. In this paper, we propose an efficient spammer detection system (which we call MTD-Spamguard) wherein the notion of MTD is applied to increase the robustness of well-known machine learning classifiers against the adaptive spammers in SNSs. The system introduces a new method of MTD wherein the concept of differential immunity of different classifiers is employed to detect the spammers. To classify a single user in the test dataset, we pick one of the appropriate trained classifiers from multiple classifiers and then use its classification output. To choose the appropriate classifier, we design an effective classifier switching strategy by formulating the interaction of users (normal users and spammers) and detector (which hosts the machine learning classifier) as a repeated Bayesian Stackelberg game. The classifier switching strategy provides strong Stackelberg equilibrium between users and detector, maximizing the accuracy of classification and reducing the misclassification of spammers. The system achieves 30% gain in classification accuracy over the Facebook dataset (constructed in our recent work).

Symmetric mechanism design

Designers of economic mechanisms can often benefit by using discriminatory mechanisms which treat agents asymmetrically. This paper studies the extent to which a policy prohibiting biased mechanisms is effective in achieving fair outcomes. Our main result is a characterization of the class of social choice functions that can be implemented by symmetric mechanisms. When the solution concept used is Bayes–Nash equilibrium, symmetry is typically not very restrictive and discriminatory social choice functions can be implemented by symmetric mechanisms. Our characterization in this case is based on a ‘revelation principle’ type of result, where we show that a social choice function can be symmetrically implemented if and only if a particular kind of (indirect) symmetric mechanism implements it. When implementation in dominant strategies is considered, only symmetric social choice functions can be implemented by symmetric mechanisms. We illustrate our results in environments of voting with private values, voting with a common value, and assignment of indivisible goods.

Applying a Bayesian Stackelberg game for securing a chemical plant

Applying a Bayesian Stackelberg game for securing a chemical plant

Investment Efficiency and Product Market Competition

Does more competition lead to more information production and greater investment efficiency? This question is largely unexplored in the finance literature. This article provides both a model and a series of extensive empirical tests. The model features a 2-stage Bayesian game in differentiated products market competition. We find that competition causes firms to acquire less information and investments to become more inefficient relative to a first-best case with the same market structure. Empirically, the panel regression analysis provides strong support for the theory and shows that investment is more efficient in concentrated industries.

Benefits from Non-Competing Persuaders

I study Bayesian persuasion games with multiple persuaders in which the persuaders are non-competing: all persuaders want the decision maker to take the same action, regardless of the state. In the case of a single persuader, it is known from previous research that the persuader-optimal information design leaves the decision maker with no surplus. In this paper, I show that with two or more non-competing persuaders and independent tests, there are always equilibria in which the decision maker receives surplus. If there is exogenous noise then the decision maker receives surplus in every symmetric equilibrium, provided the number of persuaders is sufficiently large; asymptotically, the decision maker learns the true state in every Pareto optimal symmetric equilibrium with infinitely many persuaders. Moreover, with sufficient exogenous noise, having more than one persuader not only improves the welfare of the decision maker but also improves the welfare of the persuaders.

A new methodology for surveys and its application to forced response

The response technique in this paper provides a researcher with private information, which causes participants to be unsure which response associates them with the stigmatized characteristic, encouraging honesty and obedience. To prevent the researcher from exploiting the information, the paper suggests restrictions on its structure. Unlike most prior literature, this paper models the survey as a Bayesian game. In the application to forced response, participants should always obey commands as it is a dominant strategy. By applying this methodology to Warner’s method, respondents have a stronger incentive to reply honestly without any loss of information.

Uniqueness, stability and comparative statics for two-person Bayesian games with strategic substitutes

This paper considers a class of two-player symmetric games of incomplete information with strategic substitutes. First, we provide sufficient conditions under which there is either a unique equilibrium which is stable (in the sense of best-reply dynamics) and symmetric or a unique (up to permutations) asymmetric equilibrium that is stable (together with an unstable symmetric equilibrium). Thus, (i) there is always a unique stable equilibrium, (ii) it is either symmetric or asymmetric, and hence, (iii) a very simple local condition—stability of the symmetric equilibrium (i.e., the slope of the best-response function at the symmetric equilibrium)—identifies which case applies. Using this, we provide a very simple sufficient condition on primitives for when the unique stable equilibrium is asymmetric (and similarly for when it is symmetric). Finally, we show that the conditions guaranteeing the uniqueness described above also yield novel comparative statics results for this class of games.

Strong quantum solutions in conflicting-interest Bayesian games

Quantum entanglement has been recently demonstrated as a useful resource in conflicting interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. General setting for such games is that of correlated strategies where the correlation between competing players is established through a trusted common adviser; however, players need not reveal their input to the adviser. So far, quantum advantage in such games has been revealed in a restricted sense. Given a quantum correlated equilibrium strategy, one of the players can still receive a higher than quantum average payoff with some classically-correlated equilibrium strategy. In this work, by considering a class of asymmetric Bayesian games, we show the existence of games with quantum correlated equilibrium where average payoff of both the players exceed respective individual maximum for each player over all classically-correlated equilibriums.

Bayesian games with a continuum of states

We show that every Bayesian game with purely atomic types has a measurable Bayesian equilibrium when the common knowledge relation is smooth. Conversely, for any common knowledge relation that is not smooth, there exists a type space that yields this common knowledge relation and payoffs such that the resulting Bayesian game does not have any Bayesian equilibrium. We show that our smoothness condition also rules out two paradoxes involving Bayesian games with a continuum of types: the impossibility of having a common prior on components when a common prior over the entire state space exists, and the possibility of interim betting/trade even when no such trade can be supported ex ante.

Secrecy Capacity in CRN With Malicious Energy Harvester Using Game Theoretic Techniques

In this paper, an underlay-based cognitive radio network (CRN) consisting of a secondary transmitter (ST), a secondary receiver (SR), an energy harvesting node (EHN), and a primary transmitter-receiver pair, is considered. The EHN is an energy constrained node and is thereby, assumed to have a power splitter at its receiver to decode information and harvest energy simultaneously from the received RF signal. The EHN behaves maliciously and decodes ST’s messages when it is granted with a permission to (only) harvest energy from the received RF signal, thereby reducing the secrecy capacity of the ST-SR link. Since both ST and EHN are selfish with conflicting interests, we model the interaction between them as a Stackelberg game (SG). Further, we analyze the behavior of the nodes in a non-cooperative game (NCG) theoretic framework and prove the existence of a unique Nash equilibrium (NE) strategy. Simulation results show that the SG framework performs better than the NCG framework, in terms of the achievable secrecy capacity of the ST-SR link. Thereby the proposed SG model is applied to the considered CRN with multiple STs and a unique equilibrium is found. In case the STs possess limited channel state information (CSI), we model the competition among the STs as a Bayesian game and found its equilibrium solution, known as Bayesian NE (BNE). Simulation results demonstrate that BNE performs better than the NE when the STs possess limited CSI.