This paper introduces a new game theoretic equilibrium which is based upon the Bayesian subjective view of probability, BEIC （Bayesian equilibrium iterative conjectures）. It requires players to make predictions, sta...This paper introduces a new game theoretic equilibrium which is based upon the Bayesian subjective view of probability, BEIC （Bayesian equilibrium iterative conjectures）. It requires players to make predictions, starting from first order uninformative predictive distribution functions （or conjectures） and keep updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. Information known by the players such as the reaction functions are thereby incorporated into their higher order conjectures and help to determine the convergent conjectures and the equilibrium. In a BEIC, conjectures are consistent with the equilibrium or equilibriums they supported and so rationality is achieved for actions, strategies and conjectures. The BEIC approach is capable of analyzing a larger set of games than current Nash Equilibrium based games theory, including games with inaccurate observations, games with unstable equilibrium and games with double or multiple sided incomplete information games. On the other hand, for the set of games analyzed by the current games theory, it generates far lesser equilibriums and normally generates only a unique equilibrium. It treats games with complete and perfect information as special cases of games with incomplete information and noisy observation whereby the variance of the prior distribution function on type and the variance of the observation noise term tend to zero. Consequently, there is the issue of indeterminacy in statistical inference and decision making in these games as the equilibrium solution depends on which variances tends to zero first. It therefore identifies equilibriums in these games that have so far eluded the classical theory of games. Finally, it also resolves inconsistencies in equilibrium results by different solution concepts in current games theory such as that between Nash Equilibrium and iterative elimination of dominated strategies and that between Perfect Bayesian Equilibrium and backward induction （Subgame Perfect Equilibrium）.展开更多
Wireless Mesh Networks （WMNs） have many applications in homes, schools, enterprises, and public places because of their useful characteristics, such as high bandwidth, high speed, and wide coverage. However, the sec...Wireless Mesh Networks （WMNs） have many applications in homes, schools, enterprises, and public places because of their useful characteristics, such as high bandwidth, high speed, and wide coverage. However, the security of wireless mesh networks is a precondition for practical use. Intrusion detection is pivotal for increasing network security. Considering the energy limitations in wireless mesh networks, we adopt two types of nodes： Heavy Intrusion Detection Node （HIDN） and Light Intrusion Detection Node （LIDN）. To conserve energy, the LIDN detects abnorrml behavior according to probability, while the HIDN, which has sufficient energy, is always operational. In practice, it is very difficult to acquire accurate information regarding attackers. We propose an intrusion detection model based on the incomplete inforrmtion game （ID-IIG）. The ID-IIG utilizes the Harsanyi transformation and Bayesian Nash equilibrium to select the best strategies of defenders, although the exact attack probability is unknown. Thus, it can effectively direct the deployment of defenders. Through experiments, we analyze the perforrmnce of ID-IIG and verify the existence and attainability of the Bayesian Nash equilibrium.展开更多
The present study discusses the relationships between two independently developed models of games with incomplete information, hypergames （Bennett, 1977） and Bayesian games （Harsanyi, 1967）. The authors first show...The present study discusses the relationships between two independently developed models of games with incomplete information, hypergames （Bennett, 1977） and Bayesian games （Harsanyi, 1967）. The authors first show that any hypergame can naturally be reformulated in terms of Bayesian games in an unified way. The transformation procedure is called Bayesian representation of hypergame. The authors then prove that some equilibrium concepts defined for hypergames are in a sense equivalent to those for Bayesian games. Furthermore, the authors discuss carefully based on the proposed analysis how each model should be used according to the analyzer＇s purpose.展开更多
文摘This paper introduces a new game theoretic equilibrium which is based upon the Bayesian subjective view of probability, BEIC （Bayesian equilibrium iterative conjectures）. It requires players to make predictions, starting from first order uninformative predictive distribution functions （or conjectures） and keep updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. Information known by the players such as the reaction functions are thereby incorporated into their higher order conjectures and help to determine the convergent conjectures and the equilibrium. In a BEIC, conjectures are consistent with the equilibrium or equilibriums they supported and so rationality is achieved for actions, strategies and conjectures. The BEIC approach is capable of analyzing a larger set of games than current Nash Equilibrium based games theory, including games with inaccurate observations, games with unstable equilibrium and games with double or multiple sided incomplete information games. On the other hand, for the set of games analyzed by the current games theory, it generates far lesser equilibriums and normally generates only a unique equilibrium. It treats games with complete and perfect information as special cases of games with incomplete information and noisy observation whereby the variance of the prior distribution function on type and the variance of the observation noise term tend to zero. Consequently, there is the issue of indeterminacy in statistical inference and decision making in these games as the equilibrium solution depends on which variances tends to zero first. It therefore identifies equilibriums in these games that have so far eluded the classical theory of games. Finally, it also resolves inconsistencies in equilibrium results by different solution concepts in current games theory such as that between Nash Equilibrium and iterative elimination of dominated strategies and that between Perfect Bayesian Equilibrium and backward induction （Subgame Perfect Equilibrium）.
基金This work was partially supported by the National Natural Science Foundation of China under Cxants No. 61272451, No. 61103220, No. 61173154, No. 61173175 the National Critical Patented Projects in the next generation broadband wireless mobile communication network under Grant No. 2010ZX03006-001-01.
文摘Wireless Mesh Networks （WMNs） have many applications in homes, schools, enterprises, and public places because of their useful characteristics, such as high bandwidth, high speed, and wide coverage. However, the security of wireless mesh networks is a precondition for practical use. Intrusion detection is pivotal for increasing network security. Considering the energy limitations in wireless mesh networks, we adopt two types of nodes： Heavy Intrusion Detection Node （HIDN） and Light Intrusion Detection Node （LIDN）. To conserve energy, the LIDN detects abnorrml behavior according to probability, while the HIDN, which has sufficient energy, is always operational. In practice, it is very difficult to acquire accurate information regarding attackers. We propose an intrusion detection model based on the incomplete inforrmtion game （ID-IIG）. The ID-IIG utilizes the Harsanyi transformation and Bayesian Nash equilibrium to select the best strategies of defenders, although the exact attack probability is unknown. Thus, it can effectively direct the deployment of defenders. Through experiments, we analyze the perforrmnce of ID-IIG and verify the existence and attainability of the Bayesian Nash equilibrium.
基金supported by Grant-in-Aid for Japan Society for the Promotion of Science(JSPS) Fellows, No.21-9482
文摘The present study discusses the relationships between two independently developed models of games with incomplete information, hypergames （Bennett, 1977） and Bayesian games （Harsanyi, 1967）. The authors first show that any hypergame can naturally be reformulated in terms of Bayesian games in an unified way. The transformation procedure is called Bayesian representation of hypergame. The authors then prove that some equilibrium concepts defined for hypergames are in a sense equivalent to those for Bayesian games. Furthermore, the authors discuss carefully based on the proposed analysis how each model should be used according to the analyzer＇s purpose.
