Bilevel Optimization Problem CO Workshop - Aussois - … Security Games Randomization make defender unpredictable Stackelberg Security game Defender: Commits to mixed strategy Adversary: Conduct surveillance and best responds Target #1 Target #2 Target #1 5, -3 -1, 1 Target #2-5, 4 2, -1 Adversary Defender 55.6% 44.4% 10/72 7/14/2018 of EECS, U.C. Such optimization problems are commonly found in transportation, engineering design, game playing and business models. Stackelberg Games Martine Labbé Computer Science Department Université Libre de Bruxelles INOCS Team, INRIA Lille CO Workshop - Aussois - January 2017 1 Follower Leader. The Stackelberg game is a game problem in which the decision-makers are in a master-slave relationship; that is, the status of game players belonging to the two decision-making layers is inequitable, and the players in the upper-layer game are more influential than the lower-layer players. 3 Stackelberg game analysis 3.1 Non-cooperative backhaul spectrum payment selection game In this section, in order to solve the best responses of the FBSs, the following Lemma 1 is first introduced as following. A solution at the upper level may be considered feasible only if it is optimal for a parametric lower level optimization problem. 2008. 2. After the Introduction, Section 2 reviews the theory of static games. Playing games for security: An efficient exact algorithm for solving Bayesian Stackelberg games. IEEE Communications Surveys & Tutorials 19, 4 (2017), 2322--2358. The monograph by Stackelberg [35] provided a further contribution to the theory of games, motivated by the analysis of market economy. Stackelberg Equilibria in Extensive-Form Games," in AAAI Conference on Arti cial Intelligence, 2015. A survey on mobile edge computing: The communication perspective. Berkeley. Open-loop solutions, where the controls EE228a, Fall 2002 2 Outline •Introduction • Complete-Information Strategic Games – Static Games – Repeated Games – Stackelberg Games • Cooperative Games – Bargaining Problem – Coalitions. Section 3 introduces the basic framework of di erential games for two players. Other quantities of interest, aside from the mean field term, include variance, skewness, kurtosis, value at risk, success probability, mean-variance payoff, etc. games, the later paper of Nash [30] provided a concept of solution for general non-cooperative games for N players. How does the Stackelberg equilibrium compare with the Cournot? Stackelberg Games with Applications to Security Chris Kiekintveld Bo An Albert Xin Jiang . Outline Motivating real-world applications Background and basic security games Scaling to complex action spaces Modeling payoff uncertainty: Bayesian Security Games Stackelberg Model Let’s assume a linear demand P(Q)=a-bQ Mc 1=Mc 2=c In sequential games we first solve the problem in the second period and afterwards the problem in the 1st period. Di erent concepts of solution are discussed, including Pareto optima, Nash and Stackelberg equi-libria, and the co-co (cooperative-competitive) solutions. Mean field-type games differ from mean field game since it takes into account higher-order statistics of the states such as the variance. [2]B. Bo sansk y, S. Branzei, K. A. Hansen, P. B. Miltersen, and T. B. S˝rensen, \Computation of stackelberg equilibria of nite sequential games," in Proceedings of Web and Internet Economics: 11th International Conference (WINE), pp. PART I : Bilevel optimization CO Workshop - Aussois - January 2017 2. games. 5.1. The theory of differential games was first developed by Isaacs [25], followed by other authors; 3.3. They are also known as Stackelberg games in the operations research community. Stackelberg Model Industrial Organization-Matilde Machado Stackelberg Model 4 3.3. Google Scholar; Praveen Paruchuri, Jonathan P Pearce, and et al. Therefore, the backward induction method will be used in the following section to obtain the SE for the Stackelberg game formulated above. A Short Tutorial on Game Theory EE228a, Fall 2002 Dept. 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