Non-additive Security Games

We have investigated the security game under non-additive utility functions

Double-oracle sampling method for Stackelberg Equilibrium approximation in general-sum extensive-form games

The paper presents a new method for approximating Strong Stackelberg Equilibrium in general-sum sequential games with imperfect information and perfect recall. The proposed approach is generic as it does not rely on any specific properties of a particular game model. The method is based on iterative interleaving of the two following phases: (1) guided Monte Carlo Tree Search sampling of the Follower's strategy space and (2) building the Leader's behavior strategy tree for which the sampled Follower's strategy is an optimal response. The above solution scheme is evaluated with respect to expected Leader's utility and time requirements on three sets of interception games with variable characteristics, played on graphs. A comparison with three state-of-the-art MILP/LP-based methods shows that in vast majority of test cases proposed simulation-based approach leads to optimal Leader's strategies, while excelling the competitive methods in terms of better time scalability and lower memory requirements

A Game Theoretic Model for the Optimal Disposition of Integrated Air Defense System Assets

We examine the optimal allocation of Integrated Air Defense System (IADS) resources to protect a country\u27s assets, formulated as a Defender-Attacker-Defender three-stage sequential, perfect information, zero-sum game between two opponents. We formulate a trilevel nonlinear integer program for this Defender-Attacker-Defender model and seek a subgame perfect Nash equilibrium, for which neither the defender nor the attacker has an incentive to deviate from their respective strategies. Such a trilevel formulation is not solvable via conventional optimization software and an exhaustive enumeration of the game tree based on the discrete set of strategies is intractable for large problem sizes. As such, we test and evaluate variants of a tree pruning algorithm and a customized heuristic, which we benchmark against an exhaustive enumeration. Our tests demonstrate that the pruning strategy is not efficient enough to scale up to a larger problem. We then demonstrate the scalability of the heuristic to show that the model can be applied to a realistic size problem

Using Double Oracle Algorithm for Classification of Adversarial Actions

Diplomová práce se zabývá použitím algoritmu inkrementálního generování strategií v nekonečných hrách. Konkrétně se zaměřuje na jeho využití při klasifikaci akcí útočníka. Nejprve jsme si formalizovali problém adversariální klasifikace jako hru se strikt\-ním omezením na chybu prvního typu v prostoru smířených strategií, která je téměř s nulovým součtem. K této reprezentaci jsme vytvořili algoritmus, který nám přesně určí hodnotu hry. Algoritmus inkrementálního generování strategií se v tomto případě skládá ze tří částí: z lehce upraveného LP na řešení omezené hry, z obecné optimalizační funkce pro nalezení optimální reakce útočníka a z klasifikátoru, který přibližně hledá optimální reakci obránce. Vytvořili jsme framework používající algoritmus inkrementálního generování strategií pro řešení problému klasifikace akcí útočníka a otestovali jsme ho na doménách s různorodou strukturou a~s~různě dimenzionálním prostorem akcí útočníka. Experimenty využívaly tři různé klasifikátory: rozhodovací stromy, SVM a neuronové sítě. Výsledky ukázaly, že algoritmus konverguje, ale jeho časová náročnost rapidně roste s počtem dimenzí prostoru útočníkových akcí.This thesis examines the usability of Double-Oracle algorithm for finding a~Nash equilibrium in infinite games. Especially, it focuses on finding a robust solution for classification of adversarial action. At first, we have formalized an adversarial classification problem as an almost zero-sum game with hard false-positive constraint in expectation. For this representation, we have found an algorithm, which gives us the exact value of the game. Double Oracle applied in this game consists of three parts: slightly modified LP for solving the restricted game, general optimization for finding the attacker's best response, and a classifier for an approximation of the defender's best response. We have created a framework for using DO for classification of adversarial actions, and we have evaluated it on predefined domains with various structures and a~various number of dimensions. The experiments have been performed with three classifier types: decision tree, SVM, and neural network. The experimental results have shown that the algorithm converges, but the computation time grows fast with the number of dimensions