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Data Analysis
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
Raymond R. Hill, Darryl K. Ahner
Games are expressed in normal form or extensive form. Normal form games restrict each player to act simultaneously and are usually expressed in the form of a matrix. The solution to these games is the best payoff for each player such that neither player can do any better by deviating from their strategy. This means that given one player chooses to play a specific strategy, the other player chooses the best response to that strategy such that their utility, or benefit, is at least as good as all other responses. Thus, the best response need not be unique. The strategy played is known as the Nash equilibrium. The Nash equilibrium may not be unique and in some cases may not exist. However, in a mixed strategy game where each player's strategies are played probabilistically, at least one Nash equilibrium will always exist.
Cyber-resilience
Published in Stavros Shiaeles, Nicholas Kolokotronis, Internet of Things, Threats, Landscape, and Countermeasures, 2021
E. Bellini, G. Sargsyan, D. Kavallieros
The use of the game-theoretic approach allows a better flexibility to adapt the modeling by allowing for different attacker models and behaviors in different settings and provides a pragmatic method to characterize the impacts of different types of cyber-attacks. It helps to identify mitigation measures, either in terms of cyber layer security reinforcements or in terms of developing new operational planning approaches to reduce attack impacts, depending on problem formulation. A game is defined as the interactions between individual players or the cooperative behavior between them. The players will choose specific strategy which is actually a complete decision-making plan for all possible actions the player may take for any circumstance that may face. Two types of strategies exist:Pure strategy: in which a unique action has been specified for a situationMixed strategy: which specifies a probability distribution for all possible actions in a situation (meaning in each pure strategy)
Game Theory
Published in N.V.S. Raju, Operations Research, 2019
Startegy: A startegy for a player has been defined as a set of rules or alternative courses of action available to him in advance, by which player decides the course of action that he should adopt. Startegy may be of two types: Pure Strategy: If the players select the same strategy each time, then it is referred to as pure-strategy. In this case each player known exactly what the other is going to do i.e., there is a deterministic situation and the objective of the players is to maximize gains or to minimize losses.Mixed Strategy: When the players use a combination of strategies and each player always kept guessing as to which course of action is to be selected by the other player at a particular occasion then this is known as mixed-strategy. Thus, there is a probabilistic situation and objective of the player is to maximize expected gains or to minimize losses. Thus, mixed strategy is a selection among pure strategies with fixed probabilities.
An adaptive defense mechanism to prevent advanced persistent threats
Published in Connection Science, 2021
Yi-xi Xie, Li-xin Ji, Ling-shu Li, Zehua Guo, Thar Baker
Case 2: If the attackers do not consider launching attacks with intensity 1, the reduced payoff matrix listed in Table 3 will be obtained by iterated elimination of strictly dominated strategies. In this case, no pure strategy Nash equilibrium exists. Based on Definition 2 and 3, the mixed strategy Nash equilibrium is calculated as (p = 0.91, q = 0.82). In other words, the attacker will select attack intensity 2 with a probability of 0.82 and attack intensity 3 with a probability of 0.18; the defender will choose defense intensity 4 with a probability of 0.91 and defense intensity 5 with a probability 0.09. For both attackers and defenders, the mixed strategy of Nash equilibrium is an optimal response for any strategies of the opponent’s strategies (pure or mixed). In case 2, URS is much worse than the game-based strategies. SSE becomes more advanced than URS but deems sub-optimal to NE. In the Markov game, the attacker has the inherent advantage of reconnaissance because the attacker is aware of the defender strategy in each state. NE’s defense utility is about 9% higher than URS.
Enhancing cyber-physical security in manufacturing through game-theoretic analysis
Published in Cyber-Physical Systems, 2018
Zach DeSmit, Aditya U. Kulkarni, Christian Wernz
The attacker–defender game discussed above illustrates a game where the strategies used by the players is considered pure; each player chooses a single strategy with certainty. Pure strategy games are models for games where no NE strategy profiles exist. Mixed strategy games are a generalisation of pure strategy games that guarantee the existence of an NE strategy profile. In mixed strategy games, each player can probabilistically choose a strategy from its set of pure strategies. Thus, in a mixed strategy game, a player’s strategy is a probability distribution defined over the set of pure strategies for that player. Once again, we will use the NE condition to characterise the best strategy profile for the players, where the best strategy profile is any mixed strategy profile that qualifies as an NE strategy profile.
Strategic joining and information disclosing in Markovian queues with an unreliable server and working vacations
Published in Quality Technology & Quantitative Management, 2021
In this section, we analyze customers’ optimal strategies for joining or balking in four information situations. In the observable cases (i.e. fully observable case and partially observable case), we will give customer optimal joining threshold policy. In the unobservable cases (i.e. fully unobservable case and almost unobservable case), we will prove that there exist Nash equilibrium mixed strategies. Note that Nash equilibrium is the one where no customer has an incentive to deviate from it when other customers adopt it and a mixed strategy corresponds to a probability under which customers select an action between joining and balking.