A Brief Survey Of Stochastic Game Methods

With cyber war, nations are able to skip the battlefield. Gone are the days where troops line up across from each other hoping to do damage to the other. Clarke explains that people, industries, governments, companies and organizations can be possible targets and are vulnerable to these attacks. Keeping that in mind should help these targets become defensive minded and shield off attacks before they happen. As we all know, the prevention is better than the

Lately active defense in cyber security has been a very popular approach in protecting assets in cyberspace as well as mitigating the increase of cyber threats. Current defenses such as firewalls, antivirus, strong security policies and security patch updates aren’t sufficient enough to protect against the rapidly changing threat landscape. Many hackers can easily bypass traditional

The decisions made by one economic actor not only affects her payoff, but the payoff of one or more other economic actors. Schmidt (2003) states that Game theory was invented in order to satisfy a mathematical curiosity. The difficulty at the outset was to find a theoretical solution to the problem posed by uncertainty in games of chance (Schmidt, 2003). He further stated that the first completed formula of mathematical strategies was sketched by Boral. The application of game theory to economics posed a more fundamental problem due to the distance of separating several major concepts articulated in Theory of Games and Economic Behavior. Economics

Games can be very hard. States can be only observes to a certain extend. Multiple agents choose Actions, stochastic pays off and state transition depends on state and other

Today however, a new type of warfare has emerged and occurs when outside entities conduct an attack on a power grid, network, or both with the intent of causing damage. This type of warfare is called cyber warfare. In the United States computers control everything. It is no secret that hostile countries and terrorist organizations are cognizant and they know our economy, security, and infrastructure can be crippled by a successful cyber-attack. Examples of potential targets for cyber terrorists include military bases, water systems, banking facilities, air traffic control centers and power plants. Even the Commander in Chief, President Obama has stated the threat of a cyber war is real and we must prepare for it and increase our security measures. First, this paper will discuss cyberterrorism and cyber-attacks as they pose a direct threat to national security and the economy. Then, we will review cyber-attacks against the U.S. from China, Iran, and Russia along with the impact and possible ramifications from those attacks. Finally, this paper discusses U.S. strategies to minimize the impact of cyber-attacks.

In the state of nature game, we are giving two options; first you are giving an automatic grade of B for just participating in the game. Then where it gets complicated is when you are giving the chance to get an A, but in order to get the A you have to ask for it then if more than one person asks for an A everyone automatically gets an F, but in the case when one person ask for an A then where as everyone else asks for a B, the people who asks for the B would all get a F then the one who asks for the A gets an A.

Game theory cannot always predict reliable outcomes for real-life situations as it is more an

Game theory is concerned with predicting the outcome of games of strategy in which the participants (for example two or more businesses competing in a market) have incomplete information about the others' intentions (Gittins, 2012)

This is an argument between the conceptuality and the practicality of Nash equilibrium in Economics. To understand it we need to first look into what economics is about, which is the study of social and human interaction and rational decision making quantitatively. Nash equilibrium can act as a tool to provide an insight into such interaction. In the first part of this essay, I am going to evaluate why the statement ‘economics without the concept of Nash equilibrium is conceptually flawed’ is true, by looking into the importance of rationality in economics and the mechanism of the Nash equilibrium. In the second part, I am going to assess why the argument for ‘Economics with the concept of Nash equilibrium is practically useless’ is true

In 1950, puzzles with the structure of the Prisoner’s dilemma were devised by Merrill Flood and Melvin Dresher as part of the Rand Corporation’s investigations into game theory, which they believed could be applied in the context of nuclear strategy. The title, “prisoner’s dilemma” was coined later by Albert Tucker.

In this game tree, the two player’s state of minds and actions are displayed. Consider the case scenario of Boeing and General Electric (GE) playing a sequential game, GE makes the first move in the process followed by Boeing based on their interpretation of GE’s

The scientific field of game theory is the usage of mathematics to predict and analyze “conflict, cooperation, and behaviors of thinking people” and the different strategies that can be applied in each case. Using mathematical fields such as calculus, statistics, and others, people who study game theory are able to formulate models and find the outcomes of a variety of different strategies. More importantly, game theory is not limited to games such as chess or poker, but a wide variety of fields including economics, computer science, biology and even political science. To understand why game theory underlies these other fields, one must first understand what a game is.

John F. Nash shared the 1994 Nobel Prize with John Harsanyi and Reinhard Selten in economics for their work on the theory of non-cooperative games, in other words John Nash received a Nobel Prize for his work in Game theory. Except for one course in economics that he took as an undergraduate, Nash had not any formal training in economics. John Nash had a Ph.D. in mathematics in 1950, but the Nobel Prize he received four decades later was for the contribution he made to game theory in his 1950 Ph.D. thesis. In his work, he introduced the distinction between cooperative and non-cooperative games. In non-cooperative games every player is self-enforced, and in cooperative games, players can make agreements with other players. Nash’s contribution is the concept of equilibrium for non-cooperative games, which later came to be called a Nash equilibrium. In Nash equilibrium no player can improve his position by choosing a different strategy. Nash explained that as long as mixed strategies are allowed, for a broad class of games, at least one equilibrium exist. Another Nash’s contribution is his reasoning about “the bargaining problem,” before Nash, economist thought the share of gains each of two parties to a bargain received was always indeterminate. But Nash got further by suggesting four conditions and showed mathematically that a unique solution

The internet is an integral way of conducting daily business from government agencies to entertainers. Protection of attack, damage, or unauthorized access is necessary with the increase of mobile users, digital applications and data networks. A cyber-security problem can be viewed as a conflict-resolution scenario that typically consists of a security system and at least two decision makers (e.g. attacker and defender) that can each have competing objectives. For instance, the defender may be interested in ensuring that the system performs at or above a certain acceptable level. The attacker’s objective may be to disrupt the system and degrade it. Game theory is a well-established tool that can be used to analyze such problems. In this work, we present a brief survey of how game theory can be used to find appropriate strategies for both the attacker and the administrator (defender). We model the interactions between them as a stochastic game. Various formulations of game theory will be presented to deal with different cyber security situations. We will present mathematical models of security systems to analyze the system’s performance and to predict the likely behavior of key decision makers that influence/control the system.

In this type of games the players have little information about their opponents’ payoff functions but they know the actions of all other players that were in the past. An example for those games is the Intrusion detection game, which is a 2-player zero-sum stochastic (Markov)