On Game-Theoretic Risk Management (Part One) - Towards a Theory of Games with Payoffs that are Probability-Distributions (original) (raw)
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Probabilistic Risk Analysis and Game Theory
Risk Analysis, 2002
The behavioral dimension matters in Probabilistic Risk Analysis (PRA) since players throughout a system incur costs to increase system reliability interpreted as a public good. Individual strategies at the subsystem level generally conflict with collective desires at the system level. Game theory, the natural tool to analyze individual-collective conflicts that affect risk, is integrated into PRA. Conflicts arise in series, parallel, and summation systems over which player(s) prefer(s) to incur the cost of risk reduction. Frequently, the series, parallel, and summation systems correspond to the four most common games in game theory, i.e., the coordination game, the battle of the sexes and the chicken game, and prisoner's dilemma, respectively.
arXiv (Cornell University), 2015
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria in games where the payoffs are probability distributions. Our approach is "data driven" in the sense that we assume empirical data (measurements, simulation, etc.) to be available that can be compiled into distribution models, which are suitable for efficient decisions about preferences, and setting up and solving games using these as payoffs. While preferences among distributions turn out to be quite simple if nonparametric methods (kernel density estimates) are used, computing Nash-equilibria in games using such models is discovered as inefficient (if not impossible). In fact, we give a counterexample in which fictitious play fails to converge for the (specifically unfortunate) choice of payoff distributions in the game, and introduce a suitable tail approximation of the payoff densities to tackle the issue. The overall procedure is essentially a modified version of fictitious play, and is herein described for standard and multicriteria games, to iteratively deliver an (approximate) Nash-equilibrium. An exact method using linear programming is also given.
Applying Game Theory in Risk Management
Annals of the University of Oradea: Economic Science, 2016
This article is devoted to analysis methods of application of game theory in conflict situations or competition in the economy. There are examples of the use of game theory in the identification, sizing, analysis and risk management. There is described the defining concepts of game theory in terms of their application in risk management. It is shown how to use the decision theory in risk management, which is part of operational research and decision-making process, based on various mathematical models. The decision theory refers performing various actions, to achieve well-defined goals in uncertain circumstances and under risk situations. The quality of decision is subject to a complex set of preconditions, it's seen determines by the quality of used information and held managerial skills and applied by decision makers. The Choice between different alternatives of optimal decision is based on economic calculations of rationality, but also filled with other criteria that are not ...
Game-theoretic computing in risk analysis
Wiley Interdisciplinary Reviews: Computational Statistics, 2012
Risk analysis, comprising risk assessment and risk management stages, is one of the most popular and challenging topics of our times because security and privacy, and availability and usability culminating at the trustworthiness of cybersystems and cyber information is at stake. The precautionary need derives from the existence of defenders versus adversaries, in an everlasting Darwinian scenario dating back to early human history of warriors fighting for their sustenance to survive. Fast forwarding to today's information warfare, whether in networks or healthcare or national security, the currently dire situation necessitates more than a hand calculator to optimize (maximize gains or minimize losses) risk due to prevailing scarce economic resources. This article reviews the previous works completed on this specialized topic of game-theoretic computing, its methods and applications toward the purpose of quantitative risk assessment and cost-optimal management in many diverse disciplines including entire range of informaticsrelated topics. Additionally, this review considers certain game-theoretic topics in depth historically, and those computationally resourceful such as Neumann's two-way zero-sum pure equilibrium and optimal mixed strategy solutions versus Nash equilibria with pure and mixed strategies. Computational examples are provided to highlight the significance of game-theoretic solutions used in risk assessment and management, particularly in reference to cybersystems and information security.
Game theory in infrastructure security
Critical Infrastructure Security, 2012
Game-theoretic security models have gained popularity in infrastructure security in recent years, due to the fact that game theory is suitable for dealing with intelligent threats. In this chapter, we briefl y discuss some of the key concepts in game theory, categorize game-theoretic models in infrastructure security and give some examples, and fi nally discuss some of the limitations of gametheoretical models.
Games over Probability Distributions Revisited: New Equilibrium Models and Refinements
Games
This article is an overview of recent progress on a theory of games, whose payoffs are probability distributions rather than real numbers, and which have their equilibria defined and computed over a (suitably restricted yet dense) set of distributions. While the classical method of defining game models with real-valued utility functions has proven strikingly successful in many domains, some use cases from the security area revealed shortcomings of the classical real-valued game models. These issues motivated the use of probability distributions as a more complex object to express revenues. The resulting class of games displays a variety of phenomena not encountered in classical games, such as games that have continuous payoff functions but still no equilibrium, or games that are zero-sum but for which fictitious play does not converge. We discuss suitable restrictions of how such games should be defined to allow the definition of equilibria, and show the notion of a lexicographic Na...
An axiomatic approach to choice under uncertainty with catastrophic risks
Resource and Energy Economics, 2000
This paper analyses decision under uncertainty with catastrophic risks, and is motivated by problems emerging from global environmental risks. These are typically low-probability events with major irreversible consequences. For such risks, the Von Neumann-Morgens-Ž . tern NM axioms for decision making under uncertainty are not appropriate, since they are shown here to be insensitive to low-probability events. The paper introduces an alternative set of axioms requiring sensitivity to both low-and large-probability events. Through a new representation theorem in functional analysis, the results characterize all the operators whose maximization leads to the fulfillment of these axioms. They involve a convex combination of expected utility and a criterion based on the desire to avoid low probability and potentially catastrophic events. It is shown that the new axioms help resolve the Allais paradox. Open questions about risk aversion, games under uncertainty and calculus of variations are discussed. q
Of threats and costs: A game-theoretic approach to security risk management
Performance Models and Risk Management …, 2011
Security is one of the main concerns in current telecommunication networks: the service providers and individual users have to protect themselves against attacks, and to this end a careful analysis of their optimal strategies is of essential importance. Indeed, attackers and defenders are typically agents trying strategically to design the most important damages and the most secure use of the resources, respectively, and the natural modelling framework of these interactions is that of noncooperative game theory. This chapter aims at providing a comprehensive review of game-theoretic aspects of security. We first describe the basics on game theory through simple security problems, and then present and discuss some specific problems in more detail. Finally, we also deal with security economics, focussing on the selfish relationships between customers and providers as well as between competing providers, which represents another important aspect of our non-standard approach towards security risk assessement.
From the Editors—Games and Decisions in Reliability and Risk
Decision Analysis, 2012
T he objective of this special issue is to introduce a new theme, the use of game and decision theory in reliability modeling and risk analysis, which was the focus of the First Symposium on Games and Decisions in Reliability and Risk (GDRR) held at the George Washington University on May 27-28, 2009. The issue considered papers presented at the Second Symposium on GDRR (http://www.mi.imati.cnr.it/conferences/gdrr11.html), held at the Hotel Villa Carlotta, Belgirate (VB), Lake Maggiore, Italy, on May 19-21, 2011, and also was open to the public for submission of papers relevant to the theme. The contributors to the special issue include Sevillano,