Strategic defense and attack for series and parallel reliability systems

Kovenock and Roberson’s (2010) paper has the potential to advance the research frontier, but has deficiencies. This paper suggests how Kovenock and Roberson’s (2010) paper can be developed into a more substantial paper. Kovenock and Roberson’s (2010) paper consists of three sections. The first section is an introduction which is OK but has no results. The second section, titled “Model and Main Result”, provides no contribution beyond Hausken (2008a). It consists of equations (1)-(10) which are equivalent to equations developed by Hausken (2008a), and equation (11) which is equivalent to the requirement u≥0 and U≥0 provided after equation (17) in Hausken (2008a). The third section quotes Hausken (2008a) once in one sentence which means that section 3 does not belong as a comment on the paper written by Hausken (2008a). The authors are encouraged to develop a new paper based on many interesting ideas in this note. The new paper should develop further the idea of mixed strategies presented in section 3. The new paper may be titled: “Strategic Defense and Attack for Series and Parallel Reliability Systems when Allowing Mixed Strategies”.

[1]  J. Neumann,et al.  The Theory of Games and Economic Behaviour , 1944 .

[2]  K. Hausken.  Production and Conflict Models Versus Rent-Seeking Models , 2005 .

[3]  Kjell Hausken,et al.  THE STABILITY OF ANARCHY AND BREAKDOWN OF PRODUCTION , 2006 .

[4]  Gregory Levitin,et al.  Optimal separation of elements in vulnerable multi-state systems , 2001, Reliab. Eng. Syst. Saf..

[5]  Roman M. Sheremeta,et al.  An experimental investigation of Colonel Blotto games , 2009, SSRN Electronic Journal.

[6]  Herbert A. Simon,et al.  The Sciences of the Artificial , 1970 .

[7]  Anindya Ghose,et al.  The Economic Incentives for Sharing Security Information , 2004, Inf. Syst. Res..

[8]  K. Menninger.  On war. , 1973, Bulletin of the Menninger Clinic.

[9]  T. Sandler,et al.  What do we know about the substitution effect in transnational terrorism , 2003 .

[10]  Gregory Levitin,et al.  Protection vs. false targets in series systems , 2009, Reliab. Eng. Syst. Saf..

[11]  J. Hirshleifer.  Anarchy and its Breakdown , 1995, Journal of Political Economy.

[12]  Vicki M. Bier,et al.  Optimal Allocation of Resources for Defense of Simple Series and Parallel Systems from Determined Adversaries , 2003 .

[13]  G. Woo.  Quantitative Terrorism Risk Assessment , 2002 .

[14]  Gregory Levitin,et al.  Survivability maximization for vulnerable multi-state systems with bridge topology , 2000, Reliab. Eng. Syst. Saf..

[15]  K. Hausken.  Probabilistic Risk Analysis and Game Theory , 2002, Risk analysis : an official publication of the Society for Risk Analysis.

[16]  Lawrence A. Gordon,et al.  The economics of information security investment , 2002, TSEC.

[17]  H. Kunreuther,et al.  Interdependent Security , 2003 .

[18]  Larry Samuelson,et al.  Choosing What to Protect: Strategic Defensive Allocation Against an Unknown Attacker , 2005 .

[19]  Vicki M. Bier,et al.  Protection of simple series and parallel systems with components of different values , 2005, Reliab. Eng. Syst. Saf..

[20]  Kjell Hausken.  Defense and attack of complex and dependent systems , 2010, Reliab. Eng. Syst. Saf..

[21]  Lawrence A. Gordon,et al.  Sharing Information on Computer Systems Security: An Economic Analysis , 2003 .

[22]  K. Hausken.  Income, interdependence, and substitution effects affecting incentives for security investment , 2006 .

[23]  Gregory Levitin,et al.  Optimal multilevel protection in series-parallel systems , 2003, Reliab. Eng. Syst. Saf..

[24]  Ross J. Anderson.  Why information security is hard - an economic perspective , 2001, Seventeenth Annual Computer Security Applications Conference.

[25]  S. Skaperdas.  CONFLICT AND ATTITUDES TOWARD RISK , 1990 .

[26]  Dan Kovenock,et al.  Suicide Terrorism and the Weakest Link , 2009, SSRN Electronic Journal.

[27]  Gregory Levitin.  Maximizing survivability of acyclic transmission networks with multi-state retransmitters and vulnerable nodes , 2002, Reliab. Eng. Syst. Saf..

[28]  Gregory Levitin,et al.  Optimizing survivability of vulnerable series-parallel multi-state systems , 2003, Reliab. Eng. Syst. Saf..

[29]  Vicki M. Bier,et al.  Game-Theoretic and Reliability Methods in Counterterrorism and Security , 2006 .

[30]  Gregory Levitin,et al.  Optimizing survivability of multi-state systems with multi-level protection by multi-processor genetic algorithm , 2003, Reliab. Eng. Syst. Saf..

[31]  Gregory Levitin.  Optimal Defense Strategy Against Intentional Attacks , 2007, IEEE Transactions on Reliability.

[32]  I. M. Destler,et al.  Protecting the American Homeland , 2003 .

[33]  M. Naceur Azaiez,et al.  Optimal resource allocation for security in reliability systems , 2007, Eur. J. Oper. Res..

[34]  Gregory Levitin,et al.  False targets efficiency in defense strategy , 2009, Eur. J. Oper. Res..

[35]  S. Skaperdas.  Contest success functions , 1996 .

[36]  Eric van Damme,et al.  Non-Cooperative Games , 2000 .

[37]  Gregory Levitin,et al.  Efficiency of even separation of parallel elements with variable contest intensity. , 2008, Risk analysis : an official publication of the Society for Risk Analysis.

[38]  Gregory Levitin,et al.  Optimal allocation of multi-state elements in linear consecutively connected systems with vulnerable nodes , 2003, Eur. J. Oper. Res..

[39]  Vicki M. Bier,et al.  Subsidies in Interdependent Security With Heterogeneous Discount Rates , 2007 .

[40]  John A. Major.  Advanced Techniques for Modeling Terrorism Risk , 2002 .

[41]  Kjell Hausken.  Strategic defense and attack for reliability systems , 2008, Reliab. Eng. Syst. Saf..

[42]  J. Hirshleifer.  Conflict and rent-seeking success functions: Ratio vs. difference models of relative success , 1989 .

[43]  V. Bier,et al.  Perfect aggregation for a class of general reliability models with Bayesian updating , 1995 .