Modeling Interdependent Risks

In an interdependent world the risks faced by any one agent depend not only on its choices but also on those of all others. Expectations about others' choices will influence investments in risk management and the outcome can be suboptimal for everyone. We model this as the Nash equilibrium of a game and give conditions for such a suboptimal equilibrium to be tipped to an optimal one. We also characterize the smallest coalition to tip an equilibrium, the minimum critical coalition, and show that this is also the cheapest critical coalition, so that there is no less expensive way to move the system from the suboptimal to the optimal equilibrium. We illustrate these results by reference to airline security and the control of infectious diseases via vaccination.

[1]  Howard Kunreuther,et al.  The Vaccination Game , 2005 .

[2]  G. Heal,et al.  Formation of International Environmental Agreements , 1994 .

[3]  Howard Kunreuther,et al.  Supermodularity and Tipping , 2006 .

[4]  W. Polonsky,et al.  The Tipping Point , 2007, The Diabetes educator.

[5]  William R. Easterly,et al.  Empirics of Strategic Interdependence: The Case of the Racial Tipping Point , 2008 .

[6]  Thomas C. Schelling,et al.  Dynamic models of segregation , 1971 .

[7]  H. Kunreuther,et al.  IDS Models of Airline Security , 2005 .

[8]  Carson C. Chow,et al.  Small Worlds , 2000 .

[9]  H. Kunreuther,et al.  Interdependencies within an Organization , 2004 .

[10]  Gesine Reinert,et al.  Small worlds , 2001, Random Struct. Algorithms.

[11]  V. Rich.  Personal communication , 1989, Nature.

[12]  T. Schelling.  Micromotives and Macrobehavior , 1978 .

[13]  Avinash Dixit,et al.  A General Model of R&D Competition and Policy , 1988 .

[14]  Carl Shapiro,et al.  Dynamic R&D Competition , 1985 .

[15]  Paul R. Milgrom,et al.  Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities , 1990 .

[16]  J. Geanakoplos,et al.  Multimarket Oligopoly: Strategic Substitutes and Complements , 1985, Journal of Political Economy.

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

[18]  T. Sandler,et al.  Collective Action and Transnational Terrorism , 2003 .

[19]  R. Zeckhauser,et al.  The Ecology of Terror Defense , 2003 .

[20]  Avinash Dixit,et al.  Clubs with Entrapment , 2003 .

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

[22]  V. Bier.  Choosing What to Protect , 2007, Risk analysis : an official publication of the Society for Risk Analysis.