Fight or Flight? Defending Against Sequential Attacks in the Game of Siege

This paper examines theory and behavior in a two-player game of siege, sequential attack and defense. The attacker’s objective is to successfully win at least one battle while the defender’s objective is to win every battle. Theoretically, the defender either folds immediately or, if his valuation is sufficiently high and the number of battles is sufficiently small, then he has a constant incentive to fight in each battle. Attackers respond to defense with diminishing assaults over time. Consistent with theoretical predictions, our experimental results indicate that the probability of successful defense increases in the defenders valuation and it decreases in the overall number of battles in the contest. However, the defender engages in the contest significantly more often than predicted and the aggregate expenditures by both parties exceed predicted levels. Moreover, both defenders and attackers actually increase the intensity of the fight as they approach the end of the contest.

[1]  Drew Fudenberg,et al.  Preemption, Leapfrogging, and Co­mpetition in Patent Races , 1983 .

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

[3]  Charles A. Holt,et al.  Risk Aversion and Incentive Effects , 2002 .

[4]  Shengle Lin,et al.  Gradual Information Diffusion and Asset Price Momentum , 2010 .

[5]  Colin Camerer.  Behavioral Game Theory: Experiments in Strategic Interaction , 2003 .

[6]  Rachel T. A. Croson,et al.  The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos , 2005 .

[7]  J. Vickers,et al.  Racing with Uncertainty , 1987 .

[8]  Kevin D. Glazebrook,et al.  Shoot-Look-Shoot: A Review and Extension , 2004, Oper. Res..

[9]  Michael R. Baye,et al.  The all-pay auction with complete information , 1990 .

[10]  Roman M. Sheremeta,et al.  Endowment Effects in Contests , 2009 .

[11]  Casper G. de Vries,et al.  An experimental examination of rational rent-seeking , 1998 .

[12]  Dan Kovenock,et al.  Terrorism and the Optimal Defense of Networks of Targets , 2008 .

[13]  Peter J. Coughlin.  Pure strategy equilibria in a class of systems defense games , 1992 .

[14]  C. Plott,et al.  NONSPECULATIVE BUBBLES IN EXPERIMENTAL ASSET MARKETS: LACK OF COMMON KNOWLEDGE OF RATIONALITY VS. ACTUAL IRRATIONALITY , 2001 .

[15]  B. Huberman,et al.  Searching for the sunk cost fallacy , 2007 .

[16]  Balázs Szentes,et al.  Three-object two-bidder simultaneous auctions: chopsticks and tetrahedra , 2003, Games Econ. Behav..

[17]  Rann Smorodinsky,et al.  All-Pay Auctions - An Experimental Study , 2006 .

[18]  John Dickhaut,et al.  Does information transparency decrease coordination failure? , 2010, Games Econ. Behav..

[19]  J. Hirshleifer.  From weakest-link to best-shot: The voluntary provision of public goods , 1983 .

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

[21]  Roman M. Sheremeta,et al.  Can groups solve the problem of over-bidding in contests? , 2009, Soc. Choice Welf..

[22]  M. Kremer,et al.  The O-Ring Theory of Economic Development , 1993 .

[23]  J. Snyder.  Election Goals and the Allocation of Campaign Resources , 1989 .

[24]  U. Fischbacher.  z-Tree: Zurich toolbox for ready-made economic experiments , 1999 .

[25]  Daniela Puzzello,et al.  An experimental investigation of overdissipation in the all pay auction , 2010 .

[26]  Gregory Levitin,et al.  Resource Distribution in Multiple Attacks Against a Single Target , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[27]  Roman M. Sheremeta.  Expenditures and Information Disclosure in Two-Stage Political Contests , 2010 .

[28]  Sergiu Hart,et al.  Discrete Colonel Blotto and General Lotto games , 2008, Int. J. Game Theory.

[29]  Henrik Orzen,et al.  The appearance of homo rivalis: Social preferences and the nature of rent seeking , 2008 .

[30]  Yaakov Kareev,et al.  Do the Weak Stand a Chance? Distribution of Resources in a Competitive Environment , 2009, Cogn. Sci..

[31]  Roman M. Sheremeta.  Experimental Comparison of Multi-Stage and One-Stage Contests , 2009, Games Econ. Behav..

[32]  Robert J. Reilly,et al.  Do too many cooks always spoil the stew? An experimental analysis of rent-seeking and the role of a strategic buyer , 1998 .

[33]  B. Roberson.  The Colonel Blotto game , 2006 .

[34]  Martin Shubik,et al.  Systems Defense Games: Colonel Blotto, Command and Control , 1981 .

[35]  Ross J. Anderson,et al.  The Economics of Online Crime , 2009 .

[36]  J. Vickers,et al.  A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease? , 1993 .

[37]  Wolfgang Leininger,et al.  Patent competition, rent dissipation, and the persistence of monopoly: The role of research budgets , 1991 .

[38]  J. Vickers,et al.  Perfect Equilibrium in a Model of a Race , 1985 .

[39]  J. Riley,et al.  Politically Contestable Rents And Transfers , 1989 .

[40]  Jacob K. Goeree,et al.  Quantal Response Equilibrium and Overbidding in Private-Value Auctions , 2002, J. Econ. Theory.

[41]  Kjell Hausken.  Strategic defense and attack for series and parallel reliability systems , 2008, Eur. J. Oper. Res..

[42]  Roman M. Sheremeta,et al.  The attack and defense of weakest-link networks , 2010, Public Choice.

[43]  Dmitriy Kvasov,et al.  Contests with limited resources , 2007, J. Econ. Theory.

[44]  E. Lavernia,et al.  An experimental investigation , 1992, Metallurgical and Materials Transactions A.

[45]  Derek J. Clark,et al.  Asymmetric Conflict , 2007 .

[46]  Dan Kovenock,et al.  Multi-Battle Contests , 2006, Games Econ. Behav..

[47]  Roman M. Sheremeta,et al.  Contest Design: An Experimental Investigation , 2009 .

[48]  J. N. Cooper,et al.  Some Problems of Attack and Defense , 1967 .

[49]  Dan Kovenock,et al.  STRATEGIC DEFENSE AND ATTACK FOR SERIES AND PARALLEL RELIABILITY SYSTEMS: COMMENT , 2012 .