The Bodyguard Allocation Problem

In this paper, we introduce the Bodyguard Allocation Problem (BAP) game, that illustrates the behavior of processes with contradictory individual goals in distributed systems. In particular, the game deals with the conflict of interest between two classes of processes that maximize/minimize their distance to a special process called the root. A solution of the BAP game represents a rooted spanning tree in which there exists a condition of equilibrium with maximum social welfare. We analyze the inefficiency of equilibria of the game based on both a completely cooperative and noncooperative approach. Additionally, we design two algorithms, CBAP and DBAP, that provide approximated solutions for the BAP game. We prove that both algorithms always terminate in a configuration with equilibrium and we analyze their running time based on the approach of cooperation used. We perform experimental simulations to compare the overall quality of equilibria obtained by the proposed algorithms.

[1]  Tim Roughgarden,et al.  Selfish routing and the price of anarchy , 2005 .

[2]  Hector Garcia-Molina,et al.  Streaming Live Media over a Peer-to-Peer Network , 2001 .

[3]  Joseph Y. Halpern.  Computer Science and Game Theory: A Brief Survey , 2007, ArXiv.

[4]  Gordon T. Wilfong,et al.  The stable paths problem and interdomain routing , 2002, TNET.

[5]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[6]  Noam Nisan,et al.  Algorithmic Mechanism Design , 2001, Games Econ. Behav..

[7]  J. Hopcroft,et al.  Are randomly grown graphs really random? , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Edsger W. Dijkstra,et al.  Self-stabilizing systems in spite of distributed control , 1974, CACM.

[9]  Shrisha Rao,et al.  Distributed Systems: An Algorithmic Approach , 2008, IEEE Distributed Systems Online.

[10]  Sébastien Tixeuil,et al.  Selfish Stabilization , 2006, SSS.

[11]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Ajoy Kumar Datta,et al.  Self-stabilizing depth-first token circulation in arbitrary rooted networks , 2000, Distributed Computing.

[13]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[14]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[15]  Dinesh C. Verma,et al.  ALMI: An Application Level Multicast Infrastructure , 2001, USITS.

[16]  Shlomi Dolev,et al.  Self-Stabilizing Depth-First Search , 1994, Inf. Process. Lett..

[17]  Athanasios D. Panagopoulos,et al.  A survey on game theory applications in wireless networks , 2010, Comput. Networks.

[18]  Michael Dahlin,et al.  BAR fault tolerance for cooperative services , 2005, SOSP '05.

[19]  B. Bollobás.  The evolution of random graphs , 1984 .

[20]  Sébastien Tixeuil,et al.  An exercise in selfish stabilization , 2008, TAAS.

[21]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[22]  H. Lilliefors.  On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown , 1967 .

[23]  Ajay D. Kshemkalyani,et al.  Distributed Computing: Principles, Algorithms, and Systems , 2008 .

[24]  K. Arrow,et al.  The New Palgrave Dictionary of Economics , 2020 .

[25]  Sirin Tekinay,et al.  A survey of game-theoretic approaches in wireless sensor networks , 2008, Comput. Networks.

[26]  Anthony T. Chronopoulos,et al.  Algorithmic mechanism design for load balancing in distributed systems , 2002, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[27]  Andreas S. Schulz,et al.  On the performance of user equilibria in traffic networks , 2003, SODA '03.

[28]  Igor Walukiewicz,et al.  Distributed Games , 2003, FSTTCS.

[29]  Andreas S. Schulz,et al.  On the Performance of User Equilibrium in Traffic Networks , 2015 .

[30]  Ion Stoica,et al.  Robust incentive techniques for peer-to-peer networks , 2004, EC '04.

[31]  Christos H. Papadimitriou,et al.  Free-riding and whitewashing in peer-to-peer systems , 2004, IEEE Journal on Selected Areas in Communications.

[32]  Christos H. Papadimitriou,et al.  Worst-case Equilibria , 1999, STACS.

[33]  Tim Roughgarden,et al.  The price of stability for network design with fair cost allocation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[34]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[35]  Paul G. Spirakis,et al.  Game authority for robust and scalable distributed selfish-computer systems , 2010, Theor. Comput. Sci..

[36]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[37]  Bryant A. Julstrom,et al.  Edge sets: an effective evolutionary coding of spanning trees , 2003, IEEE Trans. Evol. Comput..

[38]  Joan Feigenbaum,et al.  Sharing the Cost of Multicast Transmissions , 2001, J. Comput. Syst. Sci..

[39]  David R. Karger,et al.  On approximating the longest path in a graph , 1997, Algorithmica.

[40]  E. Carpenter.  Language and Environment. , 1968 .

[41]  Shlomi Dolev,et al.  Self Stabilization , 2004, J. Aerosp. Comput. Inf. Commun..

[42]  Ajay D. Kshemkalyani,et al.  Distributed Computing: Index , 2008 .