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An exterior point linear programming method based on inclusive normal cones
Twoperson knapsack game
1.  Department of Mathematical Sciences, Tsinghua University, Beijing 
2.  Department of Industrial and System Engineering, North Carolina State University, Raleigh, NC 27695 
References:
[1] 
R. E. Bellman, "Dynamic Programming," Princeton University Press, 1957. 
[2] 
J. R. Correa, A. S. Schulz and N. E. StierMoses, Selfish routing in capacitated networks, Math. Oper. Res., 29 (2004), 961976. doi: 10.1287/moor.1040.0098. 
[3] 
A. Czumaj and B. Vöcking, Tight bounds for worstcase equilibria, in "Proc. 13th ACMSIAM Symp. on Discrete Algorithms," (2002), 413420. 
[4] 
M. R. Garey and D. S. Johnson, "Computers and Intractability: A Guide to the Theory of NPCompleteness," WH Freeman, 1979. 
[5] 
E. Horowitz and S. Sahni, Computing partitions with applications to the knapsack problem, J. ACM, 21 (1974), 277292. doi: 10.1145/321812.321823. 
[6] 
H. Kellerer, U. Pferschy and D. Pisinger, "Knapsack Problems," Springer, 2004. 
[7] 
E. Koutsoupias and C. H. Papadimitriou, Worstcase equilibria, in "Proc. 16th Symp. on Theoretical Aspects of Computer Science," (1999), 404413. 
[8] 
S. Martello and P. Toth, A mixture of dynamic programming and branchandbound for the subsetsum problem, Manage. Sci., 30 (1984), 765771. doi: 10.1287/mnsc.30.6.765. 
[9] 
S. Martello and P. Toth, Dynamic programming and strong bounds for the 01 knapsack problem, Manage. Sci., 45 (1999), 275288. doi: 10.1287/mnsc.45.3.414. 
[10] 
I. Milchtaich, Congestion games with playerspecific payoff functions, Games and Economic Behavior, 13 (1996), 111124. doi: 10.1006/game.1996.0027. 
[11] 
D. Monderer and L. Shapley, Potential games, Games and Economic Behavior, 14 (1996), 124143. doi: 10.1006/game.1996.0044. 
[12] 
J. F. Nash, Equilibrium points in $n$Person games, P. Nalt. Acad Sci., 36 (1950), 4849. doi: 10.1073/pnas.36.1.48. 
[13] 
R. M. Nauss, An efficient algorithm for the 01 knapsack problem, Manage. Sci., 23 (1976), 2731. doi: 10.1287/mnsc.23.1.27. 
[14] 
C. H. Papadimitriou and K. Steiglitz, "Combinatorial Optimization: Algorithms and Complexity," PrenticeHall, 1982. 
[15] 
D. Pisinger and P. Toth, Knapsack problems, in "Handbook of Combinatorial Optimization" (eds. DZ. Du and P. Pardalos), (1998), Kluwer Academic Publishers, 299428. 
[16] 
R. W. Rosenthal, A class of games possessing purestrategy Nash equilibrium, Int. J. Game Theory, 2 (1973), 6567. doi: 10.1007/BF01737559. 
[17] 
T. Roughgarden and É. Tardos, How bad is selfish routing?, in "Proc. 41th IEEE Symp. on Foundations of Computer Science," (2000), 93102. 
[18] 
É. Tardos, Network games, in "Proc. 36th ACM Symp. on Theory of Computing," (2004), 341342. 
[19] 
A. Vetta, Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions, in "Proc. 43th IEEE Symp. on Foundations of Computer Science," (2002), 416425. 
[20] 
Z. Wang, W. Xing and S.C. Fang, Twogroup knapsack game, Theor. Comput. Sci., 411 (2010), 10941103. doi: 10.1016/j.tcs.2009.12.002. 
show all references
References:
[1] 
R. E. Bellman, "Dynamic Programming," Princeton University Press, 1957. 
[2] 
J. R. Correa, A. S. Schulz and N. E. StierMoses, Selfish routing in capacitated networks, Math. Oper. Res., 29 (2004), 961976. doi: 10.1287/moor.1040.0098. 
[3] 
A. Czumaj and B. Vöcking, Tight bounds for worstcase equilibria, in "Proc. 13th ACMSIAM Symp. on Discrete Algorithms," (2002), 413420. 
[4] 
M. R. Garey and D. S. Johnson, "Computers and Intractability: A Guide to the Theory of NPCompleteness," WH Freeman, 1979. 
[5] 
E. Horowitz and S. Sahni, Computing partitions with applications to the knapsack problem, J. ACM, 21 (1974), 277292. doi: 10.1145/321812.321823. 
[6] 
H. Kellerer, U. Pferschy and D. Pisinger, "Knapsack Problems," Springer, 2004. 
[7] 
E. Koutsoupias and C. H. Papadimitriou, Worstcase equilibria, in "Proc. 16th Symp. on Theoretical Aspects of Computer Science," (1999), 404413. 
[8] 
S. Martello and P. Toth, A mixture of dynamic programming and branchandbound for the subsetsum problem, Manage. Sci., 30 (1984), 765771. doi: 10.1287/mnsc.30.6.765. 
[9] 
S. Martello and P. Toth, Dynamic programming and strong bounds for the 01 knapsack problem, Manage. Sci., 45 (1999), 275288. doi: 10.1287/mnsc.45.3.414. 
[10] 
I. Milchtaich, Congestion games with playerspecific payoff functions, Games and Economic Behavior, 13 (1996), 111124. doi: 10.1006/game.1996.0027. 
[11] 
D. Monderer and L. Shapley, Potential games, Games and Economic Behavior, 14 (1996), 124143. doi: 10.1006/game.1996.0044. 
[12] 
J. F. Nash, Equilibrium points in $n$Person games, P. Nalt. Acad Sci., 36 (1950), 4849. doi: 10.1073/pnas.36.1.48. 
[13] 
R. M. Nauss, An efficient algorithm for the 01 knapsack problem, Manage. Sci., 23 (1976), 2731. doi: 10.1287/mnsc.23.1.27. 
[14] 
C. H. Papadimitriou and K. Steiglitz, "Combinatorial Optimization: Algorithms and Complexity," PrenticeHall, 1982. 
[15] 
D. Pisinger and P. Toth, Knapsack problems, in "Handbook of Combinatorial Optimization" (eds. DZ. Du and P. Pardalos), (1998), Kluwer Academic Publishers, 299428. 
[16] 
R. W. Rosenthal, A class of games possessing purestrategy Nash equilibrium, Int. J. Game Theory, 2 (1973), 6567. doi: 10.1007/BF01737559. 
[17] 
T. Roughgarden and É. Tardos, How bad is selfish routing?, in "Proc. 41th IEEE Symp. on Foundations of Computer Science," (2000), 93102. 
[18] 
É. Tardos, Network games, in "Proc. 36th ACM Symp. on Theory of Computing," (2004), 341342. 
[19] 
A. Vetta, Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions, in "Proc. 43th IEEE Symp. on Foundations of Computer Science," (2002), 416425. 
[20] 
Z. Wang, W. Xing and S.C. Fang, Twogroup knapsack game, Theor. Comput. Sci., 411 (2010), 10941103. doi: 10.1016/j.tcs.2009.12.002. 
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