# American Institute of Mathematical Sciences

October  2015, 11(4): 1165-1173. doi: 10.3934/jimo.2015.11.1165

## Bounds on price of anarchy on linear cost functions

 1 Department of Management Science and Engineering, School of Economics and Management, Southeast University, Nanjing, 210096, China, China 2 School of Mathematical Sciences, Jiangsu Key Labratory for NSLSCS, Nanjing Normal University, Nanjing, 210023

Received  September 2013 Revised  August 2014 Published  March 2015

The price of anarchy (POA) is a quite powerful tool to characterize the efficiency loss of competition on networks. In this paper, we derive a bound for POA for the case that the cost function is linear but asymmetric. The result is a generalization of that of Han et. al. in the sense that the involved matrix is only assumed to be positive semidefinite, but not positive definite. Consequently, the range of application of the result is widened. We give two simple examples to illustrate our result.
Citation: Fan Sha, Deren Han, Weijun Zhong. Bounds on price of anarchy on linear cost functions. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1165-1173. doi: 10.3934/jimo.2015.11.1165
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