Non-Cooperative Game of Throughput and Hash Length for Adaptive Merkle Tree in Mobile Wireless Networks

Abstract

The restricted resources of mobile wireless networks such as limited bandwidth have resulted in stringent requirements on the available quality of service (QoS). To enhance the communication performance, mobile nodes attempt to optimize the available bandwidth of wireless networks, which, however, makes them vulnerable to the malicious attacks of adversaries owing to the open and mobile context. Furthermore, improving the security level of the communication consumes bandwidth and thus degrades the communication quality. In order to harmonize the QoS and security, in this paper, the two conflicting terms “communication player” and “security player” are considered as two individual players and are balanced using game theory. Furthermore, we construct a non-cooperative game model, wherein the utilities of the communication player and security player are maximized by controlling the number of nodes transmitted and the length of hash, respectively. We formulate the utility functions of the communication player with respect to the throughput as well as the security level of the Merkle tree for the security player. This paper considers complete information game and incomplete information game, for which we theoretically determine the pure strategy Nash equilibrium and the pure strategy Bayesian Nash equilibrium, respectively. Extensive numerical calculations are performed to comprehensively investigate the utilities of each player and the Nash equilibrium for various combinations of the concerned parameters. The results show that the presented theoretical game approach enables a mobile node to adaptively perform specific actions based on the derived Nash equilibrium. With the obtained Nash equilibrium values, both communication player's and security player's utilities reach to the maximum so that satisfactory communication quality can be realized without compromising the security.