To achieve a valid effect of wireless mesh networks against selfish nodes and selfish behaviors in the packets forwarding, an approach named mixed MPSBNS strategy is proposed in this paper. The proposed strategy is based on the Maximum Payoff Strategy (MPS) and the Best Neighbor Strategy (BNS). In this strategy, every node plays a packet forwarding game with its neighbors and records the total payoff of the game. After one round of play, each player chooses the MPS or BNS strategy for certain probabilities and updates the strategy accordingly. In MPS strategy, each node chooses a strategy that will get the maximum payoff according to its neighbor’s strategy. In BNS strategy, each node follows the strategy of its neighbor with the maximum total payoff and then enters the next round of play. The simulation analysis has shown that MPSBNS strategy is able to evolve to the maximum expected level of average payoff with faster speed than the pure BNS strategy, especially in the packets forwarding beginning with a low cooperation level. It is concluded that MPSBNS strategy is effective in fighting against selfishness in different levels and can achieve a preferable performance.
In wireless networks such as ad hoc and mesh networks, the steady operation of the networks must rely on the cooperation for which packets should be forwarded sufficiently between nodes, namely, the routers in networks. However, for the sake of saving battery life for their own communications, some nodes in wireless network do not cooperate to the basic network functioning, making the network lack trust between nodes. These nodes refuse to forward packets by dropping other’s packets and trying to use others to send their own. This noncooperative behavior is named selfish behavior, and these routers are selfish nodes. Users or nodes that want to maximize their own welfare and do not contribute to the network are defined as selfish nodes or free riders [
In the credit approach [
Reputationbased schemes observe the behavior of their neighboring nodes through promiscuous overhearing and accordingly assign them a reputation rating which is used for identifying the selfish nodes. In reputationbased schemes [
For the credit approach and reputation approach, because the system needs a central control requiring an infrastructure, this method cannot be used in the distributed environment. Game theory can easily cope with selfish behaviors and therefore was introduced to the research of selfish nodes related to wireless mesh networks. To adapt with the distributed environment, some detecting methods based on game theory were proposed in recent studies [
A distinct and novel approach named best neighbor strategy (BNS) was proposed to stimulate and enforce cooperation among such selfish nodes in an ad hoc or wireless mesh network environment, where there is no central authority to monitor their unacceptable behaviors [
In our paper, beginning with high cooperation level, BNS is able to provide a superior performance; however, it displays inferior behaviors beginning with low cooperation level, which will be discussed in the simulation sections in this paper. To improve the performance of BNS in low cooperation level, we then combine MPS and BNS to propose a scheme identified as mixed MPSBNS strategy against selfish nodes and selfish behaviors. In this paper, the basic and complete models of mixed MPSBNS strategy are firstly discussed and analyzed, respectively, with two repeated packet forwarding (RPF) games of two player and multiplayer. Then, via the simulation of the RPF games, the performance of the true BNS and the mixed MPSBNS will be compared and discussed on average payoff and cooperation level.
In this section, the restriction of the mixed MPSBNS strategy on selfish behaviors is illustrated by a simple twoplayer game. In the game, neighboring nodes p and −p are playing a repeated packet forwarding game G, which consists of
In MPSBNS strategy, each node has a strategy space
Strategy space.
MPSBNS 
ALLD 


MPS 
BNS 
Drop (D)  
Forward (F)  Drop (D)  Forward (F)  Drop (D) 
Sub strategies.
Player 1  Player 2  

F  D  
F  4, 4  3, 0 
D  0, 3  1, 1 
According to different prime strategies, there exits four states in Markov process as follows.
State (1,1): both player 1 and player 2 have MPSBNS as their prime strategies for the current game.
State (1,2): player 1 has MPSBNS as its prime strategy, and player 2 has ALLD as its primestrategy for the current game.
State (2,1): player 1 has ALLD as its prime strategy for the current game, and player 2 has MPSBNS as its prime strategy.
State (2,2): both player 1 and player 2 have ALLD as their prime strategy for the current game.
The expected payoff for player 1 in state (1,1) is simulated using Table
Payoff matrix of player 1 in the state (1,1).
Player 1  Player 2  

MPSBNS ( 
ALLD ( 

MPS 
BNS 

MPSBNS ( 

MPS 



BNS 



ALLD ( 


Let
Expected average payoff per player against selfishness.
The pure strategy means that every node in network has a uniform strategy profile (Forward or Drop) against all its neighbors. When MPSBNS is implemented as pure strategy, as shown in Table
Uniform strategy profile of MPSBNS as pure strategy.
Probability 








MPS (F or D)  

BNS (F or D) 
Scheme
The game of MPSBNS as pure strategy.
The proposed model MPSBNS is implemented using tool MATLAB. The topology size ranges from 10 × 10 to 100 × 100, and the simulation runs for 100 generations. The simulation results portrayed in Scheme
Average payoffs per player of evolution of MPSBNS as pure strategy.
Instead of having a uniform strategy profile in pure strategy, in mixed strategy, every node in topology maintains a strategy profile with different strategies against neighbors. Scheme
The strategy profile with MPSBNS as mixed strategy.
Probability 








MPS_{1}  MPS_{2} 





BNS_{1}  BNS_{2} 




The level of generosity named niceness representing the proportion of a node beginning with cooperation is introduced, and the performance metrics are explored. Scheme
The game of MPSBNS as mixed strategy.
percentage cooperation =
The evolution of game of MPSBNS is simulated by MATLAB. The game evolves for 100 generations in the 40 × 40 topology. The probability (
The average payoff of evolution of MPSBNS with mixed strategy profile.
The Percentage of cooperation of evolution of MPSBNS with mixed strategy profile.
In this section, the behavior of the topology with the induction of selfish nodes is examined under a mixed strategy profile. In the topology with selfish nodes, a proportion of nodes always behaves noncooperatively and drops packets straightway without choosing MPSBNS in the evolution. Schemes
Average payoff per player of MPSBNS with niceness against selfish nodes.
Level of cooperation of MPSBNS with niceness against selfish nodes.
The paper has proposed a mixed MPSBNS strategy based on game theory against selfish nodes and selfish behaviors in the process of packets forwarding in wireless mesh networks. Through our research, the true BNS is able to provide a superior network performance with high initial cooperation levels but behaves inferior with low initial cooperation levels. To overcome this problem, we combine BNS with MPS strategy, each of which is chosen with respective probability. In MPS strategy, every node selects the strategy which will get the maximum payoff corresponding to the strategies of its neighbors. In BNS strategy, every node follows the strategy of its neighbor having the maximum payoff. A basic MPSBNS strategic game of two players is discussed and is extended to a complicated strategic game involving multiplayer. The simulation and discussions of the proposed strategy as pure strategy and mixed strategy are carried out on performance of average payoff and cooperation level. The results conclude that MPSBNS is able to converge to the expected maximum level with various proportions of the initial percentage of cooperation and converge more rapidly than BNS. The simulation results of MPSBNS against selfishness conclude that MPSBNS behaves superior robustness than BNS defending against selfish nodes. Thus, the proposed MPSBNS strategy is much more effective and efficient in defending against selfishness in wireless networks.
This paper was supported by the National Natural Science Foundation of China (under Grants nos. 61063045 and 61262003), Guangdong Province natural Science Foundation of China (nos. S2011040003481 and S2011010001525), and Guangdong Province Science Technology Plan Foundation of China (nos. 2012B010100027 and 2012B091100161).