無線多跳網路技術包含Wireless Mesh Networks, Mobile Adhoc Networks, Wireless Sensor Networks等，可以應用在軍事、救難或商用等方面。由於具有低成本，架設容易的特性，近來年吸引了眾多研究者的關注。在無線多跳網路中，需要其他節點協助轉傳封包，才能成功到達目的點。因此節點間的合作是一項很重要的要求。為了促使節點間的合作，本論文根據賽局理論提出了兩個機制。第一個是激勵機制，我們設計了一個獲利矩陣(payoff matrix)的利益分配方法。有別於傳統研究使用囚徒困境的模式，我們則使用更接近實務的鹿兔賽局的模式。我們的方法可使協助轉傳封包越多的節點，獲得越多的利益，也利用了補償閒置時間(idle time)的方法，讓邊界的節點也能獲得合理的收入，以保障邊界節點的存在。由於鹿兔賽局有全部合作及全部不合作兩個均衡點，因此我們提出一個互動策略，稱為適應性的合作者(Adaptive-Cooperator)，來促使節點趨向全部合作。這個策略是一個主動的合作者，但是也會針對不合作的節點進行反制及懲罰，使不合作節點無法經由搭便車(free-rider)獲得利益。接著我們以賽局及進化賽局理論來分析這兩個方法的正確性及優越性，並經由模擬的結果，證明我們提出的方法是有效的。把我們的方法應用到無線多跳網路上，將使所有無線節點採取合作策略，且獲得公平及合理利潤，提升無線多跳網路的應用。

Due to the low cost, easy deployment, wireless multi-hop networks have attracted many researchers’ attention in recent years. In wireless multi-hop network, the nodes are willing to forward packets for other nodes, so as to packets can successfully reach the destination. Therefore, cooperation between nodes is a critical factor in multi-hop networks. In order to encourage nodes to cooperate in networks, two approaches that refer to game theory are proposed. The first approach is incentive mechanism for packet forwarding. We design a Stag Hunt payoff matrix that is different to traditional Prisoner’s Dilemma model. Our model stimulates nodes to forward more packets to get more profits. It also compensates idle time to increase boarder nodes’ gains to guarantees the existence of boarder nodes. The second approach is an interactive strategy, which is called as Adaptive-Cooperator to refine the two equilibrium points of the Stag Hunt game. This strategy is an active cooperator; however, it may as well punish uncooperative nodes, making them impossible to obtain gains by free-rider. Then, we make some analyses by game and evolutionary game theory to deduct the correctness of our approach. According to the simulation result, the approaches we proposed are proved effective. To apply our model to wireless multi-hop network, all nodes can tend to cooperate and get fair treatment.

Chapter 1 Introduction 1
1.1 The application of wireless multi-hop networks 2
1.2 Motivation 7
1.3 Research objective 14
1.4 Contribution and organization 15
Chapter 2 Related work 17
2.1 The schemes for enforcing cooperation 17
2.1.1 Reputation-based Scheme 17
2.1.2 Credit- exchange-based Scheme 22
2.1.3 Game theory-based Scheme 25
2.2 Introduction to game theory 29
2.2.1 History of game theory 30
2.2.2 Overview of game theory 33
2.2.3 Nash equilibrium 36
2.2.4 Prisoner’s Dilemma 38
2.2.5 One-stage packet forwarding game 40
2.2.6 Repeated game 42
2.2.7 Strategies Descriptions 43
2.2.8 Cooperative game 50
2.2.9 Evolutionary Game Theory (EGT) 52
Chapter 3 Incentive mechanism using game theory 55
3.1 Problems of the existing solution 55
3.2 Incentive-based Approach for multi-hop wireless networks 59
3.2.1 System model 60
3.2.2 Design concept 61
3.2.3 Game model 63
3.2.4 Incentive mechanism for packet forwarding 64
3.2.5 Interacting strategy 67
3.2.6 Strategy Discussion 71
3.3 Investigate our model with game theory 74
3.3.1 One-stage game and repeated game for our model 74
3.3.2 Why use evolutionary game theory 76
3.3.3 Use ESS to analyze our model 78
3.3.4 Use replicator dynamics to analyze our model 81
Chapter 4 Simulation and discussion 86
4.1 Strategy simulation 86
4.2 Numerical evaluation 94
4.3 Discussion 101
Chapter 5 Conclusion 104
Appendix A Estate distribution from Talmud 106
References 109

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