A game theoretical model for collaborative protocols in selfish, tariff free, multi hop wireless networks

A GAME THEORETICAL MODEL FOR COLLABORATIVE PROTOCOLS IN SELFISH, TARIFF-FREE, MULTI-HOP WIRELESS NETWORKS BY NG SEE KEE A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE (2005) Acknowledgments I would like to thank my supervisor, Dr Winston K.G Seah, for his assistance in many ways Table of Contents Introduction 1.1 Mobile Ad Hoc Networks 1.1.1 Network Routing 1.1.2 Medium Access Control 1.1.3 Quality of Service Provisioning 1.2 Game Theory 1.2.1 Strategic Games .10 1.2.2 Extensive Games 13 1.3 Our Contributions 15 Wireless Network Availability 19 2.1 Introduction 19 2.2 Incentive-Based Mechanisms 21 2.3 Punishment-Based Mechanisms .24 2.4 Summary 25 Punishments in Repeated Games 27 3.1 Introduction 27 3.2 Finitely Repeated Games 29 3.3 Infinitely Repeated Games 30 3.3.1 Repeated Prisoner's Dilemma 32 3.3.2 Folk Theorems .35 3.3.2.1 Nash folk theorem 36 3.3.2.2 Perfect folk theorem 36 3.4 Session-based Generous Tit-for-Tat (GTFT) 38 3.5 Do ut des strategy 40 3.6 Topology Dependent Analysis 40 3.7 Punishment, parole and rehabilitation 42 3.8 Self-Learning Repeated Game 42 3.9 Summary 44 Private Monitoring 47 4.1 Introduction 47 4.2 Aoyagi's Game for Dynamic Bertrand Oligopoly 48 4.2.1 Game Model 50 4.3 Summary 56 The Wireless Multi-hop Game 58 5.1 Introduction 58 5.2 Modelling Multi-hop Characteristics 61 5.3 Periodic Punishment Approach 65 5.4 Condition for Efficient Collusion 69 5.5 Summary 75 Playing in the Wireless Environment 78 6.1 Introduction 78 6.2 Modelling Private Observations 79 6.3 The Reporting Strategy 82 6.4 Proof of Assumption 1: Correlated Packet Arrival Signal 90 6.5 Proof of Assumption 2: Highest Unanimity at Collusion 93 6.6 Summary 101 The SRRR Protocol Framework 103 7.1 Introduction 103 7.2 Protocol Description .104 7.3 Secrets and Lies 108 7.4 Simulation Results 113 7.5 Summary 119 Conclusion 120 Bibliography 126 Summary Traditional networks are built on the assumption that network entities cooperate based on a mandatory network communication semantic to achieve desirable qualities such as efficiency and scalability With technological maturity and widespread technical know-how, a different set of network problems has emerged - clever users that alter network behavior in a way to benefit themselves at the expense of others The problem would be more pronounced in mobile ad hoc networks (MANET) where network ownership can be shared among different entities Node misbehavior can occur in various degrees At the extreme end, a malicious node may eavesdrop on sensitive data or deliberately inject fabricated, replayed or tampered packets into the network to disrupt network operations The solution is, generally, to enable network encryption and authentication This thesis, on the other hand, focuses on misbehaviors caused by selfish but rational users while keeping in mind the dangers posed by malicious ones In contrast to a malicious node, a rational node acts only to obtain the outcome that he most prefers In such a case, cooperation can still be achievable if the outcome of cooperation is to the best interest of the node MANETs, which are typically made up of wireless, battery-powered devices, will find cooperation hard to maintain because it requires the consumption of scarce resources such as bandwidth, computational power and battery power The objective of this thesis is to apply game theory to achieve collusive networking behavior in the MANET operational environment The scenarios for such behaviour to occur lies in the emerging 4th generation networks where communications over multihop wireless links, across nodes that may subscribe to different providers, are envisaged to occur Research in this area is still in its infancy and existing solutions lack technical feasibility and theoretical consistency These solutions fall into the category of pricing or punishment The pricing solution either requires a tamper-proof counter as a reliable storage of a node's wealth, or an occasional connection to a central authority where payments can be coordinated Punishment methods are often designed based on the well-established Repeated Game model and promiscuous listening may be relied on for the monitoring of other players' actions Promiscuous listening is, nevertheless, unreliable and computationally demanding In addition, the Repeated Game model (perfect and public) fails to account for imperfection in the wireless monitoring device (whether it is public or private) and proposed solutions also overlooked the need for coordinated punishment Most unforgivably, mass punishment of nodes creates a vulnerability for Denial-of-Service (DoS) attacks, threatening even the feasibility of the punishment mechanism as a solution for sustaining cooperation in MANETs The complexity of modeling MANETs and the suitability of available game models poses a significant challenge to the realization of a theoretical model for collusive MANETs protocols In this work, pricing, promiscuous listening and mass punishments are avoided altogether Our model relies on a recent work in the field of Economics on the theory of imperfect private monitoring for the dynamic Bertrand oligopoly, and adapts it to the wireless multi-hop network The model derives conditions for collusive packet forwarding, truthful routing broadcasts and packet acknowledgments under a lossy, wireless, multi-hop environment, thus capturing many important characteristics of the network layer and link layer in one integrated analysis that has not been achieved in previous works We provided a proof of the viability of the model under a theoretical wireless environment Based on the model, we proposed an SRRR protocol for demonstrating the application of our model to protocol design Finally, we proof by simulation that the SRRR protocol is resilient against selfish users under a several deception scenarios Tables Table Prisoners' Dilemma 11 Table Battle of the Sexes 12 Table Strategic form of the extensive game 14 Table Modified Prisoner's Dilemma 30 Table Control Slot Information 106 Table Example Control Slot Information During Bandwidth Reservation 109 Table Cooperative Scenario without Packet Dropping 109 Table Simple Packet Dropping 110 Table Secret Packet Dropping with Acknowledgment Lies 111 Table 10 Secret Packet Dropping with Bandwidth Lies 112 Table 11 Honest Packet Dropping 112 1.210 1.010 1 0.000 normalized punishment rate 0.001 0.002 0.003 1 1 1 0.004 0.005 0.006 0.007 0.008 0.009 0.810 0.610 0.410 0.210 0.010 % bandwidth deviation 0.00010 (no secret packet dropping), 0.00012, 0.00014, 0.00016 and 0.00018 loss rates Figure 11: Downstream Punishment for Secret Packet Dropping with Bandwidth Lies 5.000 normalized punishment rate 4.500 4.000 3.500 3.000 2.500 2.000 1.500 1.000 0.500 1.092879257 1.179566563 1.26006192 1.334365325 0.000 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 % bandwidth deviation 0.0001 loss rate (no secret packet dropping) 0.00012 loss rate 0.00014 loss rate 0.00016 loss rate 0.00018 loss rate Figure 12: Upstream Punishment for Secret Packet Dropping with Bandwidth Lies Finally, we simulated source rate deviations at the traffic generator As the deviations increase, the punishment rates decrease even for selfish nodes, both on the downstream, Figure 13, and the upstream, Figure 14 Hence deviation by the source undermines the ability to enforce punishment and therefore a rational source reveals its required bandwidth truthfully On the other hand, the result also 117 implies that our initial protocol setup phase, whereby no packets is transmitted, will not be subjected to unnecessary punishments 1.2 normalized punishment rate 0.8 0.6 0.4 0.2 0.00000 0.10000 0.20000 0.30000 0.40000 % source deviation 0.00010 (no secret dropping), 0.00012, 0.00014, 0.00016 and 0.00018 loss rates Figure 13: Downstream Punishment for Source Deviations normalized punishment rate 12 10 0.00000 0.10000 0.20000 0.30000 % source deviation 0.00010 loss rate (no secret packet dropping) 0.00012 loss rate 0.00014 loss rate 0.00016 loss rate 0.00018 loss rate Figure 14: Upstream Punishment for Source Deviations 118 0.40000 7.5 Summary This chapter serves to demonstrate the application of the Wireless Multi-hop Game model in protocol design We proposed a Selfish Resilient Resource Reservation (SRRR) protocol but is intentionally left general so that optimization issues can be left for future work It is also not the only solution possible for the Wireless Multi-hop Game model and other approaches are possible We have made several assumptions in SRRR Firstly, we assume a TDMA MAC which will require time synchronization that is hard to achieve in wireless multihop network Nevertheless, research in this area has progressed significantly Secondly, we assumed that the transmission of control information is reliable because the Wireless Multi-hop game model does not account for report losses and corruptions Error correction mechanisms may be used for rectification Thirdly, our model assures truthful QoS sharing within its neighborhood only Truthful relaying of routing information beyond the first hop is not accounted for and hence we need to assume the knowledge of a route before a flow begins To prove that our protocol encourages cooperation, we simulated against a variety of selfish scenarios including secret packet dropping, acknowledgment lies and bandwidth reservation lies, to obtain the resultant punishment rates Our simulation results have shown that truthful nodes are subjected to fewer punishments which makes truthfulness a favorable strategy 119 Conclusion Mobile Ad Hoc Networks (MANET) has made significant progresses throughout years of research efforts However, the utility of such networks still falls mainly in the domain of privately owned networks belonging to the military or governmental organizations When the market matures sufficiently for MANET to be in demand in the public domains, it will be exposed to a new strain of users They are identified as the malicious and the selfish users and their behaviors affect the availability of such networks Each will require a different approach for a solution because they arise from different causes Malicious users create network problems and these malicious activities can be protected mainly with authentication and encryption Selfish users, on the other hand, are users of the network, but are constrained by resources which make them less likely to cooperate They would require incentives or punishments to encourage cooperation and participation in network operations 120 The research presented in this thesis focuses on the selfish users and the search for a sustainable network behavior in such an environment Current MANET protocols rely heavily on mutual cooperation to support multi-hop communication These activities, for example, are the distributed arbitration of shared medium access, link reliability, route sharing and packet forwarding MANET nodes are generally assumed to be wireless nodes that draw power from a battery that has a limited lifetime until the next charge The wireless medium is also a limited resource because nodes need to share transmission time The heavy reliance on cooperation in MANET protocols and the scarcity of node resources to support cooperative functions justify the importance of this research As part of the contribution of this thesis, we provided critical analysis of the current state of development Existing incentive solutions are not practical as they rely on a tamper-proof counter or a temporal connection to a central bank for currency accounting; a tamper-proof counter is expensive and not a fool-proof solution; a connection to a central bank may not be realistic for a distributed network and wireless environment where connectivity is not assured A tariff-free MANET is, nevertheless, extremely attractive to us Preliminary investigations on punishment mechanisms, on the other hand, lack structure and persuasion in their analysis Subsequent works rely on game theory (largely repeated games with public and perfect observations) but lack consistency with the theory itself It is thus questionable whether these solutions will behave as predicted by the game theory they subscribed to Other shortcomings are the dependency on promiscuous listening which is imperfect and overloads the processor, the fragmented analysis of the routing layer (commonly limited only to the packet forwarding function) 121 where deviations at other protocol units remained a threat, and mass, networkwide, uncoordinated punishments which opens a hole for DoS attacks With so many problems, it is therefore questionable as to whether MANETs can offer a solution in a selfish environment at all The lack of a convincing solution is traceable to the lack of a systematic approach rooted to the lack of a suitable game model for the wireless, multi-hop network As the problem is fundamental, we took a distinctly different approach compared to other works In this thesis, we embarked on the mathematical formulation of a game model for MANETs as a foundation for protocol designs Through mathematics, we can provide a more complete and convincing solution as compared to simulation whereby coverage of scenarios is limited Nonetheless, a simulation is also provided for conviction and demonstration purposes Game theory is a relatively new field of mathematics In addition, the theory of imperfect private monitoring in repeated games only started to emerge over the last seven years The theory is exploited in this thesis to model an integrated analysis of transmission losses, buffer overflows, packet acknowledgments, packet forwarding and route sharing, which are all important characteristics of the wireless networks Such modeling was unachievable with earlier game theories that existing works depended on They typically miniaturize the problem by focusing only on either the packet forwarding function of the routing layer or the medium access function of the link layer Specifically, we applied Aoyagi's game of imperfect private monitoring with communication and adapted it to the wireless environment This class of game is extremely complex to analyze because of the heavy dependence on statistical inference 122 Nevertheless, our thesis provides a significant breakthrough by showing that under certain assumptions, punishment is viable, and can be coordinated based on reports generated by nodes along a packet flow path These reports are in fact packet acknowledgments which we have proven to be truthful The model requires the network to establish a commitment on the collusive bandwidth and packet loss probability, which could be a combination of transmission losses and buffer overflows, prior to the transmission of a flow The negotiation of bandwidth and link reliability can be achieved via a resource reservation mechanism The required QoS parameter sharing is also proven to be truthful within one-hop Thus, we can see that our model accounts for many important wireless characteristics such as transmission losses and buffer overflows but also ensures truthfulness in key protocol features such as route sharing, forwarding, and link reliability Our model also has a close resemblance to current MANET protocols implying that it is optimistic for us to expect current protocol designs to support collaborative behavior if small enhancements and modifications are made in accordance to the model Such features are for example the addition of a periodic reporting mechanism and a coordinated punishment scheme In contrast to previous works, we have avoided a large number of pitfalls We relied on punishments instead of a tamper-proof hardware or a connection to a central bank The punishments that we administered are coordinated by reports so that the game has well defined phases of cooperation and punishment Previous works that employ an ad hoc and uncoordinated punishment strategy will fail because punishments and deviations become indistinguishable We not rely on promiscuous listening for observing deviations but instead rely on local 123 measurements of the arriving flows and listening to periodic reports made by neighbors Non-unanimous reports in the neighborhood trigger punishments within a region thus confining DoS attacks Our analysis also integrates a large number of routing and link layer features, thus accounting for complex deviation strategies that are related to the interactions between protocol entities We tested our model in a theoretical wireless environment In this environment, well accepted models of packet generation and packet errors are used We proved by mathematical derivations and analysis that assumptions made in the Wireless Multi-hop Game model are satisfied in this environment We have also derived a collusive reporting threshold thereby making the model realizable In all, we have proven that the Wireless Multi-hop Game model will function in the theoretical wireless environment as predicted by the model Finally, we proposed an SRRR protocol for demonstrating the application of our game model in protocol design It is a resource reservation protocol that is made resilient against selfish users We further simulated the protocol against various scenarios, including secret packet dropping, acknowledgment lies and bandwidth lies, to prove that deviations are unfavorable in a simulation environment There are nevertheless limitations to our model Firstly, synchronized reporting is required although we have relaxed the requirement and applied it to a TDMA system Secondly, reports are to be reliably broadcast – a mechanism that is hard to achieve in wireless networks Thirdly, truthful route sharing is limited to 1-hop neighborhood Finally, the choice of a collaborative packet relay has been left for 124 future study In 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