Computational Models of Trust Thesis submitted in accordance with the requirements of the University of Liverpool for the degree of Doctor in Philosophy by Elisabetta Erriquez March 2012 i To my family Abstract Trust and reputation are key issues in the multi-agent systems domain. As in human societies, software agents must interact with other agents in settings where there is the possibility that they can be exploited. This suggests the need for theoretical and computational models of trust and reputation that can be used by software agents, and accordingly, much research has investigated this issue. The first part of this thesis investigates the conjecture that agents who make decisions in scenarios where trust is important can benefit from the use of a social structure, representing the social relationships that exist between agents. To this end, we present techniques that can be used by agents to initially build and then progressively update such a structure in the light of experience. As the agents in- teract with other agents they gather information about interactions and relationships in order to build the network of agents and to better understand their social environ- ment. We also show empirical evidence that a trust model enhanced with a social structure representation, used to gather additional information to select trustworthy agents for an agent’s interactions, can improve the trust model’s performance. In the second part of this thesis, we concentrate on the context of coalition formation. Coalition stability is a crucial issue. Stability is the motivation of an agent’s refusal to break from the original coalition and form a new one. Lack of trust in some of the coalition members could induce one agent to leave the coali- tion. Therefore we address the current model’s limitation by introducing an abstract framework that allows agents to form distrust-free coalitions. Moreover we present measures to evaluate the trustworthiness of the agent with respect to the whole so- ii ABSTRACT iii ciety or to a particular coalition. We also describe a way to combine the trust and distrust relationships to form coalitions which are still distrust-free. Contents Abstract ii 1 Introduction 1 1.1 Agents and Multi-Agent Systems . .2 1.2 Definition of Trust . .4 1.3 Overview and Main Contribution . .8 1.4 Publications . 10 1.5 Structure of the Thesis . 11 2 Trust 12 2.1 Trust Classification . 12 2.2 Computational Trust and Reputation Models . 15 2.3 Issues of Trust Models . 21 2.4 Testbed . 22 2.5 Trust in Coalition Formation . 26 2.5.1 Related Work in Trust in Coalition Formation . 27 2.5.2 Summary . 28 3 Building and Using Social Structures 29 3.1 Motivation . 29 3.2 Social network analysis . 30 3.3 Building the Social Structure . 32 iv CONTENTS v 3.3.1 Identifying the Social Relationships . 32 3.3.2 Basic Concepts from Graph Theory . 35 3.3.3 Building and Maintaining the Social Structure . 36 4 Evaluation Methodology 43 4.1 Experiments and Analysis . 43 4.2 Results . 49 4.3 Remarks on the Agent ART Testbed . 54 4.4 Summary . 55 5 An ATF for Trust in Coalition Formation 57 5.1 Motivation . 57 5.2 A Framework For Trust . Based On Distrust . 59 5.2.1 Coalitions with Trust . 61 5.2.2 Weak and Strong Trust . 66 5.3 Personal Extensions . 68 5.4 Aggregate Trust Measures . 74 5.4.1 Distrust Degree . 75 5.4.2 Summary . 76 5.4.3 Expected Trustworthiness . 77 5.4.4 Coalition Expected Trustworthiness . 78 5.5 Summary . 80 6 An ATF for Trust and Distrust 81 6.1 Motivation . 81 6.2 A Framework for trust and distrust: A Formal Definition . 82 6.3 Coalitions based on Trust . 85 6.3.1 Trust and Transitivity . 85 6.3.2 T-Coalitions (Trust-Coalitions) . 86 6.4 Trust-induced Inference Rules . 88 6.5 Trends in Maximal Trusted Extensions . 90 6.6 Summary . 94 CONTENTS vi 7 A Formal Analysis of Trust and Distrust 103 7.1 ACT 1 Synopsis . 105 7.2 ACT 1 Analysis . 106 7.3 ACT 2 Synopsis . 109 7.4 ACT 2 Analysis . 111 7.5 ACT 3 Synopsis . 113 7.6 ACT 4 Synopsis . 114 7.7 ACT 3 and 4 Analysis . 115 7.8 ACT 5 Synopsis . 116 7.9 ACT 5 Analysis . 118 7.10 Summary . 119 8 Conclusions and Future Work 120 8.1 Conclusions . 120 8.1.1 Building and Using Social Structures . 120 8.1.2 A Framework for Trust and Distrust . 121 8.2 Future Work . 122 8.2.1 Building and Using Social Structures . 122 8.2.2 A Framework for Trust and Distrust . 124 List of Figures 2.1 Game overview in the Agent ART Testbed from [33] . 23 3.1 Cutpoints: e, x and y . 41 3.2 Central point: l . 41 4.1 Percentage of Fulfilled Interaction for all configurations for Sim- plet and SocialSimplet. 49 4.2 Percentage of Fulfilled Interaction for all configurations for Con- nected and SocialConnected. 50 4.3 Percentage of Total Interaction for all configurations for Simplet and SocialSimplet. 50 4.4 Percentage of Total Interaction for all configurations for Connected and SocialConnected . 51 4.5 Percentage of Games Won for all configurations for Simplet and SocialSimplet. 51 4.6 Percentage of Games Won for all configurations for Connected and SocialConnected. 52 4.7 Percentage of Total Utility for all configurations for Simplet and SocialSimplet. 53 4.8 Percentage of Total Utility for all configurations for Connected and SocialConnected. 53 vii LIST OF FIGURES viii 5.1 Three simple ATFs ......................... 62 5.2 Three ATFs for four agents . 62 5.3 Two ATFs for four agents . 63 5.4 A more complex ATF ........................ 65 5.5 An ATF for weakly and strongly trusted agents . 67 5.6 S11, an ATF for Personal Extension . 69 5.7 An algorithm for generating UPE(S;a)............... 72 6.1 S12, an example of ATDF for three agents . 84 6.2 S13, an example of ATDF for four agents . 84 6.3 An example of T-Coalitions for an ATDFs ............. 87 6.4 An example for the application of the inference rule. Step 0 . 89 6.5 An example for the application of the inference rule. Step 1 . 89 6.6 An example for the application of the inference rule. Step 2 . 96 6.7 An example for the application of the inference rule. Step 3 . 96 6.8 An example of changes in Maximal Trusted Extensions in a society of three agents with increasing number of distrust relationships. Step 1 to 3 . 97 6.9 An example of changes in Maximal Trusted Extensions in a society of three agents with increasing number of distrust relationships. Step 4 to 7 . 98 6.10 Chart showing how the number of Maximal Trusted Extensions changes with the increase of Distrust Relationships, for different society sizes . 99 6.11 Chart showing how the number of Maximal Trusted Extensions changes with the increase of Distrust Relationships, for selected society sizes . 100 6.12 Chart showing how the average size of Maximal Trusted Exten- sions changes with the increase of Distrust Relationships, for dif- ferent society sizes . 101 LIST OF FIGURES ix 6.13 Chart showing how the average size of the Maximal Trusted Ex- tensions changes with the increase of Distrust Relationships, for selected society sizes . 102 7.1 ATF for Act 1 . 107 7.2 ATDF for Act 1 . 107 7.3 ATF for Act 2 . 111 7.4 ATDF for Act 2 . 111 7.5 ATF for Act 2 after applying the inference rule . 112 7.6 ATDF for Act 2 after applying the inference rule . 112 7.7 ATF for Act 3 and 4 . 116 7.8 ATDF for Act 3 and 4 . 116 7.9 ATF for Act 5 . 118 7.10 ATDF for Act 5 . 118 7.11 ATF for Act 5 after applying the inference rule . 119 7.12 ATDF for Act 5 after applying the inference rule . 119 List of Tables 4.1 Configurations settings for the evaluation: Top section contains set- tings for the Agent ART testbed and the bottom section contains the settings concerning the social structure of SocialSimplet. Dark grey cells contain parameters changed for that configuration. 47 5.1 Table showing the values of mi to calculate the Coalition Expected Trustworthiness with regard to example S4 in Figure 5.2 . 78 6.1 Table showing the values of mi to calculate the Coalition Expected Trustworthiness with regard to the example in Figure 6.4 for Step 0 and Figure 6.7 for Step 3 . 91 6.2 Table showing changes in Mtes for ATF in Figure 6.8 and Figure 6.9 92 7.1 Table showing the Maximal Trusted Extensions and the T-Coalitions in the Othello’s society S for each Act . 106 7.2 Table showing the Unique Personal Extensions of Othello and Iago in the society S for each Act . 108 7.3 Table showing the values of mi, Expected Trustworthiness, and the ei(S), Coalition Expected Trustworthiness, with regard to the Oth- ello’s society S for each Act . 108 x LIST OF TABLES xi 7.4 Table showing the Maximal Trusted Extensions and the T-Coalitions in the Othello’s society S for each Act after applying the Inference Rule . 109 7.5 Table showing the Unique Personal Extensions of Othello and Iago in the Othello’s society S for each Act after applying the Inference Rule . ..