In this section, we present background information and discussion relating to trust and reputation in general, image scoring, our adopted model of reputation, and gossiping.
3.2.1
Trust and reputation
Trust and reputation is an area that has seen significant research interest. As discussed in Chapter 2, we adopt the definition of trust as “a belief an agent
has that the other party will do what it says it will (being honest and reliable) or reciprocate (being reciprocative for the common good of both), given an
opportunity to defect to get higher payoff” (Ramchurn et al., 2005). Other
definitions are also commonly used, the most notable of which defines trust as
the probability that an agent will fulfil its obligations (Teacyet al., 2012). The
incorporation of probability into the definition of trust has allowed mechanism designers to incorporate a range of statistical tools, such as Hidden Markov
Models (Vogiatziset al., 2010) or Bayesian Networks (Reganet al., 2006; Teacy
et al., 2012).
The latter definition has become dominant over recent years, and trust and reputation models have been designed that provide robust assessments in a wide
variety of situations. Notably, HABIT (Teacyet al., 2012) and BLADE (Regan
et al., 2006) can be used independent of the representation of behaviour that
agents use. These models differ from the image scoring model adopted in this chapter in that they generate an assessment of the probability that an agent will fulfil their obligations (i.e. they adopt the second definition), whereas im- age scoring simply provides an indication of how selfish or cooperative a given potential interaction partner is (i.e. we adopt the former definition).
These systems are also robust to inaccurate or malicious assessments, since the statistical methods employed take into account the uncertainty of infor- mation regarding potential interaction partners. The robustness of trust and reputation systems to inaccurate assessments is a key concern (Josang, 2012), and the model of reputation that we adopt (namely, image scoring) does not incorporate any mechanisms to mitigate this effect. However, dealing with in- accurate assessments in this way does not increase the accuracy of assessments, but rather allows agents to identify and mitigate inaccuracies. The gossiping algorithm we propose as a mechanism to deal with inaccurate reputation assess- ments, on the other hand, increases the certainty and accuracy of assessments in the first place, before statistical measures would be needed.
Chapter 2, are typically highly complex. Teacyet al.(2012) discuss the trade-off between accuracy and necessary time or computational resources. Their pro- posed model, HABIT, can scale depending on requirements and can be specified to individual domains. However, there remain constraints on the computational requirements of their model and the image scoring and gossiping mechanisms investigated in this chapter have far reduced computational and temporal com- plexities.
There are, to our knowledge, very few systems that have combined trust and reputation with gossiping mechanisms to increase the accuracy of assessments. Perhaps the closest to the work presented in this chapter is that of GossipTrust, introduced by Zhou and Hwang (2007). In GossipTrust, agents repeatedly gos- sip reputation values. The authors propose formal constraints on the accuracy of reputation assessments, and agents gossip until a given assessment has con- verged. Furthermore, all agents gossip, as opposed to the gossip mechanism proposed in this chapter, in which only observers to an interaction gossip. As a result, GossipTrust requires significant communications overheads compared to the system we investigate here. All nodes must reach consensus in Gossip- Trust, and while this is clearly good for guaranteeing robustness to incomplete information, our results with gossiping (Section 3.5.5) suggest that this is not necessary to gain significant improvements in mechanism efficacy. Finally, the authors do not test the effects of different aggregation rules for gossiping infor- mation, and only present results from one network. In this chapter, we propose and evaluate a number of aggregation rules for gossips and present results from a wide variety of network classes.
3.2.2
Image scoring
While many reputation mechanisms have been proposed, they rarely address fully the challenges posed by decentralised MAS domains. To investigate the challenges posed by incomplete information and the effect of underlying network structure, we require an implementation of reputation with low computational
and bandwidth overheads.
Nowak and Sigmund introduced and extensively investigatedimage scoring,
a simple instantiation of reputation modelling indirect reciprocity, in which co- operation emerges without requiring subsequent interactions between the same individuals (Nowak & Sigmund, 1998; Nowak & Sigmund, 2005). This property is key to its suitability in open decentralised systems. Each agent maintains an image score for each individual it interacts with or observes interacting. Co- operative actions increase the image score by one, and selfish actions decrease it by one. When deciding whether to cooperate or not, an agent compares its strategy, an integer, with the perceived image score of the potential partner (if no data is available, it is assumed to be zero). If the strategy is less than or equal
to the image score, the agent cooperates. A population of nagents participate
inminteractions each round, and the best performing strategies are reproduced
using a genetic algorithm to provide the strategy set for the subsequent round. More detail of the model is given in Section 3.3.
Nowak and Sigmund found that cooperation emerges, but is often cyclical as non-cooperative agents invade populations of unconditionally cooperative agents and gain higher payoffs, causing the population to be subsequently dominated by conditionally cooperative agents, who are in turn superseded by uncondi- tionally cooperative agents. Agents in the setup used by Nowak and Sigmund are randomly chosen and paired from the entire population for interactions,
with the total number of interactions per round (m) being at most one order of
magnitude larger than the number of agents in the population (n).
While image scoring is effective at supporting cooperation, we can identify situations in which it might be undermined by agents having incomplete or in- sufficient information regarding potential interaction partners. Firstly, if there are a large number of interactions per round compared to the number of agents
(i.e. a high ratio of m/n), agents may have only observed a proportion of the
interaction history of a potential interaction partner. If the observed subset of interactions is unrepresentative, this may result in a decision that the agent
would not have taken given complete information. Similarly, if there are rel-
atively few interactions (i.e. a low ratio ofm/n), or agents have only recently
entered a system, then agents may have insufficient information with which to make accurate decisions. In this chapter, we evaluate the extent to which these hypotheses are correct (i.e. that both low and high numbers of interactions cause increases in selfishness due to incomplete or insufficient information), and propose gossiping as a mitigating solution.
We note that an image score is not directly equivalent to reputation. Typical
definitions of trust incorporate the notion that a trust value is the probability
that an agent will fulfil its obligations (Teacy et al., 2012), and reputation is
typically defined as a socially-accepted trust value. An image score does not represent the socially-accepted probability that an agent will fulfil its obliga- tions, but instead is a value that indicates, approximately, how cooperative or selfish an agent has been in the past. As such, image scores can be seen as a proxy for reputation.
3.2.3
Gossiping
Gossiping algorithms, initially introduced by Frieze and Grimmet (1985), per- form data aggregation and spreading in distributed systems. Loosely modelled on the dynamics of human gossip, they are effective at spreading information through networks and have low space and time complexity and minimal band- width requirements when compared to traditional spreading mechanisms (Fer- nandess & Malkhi, 2007; Kempe & Kleinberg, 2003). They have previously
been applied to constrained trust and reputation problems (Bachrach et al.,
2008; Ramchurn et al., 2004; Zhou & Hwang, 2007), and can efficiently aggre-
gate trust values without the need for complex data structures.
Typically, gossiping algorithms involve individual agents selecting a single partner and communicating a piece of information regarding a single topic or an individual (in our usage, an individual’s image score). Agents therefore receive
an aggregation rule to incorporate this information into their knowledgebase. A wide variety of implementations of gossiping have been proposed, and we describe our instantiation in Section 3.3.5.
Gossiping is an attractive solution to the problems inherent in local percep-
tion of information by agents. Sommerfeldet al.(2007) have extensively investi-
gated gossiping in humans and show that gossiping of information is an effective
substitute for direct observation. Sommerfeld et al.’s subsequent work (2008)
demonstrates that gossip is robust to propagation of inaccurate information, and concludes that humans use a majority rule: if the majority of gossips are positive, then the individual forms a positive opinion of the subject. The low overheads, high robustness when exposed to inaccurate information, and ability efficiently to spread and aggregate information in decentralised domains make gossiping highly applicable to our model.