Marsh’s Trust Model

Stephen Marsh’s seminal work on trust (Marsh 1994) is founded in the social sciences, from which he extracts real world parameters for evaluating trust from properties inherent in social networks. Marsh extracts trust properties from the disciplines of psychology, philosophy, sociology, game theory, and multi-agent systems, as well as incorporating concepts of risk and utility into his trust formalism to provide a tool for precise trust-based decision-making that is implementable in artificial agents. Marsh sees trust as a means for understanding and adapting to complex environments, such that it can be used as a tool for evaluating prior experience of the behaviour of others. From the literature, then, Marsh delineates a formalism with the following elements. First, agents and situations form the basis of the model. An agent x has knowledge, Kx(y), of another agent y if they have met at some time and

if x can remember the interaction. Knowledge Kx(y) is evaluated as a boolean variable, to either 0 or

1, meaning that an agent either knows another agent or does not. Marsh then provides a typology for trust, breaking trust down into three elements, basic, general, and situational.

Basic trust, Tx, represents the dispositional trust of x and depends on all of the experiences that have

shaped x in the past, and is evaluated over the range [-1, +1), where negative values represent distrust and positive values represent trust, and where blind trust, i.e., Tx = 1, is not acceptable because ‘blind

trust is not trust, as it it does not involve thought and consideration of things’ (Marsh 1994). Basic trust is not a measure an agent has in another agent, situation, or environment, but rather a representation of an agent’s overall beliefs about the world. For example, if x is a seller of goods in an online environment and has only ever experienced interactions with buyers who pay on time and in full, then x may be dispositionally predisposed to believe that the world, i.e. the online selling environment, is a trustworthy place where buyers are to be trusted, and Txwill be high.

General trust, Tx(y), represents the trust that a trust origin, x, has in a trust target, y, irrespective of

situation. This is also evaluated over the range [-1, +1), although Marsh notes that Tx(y) = 0 equates to

unknown trust rather than distrust, i.e., agents x and y have met for the first time and do not have any previous experience of each other to evaluate, or agent x has evaluated y’s actions over time and positive and negative experiences have drawn the general trust measure for y to 0.

Situational trust introduces context into the trust measure, Tx(y, α), which represents the trust that a

trust origin, x, has in a trust target, y, for context, α. Situational trust is also evaluated over the range [-1, +1). Marsh finds situational trust to be most important when an agent is interacting in a situation where it must determine whether or not to cooperate with another agent. It is assumed that in this scenario, an agent will cooperate if situational trust is above a certain threshold. In order to estimate situational trust, x considers the utility of the situation, Ux(α), with values over the interval [-1, +1];

the importance an agent assigns to the situation, Ix(α), with values over the interval [0, 1]; and trust in

agent y based on past experience of interacting with y in all situations, giving

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Tx ,α = x α × x α × x . Note that the concept of importance is similar to the notion of

situational trust in the McKnight and Chervany model, wherein an agent subjectively assesses not only expected utility but also the environmental constraints in place when making a decision. The estimation of general trust, Tx(y), in the situational trust calculation takes into account all data relevant

with respect to situations in which the context, γ, is similar or identical to the current context, α. A method for context-mapping, i.e., determining the similarity of situations, is not provided. Moreover, the representation of distrust and negative utility is problematic, because the multiplication of two negative numbers produces a positive outcome that is counterintuitive.

Marsh defines the notion of cooperation threshold as the optimal threshold of probability that an agent will trust another enough to engage in some action in a certain situation. This threshold varies according to agent disposition, i.e., not all trust origins calculate and exploit trust in the same way, and circumstances, i.e., the perceived utility varies across situations. The cooperation threshold is given as:

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Where perceived_riskx(α) represents the risk of cooperation assessed by the trust target, x, for the

utility of the situation, or trust purpose, α; perceived_competencex(y, α) represents the situational trust

x has in y for α, Tx(y) represents x’s general trust in y; and Ix(α) represents the importance that x

assigns to interacting in the situation. Trust plays a role in the mediation of the cooperation threshold such that very low trust ensures that cooperation is less likely to occur than if trust were high. A temporal index is also employed such that each trust element can be assessed in terms of timeframe. The trust model is implemented in agents to perform simple experiments in a testbed using the Iterated Prisoner’s Dilemma to show that agents correctly mimic human trust-based decision-making behaviour, i.e., cooperate when trust is high and defect when trust is low.

Marsh extracts most aspects of social trust from the real world, i.e., trust as confidence in expected outcome of interacting, agent disposition in forming subjective beliefs, context according to time and environment, evidence in the form of direct observations, evidentiary analysis assessing knowledge, diversity dimensions, trust measurement as probability, risk, and ways in which to form, evolve trust, and exploit trust, and integrates these parameters into a formal model, the implementation of which is shown to use trust to optimise agent systems,. However, critics suggest (Abdul-Rahman and Hailes 1997) the large number of variables in Marsh’s model leads to it being unduly large and complex. Moreover, we have seen that probability is not an appropriate way to represent trust, as uncertainty cannot be captured and multiplication of fractional numbers leads to counterintuitive results. Additionally, the notion of recommending evidence is not taken into account, nor is the concept of role.