Quality and stability of conventions

When selecting a strategy, an agent has two sources of relevant information: its own personal experience, and its observations of how other agents act (assuming

observability of interaction choices). We call the formerpersonal preference and

the lattersocial preference. In our conceptual framework, the social preference

is that determined by information gained when fulfilling theobserver role in an

interaction. We denote the strategy selected by agent x’s personal experience

asperx,d,r, and that selected by its social experiencesocx,d,r. These are defined

with respect to a dimensiondand a roler, such that agents can learn a different

strategy for each role and dimension (i.e.socx,d,speaker selects a strategy for an

agentxbased on information received on agents fulfilling thespeakerrole, when

xis fulfilling theobserverrole). In many domains, system designers also expect

agents to engage in some exploration of the strategy space. The process of

strategy selection discussed here relates to selectionafter the agent has decided

not to explore.

Intuition regarding conventions and norms illustrates the distinction between social and personal choice: typically, we imitate others (i.e. choose social prece- dence) on entering a new system, when we have relatively little experience, and subsequently place more weighting on personal preference as we gain more experience.

Ideally, we would like the strategy selected by each choice to be the same, implying that the choice suggested by convention is the best choice for the agent and vice-versa. If this is true for all agents in the convention, then the

convention can be consideredstable, as no agent is likely to act otherwise.

We define an agent’sdissonance as an indication of whether there is a dif-

ference between that agent’s personal and social strategy preferences:

diss(x) =        0 ifper(x) =soc(x) 1 otherwise

We can then define average dissonance over the population: averageDissχ(φ, t) = X x∈χ(φ,t) diss(x) |χ(φ, t)|

An important measure of convention quality is the benefit an agent gains from adhering to it. In the investigation of convention emergence in humans performed by Garrod (1994), an individual gains the most benefit (i.e. any benefit at all) from selecting the strategy most represented in the joint history of the interaction participants. An agent can estimate this by inspecting its own

interaction history. Therelative benefit an agentxgets by selectingσis:

relBen(σ, x) =Px(σ)−histScore(σ, x)

where histScore(σ, x) is the payoff x estimates it will gain based on its own

interaction history andPx(σ) is the actual payoffxattains for selectingσ. Note

that this benefit will change depending on which neighbour the agent interacts with, and that it is not always positive. For example, consider driving on the left or right. As a thought experiment, one can imagine a time when there was no convention on which side to drive. The relative benefit of people adhering to an emerging convention of driving on one side would be large, given the experience of not knowing which side people would drive on. However, once the convention is established, the additional benefit of adhering is low, and we do not notice the additional payoff we get by being part of the convention. Were we to defect, however, and drive on the “wrong side”, we would incur significant negative payoff. If an agent that has a history of mixed choices is situated next to agents adhering strongly to one convention, then the relative benefit of selecting a strategy not defined by the convention is likely to be negative, as

the payoff will be zero but the histScorewill be positive. The relative benefit

therefore encapsulates that conventions aresocialchoices, in that an agent must

with. Finally, we can also definerelBenχ(σ) as the average relative benefit the

agent setχattains by selecting strategyσ.

relBenχ(σ) =

X

x∈χ(φ,t)

relBen(σ, x)

|χ(φ, t)|

While a number of these metrics are not fully computable in practical sce- narios, estimates for each of them can be obtained. Given that the question of whether a convention exists or not, and determining its quality, support or stability, are inherently uncertain processes in the real world, we consider it reasonable to estimate these metrics. Our notion of conventions and related metrics is defined in a formalism within which a wide variety of models of con- vention emergence can be expressed. As such, our metrics can be calculated in these models for detailed analysis of their behaviour. We expect that analysis of such systems using our metrics will reveal additional details about the na- ture of conventions from which novel mechanisms for manipulating convention emergence can be designed.