Conventions are generally thought of as socially accepted expectations of be-
haviour, and represent an aggregation of a population’s choices in its individual
interactions. System designers are typically concerned with reducing the cost associated with malcoordination between agents, and conventions are a useful abstraction for analysing the behaviour of large numbers of agents, to support this aim.
There have been a wide variety of definitions proposed in the literature.
Lewis (1969) defines a convention as a regularity in the behaviour of a popu-
lation in repeated iterations in the same situation, subject to constraints such as the proportion of agents that conform to the regularity and the proportion of agents that expect others to conform. Goyal (1997) describes conventions as an arbitrary solution to a social problem, wherein individuals only conform because they expect others to conform. Shoham and Tennenholtz (1997) ap- proach conventions from a game-theoretic perspective, defining a convention as a restriction of agents’ decisions to a single choice in a given coordination game. Kittock (1993) considers a convention to exist when a high proportion of agents use the same given strategy.
4.2.1
The role of expectations
Uniting these definitions is the theme of mutual expectation in repeated itera- tions in similar situations: agents make choices based on the expected choices of others. As such, conventions are primarily necessary where agents’ decisions
involveexternalities, in which the individual’s choice (and utility) depends par-
tially or wholly on the choice of others, and vice-versa (Schelling, 1973). In such systems, conventions provide a mechanism for (i) generating a set of mu- tual expectations that resolve coordination problems, and (ii) influencing agent strategy selection towards mutually and societally beneficial outcomes.
Consider the El Farol bar problem (Arthur, 1994; De Caraet al., 1999), in
which agents must decide on which day of the week to visit a bar. Each agent desires the number of other individuals present to be within a certain range, such that the bar is not too empty or too busy. There is no salient difference between any of the days, and an agent’s decision is based purely on its expectation of what others will do. However, their decisions are in turn also based on such expectations. This loop of mutual expectations leads to infinite regress without resolution if there are no external factors to break it. Lewis (1969) called these
expectations nthorder expectations, such that “I expect that you expect me to
dox” is a second-order expectation.
Lewis (1969), and many subsequent works on convention emergence (e.g. Young (1993), Garrod (1994), and Boyer & Orlean (1992)), identify two prin- cipal mechanisms by which higher order expectations can be generated and
subsequently resolved: salience andprecedence.
• Salience is some feature of a potential choice that marks it out as more
likely to be chosen by others. Lewis (1969) notes that this may not be an advantageous feature, but merely marked out as noticeable by some property.
• Precedence is a special form of salience: the choice is more expected be-
as the primary driver behind the emergence of conventions, through “grad- ual accretion”.
Schelling (1973) was among the first to argue that either salience or prece- dence is necessary to break the infinite loop resulting from reasoning on higher- order expectations. Boyer and Orlean (1992) take this further, arguing that coordination problems cannot be solved using purely individual rationality, due
to this regress. Shoham and Tennenholtz (1997) discuss the concept ofsocially
rational choices, which embody the idea of an optimal choice for the society.
Such a choice might manifest as the highest expected aggregate utility, or some
other notion of best for the society, which may or may not be consistent with
individual rationality. Conventions are a way of facilitating socially-rational de- cisions when agents are given a set of choices that are otherwise indistinguishable (and thus not amenable to decisions based on individual rationality).
Lewis (1969), Garrod (1994), and Boyer and Orlean (1992) all argue that conventions are self-reinforcing. Once a set of mutual expectations is created, subsequent choices based on those expectations serve to increase their strength. Lewis (1969) uses the analogy of a fire: “under favorable conditions, a sufficient concentration of heat spreads and perpetuates itself”. Existing research into convention emergence has thus focused on two main questions: (i) what con- ditions are favourable for convention emergence, and (ii) how can an emerging convention become established throughout a population?
The above discussions indicate limitations in existing definitions of conven- tions, in that (i) they assume near-universal conformity is either an ideal or attainable goal, disregarding situations in which we desire or can only attain multiple (or partially adopted) conventions (i.e. Section 4.2 and typically held definitions of conventions), (ii) they provide no way to quantify the desirabil- ity of conventions (i.e. whether agents or designers prefer one convention over another) or their potential for establishment (Section 4.2, and the lack of quan- tifiable metrics in works discussed), and (iii) they provide no way to fully de- scribe the evolution of a convention from uncoordinated individual choices to
the emergence of an aggregate consensus (Section 4.2.1: the majority of work examines the processes of initial emergence), which is an important step towards developing effective mechanisms for managing conventions.
4.2.2
The convention life cycle
A complete theory of conventions must account for the evolution of a conven- tion from a set of uncoordinated behaviours between interacting agents to the establishment of regular, expected choices. There have been a number of efforts investigating the mechanisms through which this occurs, but limited attempts to unify the results into a single cohesive framework. Hollander and Wu (2011) provide an overview of norms-related literature (norms being a form of con- vention in which adherence is motivated through sanctions or incentives), and outline a norm life cycle containing several processes: creation, transmission, recognition, enforcement, acceptance, modification, internalisation, emergence, forgetting, and evolution. Their view of the life cycle is focused on the agent perspective, while we consider the convention life cycle from the perspective of a convention as an entity in itself. Strictly speaking, in this thesis we focus on the
emergencephase in the characterisation presented by Hollander and Wu (2011),
and we do not discuss agent specific processes such as internalisation, forgetting, or the representation of conventions or norms.
At the beginning of the convention life cycle, salience or precedence causes a given strategy or choice to be selected with greater regularity than others. The expected utility of a strategy is a form of salience, since choices with a higher expected utility are more likely to be selected than those with lesser utility. Assuming that agents have different interaction partners over time, the mutual expectations that arise from salience and precedence will spread. At some point such a strategy is considered a convention, and typically system designers hope that it will spread throughout the population.
Research into how salience and precedence contribute to convention emer- gence has seen significant attention (e.g. Lewis (1969), Sen & Airiau (2007), Vil-
latoroet al.(2009a)), but there has been little research on the process by which a convention grows or dissipates once a system of mutual expectation emerges, or on how it might become established across a whole population. Much work in the area adopts the convention definition proposed by Kittock (1993), in which a convention exists when a proportion of the population (typically 90–100%) adheres to it a proportion of the time (again, typically considered to be 90– 100%). However, this offers little insight into the middle and latter stages of the convention life cycle, and is insufficient for domains in which such high levels of adherence to a single convention are either undesirable or unattainable.
We identify three possible states that a convention can attain: (i) estab-
lishment as dominant convention, (ii) co-existence with other conventions, or
(iii)destabilisation and dissipation. The typical definitions, such as that of Kit-
tock (1993), are concerned purely with establishment, and do not consider the conditions under which co-existence and destabilisation might occur (or whether they are desirable or not). We therefore consider the convention life cycle as only partially understood: the forces of precedence and salience that generate the initial set of mutual expectations that eventually form a convention are well documented (Lewis, 1969; Vylder, 2007; Young, 1993; Young, 1996), but the middle and latter stages of convention emergence have seen only limited research (notable examples include Villatoro (2011), Hollander & Wu (2011), and Boyer and Orlean (1992)). Moreover, the typically adopted definitions and models of conventions do not account for more than one convention existing in
a population (with some exceptions, such as De Cara et al. (1999) and Villa-
toro (2011)), and do not support quantitative analysis of a convention’s quality, support or stability. In the next section, we review the major research contri- butions relating to conventions, and describe how they fit within the convention life cycle.