2.4 Games
2.4.2 Other Games
A number of other games have been explored within the notion of convention emergence that do not conform to the traditional definition of a coordination game as proposed by Lewis [1969] and Schelling [1980].
The El Farol Bar problem is an example of acongestion problem where the payoff that the agent receives for a particular choice is related to the number of other agents choosing the same. The problem as originally formulated by Arthur [1994] is that of attending a popular bar on a given night or staying home. If the bar is not too crowded (60% of its capacity) the player enjoys themselves more than if they had stayed at home. If the baristoo crowded the player does not enjoy themselves and would have been better off remaining at home. It is impossible to definitively say ahead of time how many others will be attending the bar on the same night, all players decide whether to attend or not at the same time. As such players must rely on their expectations (and
higher order meta-expectations [Lewis, 1969]) on the behaviour of others in order to deduce whether to attend or not. The optimal outcome to the El Farol Bar problem is one of several conventions existing simultaneously with subsets of agents (of size below the crowdedness threshold) each electing to attend on different days. Systems naturally emerging this outcome have been shown to be unlikely however. Cara et al. [1999] show that most initial conditions tend to the case where agents have failed to coordinate the optimal behaviour amongst themselves and instead perform no better than at random. Whitehead [2008] model the El Farol Bar problem using a reinforcement learning model. They find that the agents generally minimise their bad experiences and maximise the good ones when learning in this manner but show that the resultant behaviour of this is a partitioning of the agents into two distinct sets of those who always attend and those who never attend rather than the mutually beneficial solution of attending on disparate days. In this regard both show that the El Farol Bar problem is another type of game that would benefit from external cooperation or coordination.
The language coordination game (or naming game [Steels, 1998]) represents the emergence of a communicative capability between agents using conventions and norms. Each agent has a set of words and a set of concepts and an inter- nal mapping between them. They attempt to communicate concepts to other agents using the words they map to them and are rewarded if the other agent correctly understands their communication. In this regard it is similar to the pure coordination game; if agents both have the same mapping they are re- warded positively, if they differ they are rewarded negatively and in both cases the agent is able to learn from the interaction. The difference lies in the fact that the interaction only uses a small part of the lexicon (the mapping) that the agent has, individual parts of the lexicon are updated and changed rather than the whole action choice. This changes the underlying dynamic and means that multiple conventions are more likely as multiple different lexicons are present within the system. Additionally, it introduces the concept of the quality of a
convention, with better mappings being better quality (the case of mapping each word to a single concept would make communication easier but be a poor quality lexicon for instance). The game also allows for much larger numbers of possible conventions than in other versions of the coordination game (WC where W and C are the numbers of words and concepts respectively). Never- theless, widespread convention adoption is possible. Salazar et al. [2010] utilise a spreading mechanism to transfer partial information and show that this can be used to encourage rapid convention emergence which produces high-quality conventions regardless of noise in the system. Whilst this differs substantially from the convention emergence approaches in other work it shows that encour- aging conventions can happen even in large convention spaces with minimal adjustments. Lakkaraju & Gasser [2008] similarly show that convergence can be encouraged by using additional information to predict others lexicons. They utilise an additional “Text Observation Game” where agents are able to hear sentences formed using other’s lexicons and use various metrics to predict the lexicon. However, both of these approaches require modifications to the agents to allow them to perform these additional tasks. Franks et al. [2013] instead take a different approach and instead insert agents with high-quality lexicons into the system to encourage emergence to them. They show that a relatively small number of these placed at influential locations can facilitate convention emergence to the desired convention.
Both of these games offer a distinct and differing view at convention emer- gence than that found from the pure coordination game. Whether the findings of this thesis are applicable in these disparate cases is something we discuss in Chapter 6.