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Unit 9

Game Theory

9.7 Language

THE NAME GAME

Human language seems to be a large part of what makes us unique beings. We said in the introduction to this unit that game theory can be thought of as the mathematical study of human interactions. Language is arguably the most fundamental of these interactions. It is, in fact, hard to imagine interactions without language in the first place. Yet, how does a group of people agree on which words to use for particular objects? How is this set of agreements passed along to offspring? In 1999, in a paper written by Nowak, Plotkin, and Krakauer at the Princeton Institute for Advanced Study, principles of game theory were used to illuminate how language can develop.

Imagine a group of human ancestors, a troop of hominids, if you like. Suppose that this group is just starting to communicate about specific objects in their environment. Perhaps they have become concerned with communicating specific threats or other important information more efficiently-knowing the location of a hungry leopard or of a grove of fruit-laden trees is often critical to survival. Each individual in the group develops an internal list of verbal signals, or words, that are associated with objects such as leopards or fruit trees.

In order for communication to take place, a speaker makes an association between an object and a word. A listener either has the same association or they do not. Suppose that the speaker, upon seeing a leopard, says "leopard" to the listener. If the listener has the same association, then they will think "leopard" and act accordingly. If the listener does not have the same association, then they will not understand, and there could be some negative consequence.

This implies that if the speaker and the listener have the same association, then there is some sort of payoff for both of them. That payoff could be that the listener avoids danger, or perhaps learns the location of some food. The payoff for the speaker will be the same, if we imagine that both individuals use the same word in the future. In this discussion, we will assume that, as with the Hawks and Doves game, this language game is played more than once.

When the speaker wishes to alert the listener to the presence of the leopard, there is a certain probability that the speaker will use a given word. Likewise, there is a certain probability that the listener will associate the speaker's word with the concept "leopard." The maximum payoff for these two will increase as the probability that each player uses the same word for "leopard" increases. Payoffs also increase as more players adopt the same vocabulary and associations. With this kind of payoff structure in place, there is an incentive for players to understand each other, which can lead, over time, to the development of a common language.

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PASS IT ON

Long-term development of language requires agreed-upon, object-signal associations to be passed down to new generations of speakers and listeners. How is this language transmitted to new generations?

Nowak, Plotkin, and Krakauer identified three main methods of language transmission. The first, and perhaps most intuitive, is parental transmission. Children tend to acquire the language of their parents and in this mode of transmission, greater language "fitness" (average payoff of one's list of associated signals and objects) would correlate with greater biological "fitness." In other words, the successful use of language can affect one's chances of passing on genes successfully to the next generation.

The second mode of transmission was identified to be through a role model outside of the family. In this mode, a high-status member of the group gains many young imitators. High-ranking role models illustrate the connection between language and status. So, if a child imitates the language profile of a high-status individual, that child will, on average, out-compete the children who do not imitate high-status individuals.

The final mode of transmission is simply random learning. In this scenario, there are no clear incentives for learning language from any particular individual; instead, children imitate a random mixture of adults without regard to status or payoff. This tends to maximize confusion and, thus, minimize the payoffs that can accrue from mutual understanding. Groups who transmit language via this method tend to take a significantly greater amount of time to develop a common language, as opposed to groups that use the other two transmission methods.

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