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The Interaction of Two Signaling Systems: A Game Theoretic AnalysisImagine two distinct language communities. They each have a unique language that every member of the community uses and the two groups have never interacted. Then one day, through immigration and integration, the two groups mix. Now members of one language community are interacting with members of the other language community. The following question arises: what is the resulting language when these two previously distinct language communities interact? This question can be broken down in the following ways.
First, how similar is the resulting language to the previous two languages? Second, how efficient is the resulting language; that is, how often do language users appropriately represent states of the world? Third, how quickly do the language users assimilate to their new language? Finally, how do the answers to these questions differ in cases of normal (2x2x2, two states, two signals, and two acts), synonymous (2x5x2, two states, five signals, and two acts), and ambiguous (3x2x3, three states, two signals, and three acts) communication?
These are interesting questions because thusfar they have not been addressed in the literature. While much has been done on signaling games both theoretically and experimentally, no one has tested what happens when two signaling systems interact. This scenario seems more closely related to real world communication because it is quite rare for language communities to exist independently from any interaction with other language communities. Thus, I believe this is a promising avenue for the future of research in signaling games.
This scenario applies to two real world cases. First, imagine the situation of the emergence of Spanglish. This is a case in which two similar languages (in that they share similar language histories, structures, and vocabularies) form a new language. If this were to be modeled, it would be a case in which two similar signaling systems form a new signaling system which resembles the two previous signaling systems. This scenario is covered by the model.
Second, imagine the situation in which a remote indigenous language comes to interact with a distinct language such as English. In this case, there are two unique, distinct languages (in that they do not share language histories, structures, and vocabularies) and they come to form an entirely new language. This would be modeled as two unidentical signaling systems combining to form a signaling system that does not resemble the previous two. Again, this situation is covered by the model in this paper.
Via computer simulation in Java, the following results were obtained. First, the average efficiencies for the normal and synonymous communication were similar and faster than the case of ambiguous communication. Second, the cases of negative reinforcement with noise tend to be slower than the other dynamics. Third, the ambiguous case tends to be slower than the normal and synonymous cases. Fourth, there is no apparent pattern in strategies selected and dynamics. Fifth, when there is only positive reinforcement, the languages do not change post-combination. When negative reinforcement is introduced, some change occurs.
University of Wisconsin-Madison