Wednesday, April 3, 2013

Johan van Benthem: "Games that make sense" (2008)

This is a chatty note on the various uses of game theory in semantics and pragmatics. It makes two points that I find worth mentioning.

First, van Benthem correctly points out that there are two different notions of "game" in play in semantics, and that these are sometimes confused. One is Hintikka-style verification games, and the other is Parikh-style signaling games. Although the verification games may in some sense be taken as idealized roadmap for a conversation, this fact is not completely obvious and cannot be taken for granted.

Second, he notes that signaling games have thrown a lot of the syntactic and semantic structure from logic overboard in its attempts to model the emergence of meaning. Since logic usually models hard, conventional facts about a language, this means that game-theoretic approaches to pragmatics have a hard time getting off the ground, because they take everything to be up to debate and revision in the online conversation situation. This is a false assumption in many cases.

Van Benthem writes:
Finally, from the viewpoint of natural language, we have not even reached the complete picture of what goes on in ordinary conversation. There may be games that fix meanings for lexical items and for truth or falsity of expressions whose meaning is understood. But having achieved all that, the ‘game of conversation’ only starts, since we must now convey information, try to persuade others, and generally, further our goals – and maybe a bit of the others’ as well. (p. 7)
He gives a tip of the hat to a number of people in dynamic epistemic logic and then continues:
But conversation and communication is also an arena where game theorists have entered independently, witness the earlier references in Van Rooij [42], and the recent signaling games for conversation proposed in Feinberg [22]. Again, there is an interface between logic and game theory to be developed here, and it has not happened yet. (p. 8)
But certainly a number of people are currently trying to smuggle more logical assumptions into the games, with various levels of success. 

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