Game theory and discourse anaphora

We develop an analysis of discourse anaphora—the relationship between a pronoun and an antecedent earlier in the discourse—using games of partial information. The analysis is extended to include information from a variety of different sources of information, including lexical semantics, contrastive stress, grammatical relations and decision theoretic aspects of the context. In this paper, we will develop a game theoretic treatment of some simple cases of discourse anaphora.1 Our attention will be mainly focused on short texts of the type shown in (1): (1) a. A cop saw a hoodlum. He yawned. b. A cop saw a hoodlum. He chased him. The simple texts in (1) have the interesting property that, all else being equal, the pronouns in the second sentence are taken by most speakers to be unambiguous. For example, the pronoun he in (1)a preferentially refers to the cop and not to the hoodlum. Equally in (1)b, he tends to refer to the cop and him refers to the hoodlum, and not the other way around. It is useful to compare anaphors across sentences with those that occur inside a sentence, something we will not treat in this paper. Consider in this light (2): (2) The priest told John his pants were on fire. It is our judgment that the pronoun his in (2) is fully ambiguous; the pronoun can pick out either the priest or John with little or no bias for one or the other. This intuition contrasts sharply with the intuitions about the pronouns in (1). Indeed, a speaker who wishes to refer to the hoodlum, and not the cop, in the subject of the next clause, would do well to use a definite description: ∗ Both authors wish to thank Richard Breheny and Bill Labov for valuable comments made on an earlier draft of this paper. † I acknowledge the generous support of a grant from the NIH, grant NS44266. 1 On a game theoretic approach to language, see Parikh (2001), Parikh (2006) or Parikh & Clark (2005). Myerson (1991) gives a good overview of analytic game theory. c © 2006 Kluwer Academic Publishers. Printed in the Netherlands. jolli.tex; 3/03/2006; 21:02; p.1