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By Anton Benz, Gerhard Jäger, Robert Van Rooij
Rooted in Gricean culture, this e-book concentrates on online game- and decision-theoretic (GDT) ways to the principles of pragmatics. An advent to GDT, an summary of GDT pragmatics examine up to now, its relation to semantics and to Gricean pragmatics are via contributions providing a high-level survey of present GDT pragmatics and the sphere of its functions, demonstrating that this method offers a legitimate foundation for synchronic and diachronic motives of language use.
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Extra resources for Game theory and pragmatics
Sample text
An element in [M → A]. Although strictly speaking not necessary, we can represent also the speaker’s strategy already as a function, one in [T → M ]. , H and S. The utilities of both players are given by uS (t, a) and uH (t, a). com - licensed to Universitetsbiblioteket i Tromso - PalgraveConnect - 2011-04-24 An Introduction to Game Theory for Linguists 27 Game Theory and Pragmatics In cheap talk games, the messages are not directly payoff relevant: the utility functions do not mention the messages being used.
A player i strictly prefers action a over action b exactly if the expected utility of a is higher than the expected utility of b. For mixed strategy profiles P = (P1 , . . , Pn ), we use the same notation P−i as for (pure) strategy profiles to denote the profile (P1 , . . , Pi−1 , Pi+1 , . . , Pn ) where we leave out the strategy Pi . (Pi , P−i ) denotes again the profile where we replaced Pi by Pi . Definition 4 (Mixed Nash Equilibrium) A (weak) mixed Nash equilibrium is a mixed strategy profile (P1 , .
A pure strategy corresponds to a mixed strategy Pi where Pi (a) = 1 for one action a ∈ Ai and Pi (b) = 0 for all other actions. e. the actions of going to a boxing event and going to a concert. If Adam is player 1 and Eve 2, then their strategy of playing b and c with equal probability corresponds to the strategy profile (P1 , P2 ) where Pi (b) = Pi (c) = 12 , i ∈ {1, 2}. We can calculate the expected utility of player i given a mixed strategy profile P = (P1 , . . , Pn ) and payoff profile (u1 , .