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Interpretation, Coordination and Conformity

Hykel Hosni
School of Mathematics
The University of Manchester
Manchester UK
homepage: http://www.maths.man.ac.uk/~hykel/

Séminaire CHM du Mardi 16 Novembre 2004

Résumé (version pdf)

The purpose of this seminar is to analyse the common aspects of Radical Interpretation problems and Pure Coordination games by means of the abstract mathematical framework of Rationality-as-conformity recenlty introduced by Jeff Paris and the present author. Within this abstract framework, a selection principle will be proposed as a solution for the following Conformity Game. Let possible worlds be functions from a finite set A to the binary set 2 = { 0, 1 } . The domain of the game is P+(2 A ), the set of non-empty subsets of 2 A which denotes the set of all possible worlds. The conformity game is a two-person, non-cooperative game of complete yet imperfect information whose normal form goes like this. Each player is to choose one strategy out of a set of possible choices, identical for both agents up to permutations of A and 2, where each strategy corresponds to one element of K = { f1, . . . , fk } , say. Players get a positive payoff p if they play the same strategy and nothing otherwise, all this being common knowledge. Being a game of multiple Nash-equilibria the conformity game is therefore a typical example of a pure coordination game, and as such, it is generally considered to be unsolvable within the framework of traditional game theory. Yet conformity, as intended in this game, is a form of interpretation: it is an attempt at interpreting an agent's behaviour by giving a complete description of the way she has structured her world. In other words, to figure out which will be the most common world within K, is to attach a certain meaning to each of the possible worlds, and then choose on such grounds. If nothing is known or (can be) assumed about those meanings, this interpretation problem becomes, in the sense of Davidson's, radical. Despite its lack of structure the Conformity Game contains all the crucial aspects of radical interpretation problems. And for the solution of these, the Rationality-as-conformity framework provides a triangulation-like (again the sense of Davidson's) solution by means of a procedure, the Minimum Ambiguity Reason, driven by a general form of the Charity Principle.


Contacts :Patrick Paroubek & William Turner
Dernière mise à jour : 15 octobre 2004