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Lewis's theory of convention involved getting rid of both restrictions.
Lewis' theory of convention applies to a more general class of games than pure coordination games, but pure coordination games already model a variety of important social interactions.
Others, such as Lewis, take it as impetus to develop a theory of convention that invokes neither explicit nor tacit agreement.
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The most influential philosophical theory within a broadly rational choice framework is David Lewis' theory of conventions (Lewis 1969).
We now survey some alternative theories of convention proposed in the past few decades.
David Lewis offers a theory of linguistic conventions, while Noam Chomsky and Donald Davidson argue that convention sheds no light upon language.
They only show that Lewis has not offered a complete theory of how conventions are chosen, how they evolve, and how they sustain themselves.
David Lewis (1969) provides the first systematic theory of how social convention generates linguistic meaning.
As a result of this restriction, his account invited some philosophers to pursue a misguided quest for a general analytic theory of the rationality of conventions (as noted by Bickhard 2008).
Gone are the paradoxes of property and promises intended to prove that particular virtues are devised on purpose; also missing is what some commentators think Hume's most original contribution to the theory of justice, his account of convention.
See the entry on common knowledge for discussion of this controversy and of how common knowledge informs both game theory and the philosophical study of convention.
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