AN ANALYSIS OF STRATEGY-DEPENDENT TREMBLING.
FOO KI VIN
FOO KI VIN
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Abstract
We revisit Hamilton & Slutsky’s (2005) paper on the issue of perfectness of equilibria. Selten (1965; 1975)
put forth the famous “trembling-hand” argument to eliminate some “non-sensible” equilibria. Hamilton &
Slutsky introduced the notion of “strategy-dependent trembles” where each strategy intended by a player
implies a different probability vector of errors over other strategies, and showed a negative result that almost
every Nash equilibrium in pure strategies is a strategy-dependent trembling-hand perfect equilibrium. We
first demonstrate an analysis of “strategy-dependent trembles” with a detailed example and compare it to
the conventional “trembling-hand errors”. We show that Myerson’s (1978) notion of a “proper equilibrium”
can remedy for Hamilton & Slutsky’s (2005) negative result on the perfection by accomodating “strategydependent trembles”. Lastly, in the concluding discussion we show that the analysis of “strategy-dependent
trembles” can be conducted through the framework of biased-belief functions (Heller & Winter, 2018).
Keywords
trembling-hand perfection, strategy-dependent trembles, proper equilibrium, biased-belief, weakly dominated strategies, perfection
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2020-04-13
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