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We initiate the study of trembling-hand perfection in sequential (i.e.,extensive-form) games with correlation. We introduce the extensive-form perfectcorrelated equilibrium (EFPCE) as a refinement of the classical extensive-formcorrelated equilibrium (EFCE) that amends its weaknesses off the equilibriumpath. This is achieved by accounting for the possibility that players may makemistakes while following recommendations independently at each information setof the game. After providing an axiomatic definition of EFPCE, we show that onealways exists since any perfect (Nash) equilibrium constitutes an EFPCE, andthat it is a refinement of EFCE, as any EFPCE is also an EFCE. Then, we provethat, surprisingly, computing an EFPCE is not harder than finding an EFCE,since the problem can be solved in polynomial time for general n-playerextensive-form games (also with chance). This is achieved by formulating theproblem as that of finding a limit solution (as $\epsilon \rightarrow 0$) to asuitably defined trembling LP parametrized by $\epsilon$, featuringexponentially many variables and polynomially many constraints. To this end, weshow how a recently developed polynomial-time algorithm for trembling LPs canbe adapted to deal with problems having an exponential number of variables.This calls for the solution of a sequence of (non-trembling) LPs withexponentially many variables and polynomially many constraints, which ispossible in polynomial time by applying an ellipsoid against hope approach.

Trembling-Hand Perfection and Correlation in Sequential Games