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So instead of a vector of probabilities on pure strategies, we would like to use a vector of realization weights on sequences to represent players' strategies. however, an arbitrary vector may be inconsistent. koller, megiddo, & von stengel 1994 ; showed that if the game has perfect recall, a vector of realization weights x for player 1 is consistent iff they satisfy certain linear constraints. for example in figure 1, the root is always reached, so x 1. also, x xa + xb , and xb xbe + xbf . player 2's vector has similar constraints. intuitively, these linear constraints encode the tree structure of the extensive form. the total number of constraints is at most the size of the tree. the payoff function can be computed from equations 1 and 2 easily. the resulting sequence form representation is remarkably similar to the normal form. the only major difference is that in the normal form, the only constraints are that the mixed strategy probabilities sum to 1 for each player; whereas in the sequence form, we have the linear constraints that encodes the tree structure. as a result, most of the algorithms for finding nash equilibria on normal form can be applied to the sequence form after some modifications. for two-person zero-sum games, standard lp algorithms can be directly applied to the sequence form. for two-person general sum games, we can use lemke's algorithm lemke 1965 ; , which is related to lemke-howson, to solve the resulting lcp. for general n-person games, govindan and wilson's continuation method can be modified to work on the sequence form govindan & wilson 2002 ; . since the sequence form is exponentially smaller than the corresponding normal form, algorithms on sequence form are exponentially faster than their normal form counterparts. after we have found our realization weights at a nash equilibrium, how do we actually play the game? it turns out that for perfect recall games, realization weights are closely related to behavioral strategies: the realization weight for player 1 on a just the product of player 1's behavioral strategy probabilities along the path from root to a. given the realization weights for player 1, her behavioral strategies can be easily computed. for example in figure 1, the x behavioral probabilities of choosing g is xbg . b!