This paper analyzes behavior in repeatedly played two-stage games, where

players choose actions in both stages according to best replies using 'level-n

expectations' about the opponent's actions in both stages. Level-n expecta-

tions are recursively defined in a way that a player holding level n expectations

correctly predicts the action of an opponent holding level n - 1 expectations.

A general conceptual framework to study such dynamics for two-stage games

is developed and it is shown that, contrary to results for single-stage games,

the fixed points of the dynamics depend on the level of the expectations. In

particular, for level-zero expectation, fixed points correspond to a Nash equi-

librium of a simultaneous move version of the game, whereas (under certain

conditions) fixed points converge towards the subgame perfect equilibrium of

the two-stage game if the level of expectations goes to infinity. The approach

is illustrated using a two-stage duopoly game, where firms in the first stage

invest in activities reducing their marginal costs and in the second stage en-

gage in Cournot competition. An increase in the level of expectations leads in

the long run to higher cost reducing activities and higher output of the firms,

however to lower profits. Level-two expectations are sufficient to move the

fixed-point of the dynamics to a close neighbourhood of the subgame-perfect

equilibrium.