The Path to Equilibrium in Sequential and Simultaneous Games

We study in the laboratory threeand four-player, two-action, dominance solvable games of complete information. We consider sequential and simultaneous versions of games that have the same equilibrium actions, and use mousetracking to determine which payoffs subjects pay attention to. We find slightly more equilibrium choices in sequential than in simultaneous, and an overall good fit of level k theory. Our two main findings are as follows. First, two intuitive attentional variables are highly predictive of equilibrium behavior in both versions: looking at the payoffs necessary to compute the Nash equilibrium and looking at payoffs in the order predicted by sequential elimination of strategies. Second, the sequence of lookups reveals different cognitive processes between the sequential and the simultaneous treatments, even among subjects who play the equilibrium strategy. Subjects have a harder time finding the player with a dominant strategy in the simultaneous treatment compared to the sequential treatment. However conditional on finding such player, the unraveling logic of iterated elimination of dominated strategies is performed (equally) fast and efficiently in both cases.