Strategic Complements in Two Stage, 2x2 Games

Yue Feng, Tarun Sabarwal
2018 Social Science Research Network  
Strategic complements are well understood for normal form games, but less so for extensive form games. Indeed, there is some evidence that extensive form games with strategic complementarities are a very restrictive class of games (Echenique (2004) ). We explore the extent of this restrictiveness in the context of two stage, 2 × 2 games. We find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in
more » ... set of games in which payoffs satisfy these conditions has measure zero. In contrast, the set of games that exhibit strategic complements (in the sense of increasing best responses) has infinite measure. This enlarges the scope of strategic complements in two stage, 2 × 2 games (and provides a basis for possibly greater scope in more general games). Moreover, the set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice. JEL Numbers: C60, C70
doi:10.2139/ssrn.3320646 fatcat:gnng7kvxibfyxcdo4s7slsl7hu