Strategic complements in two stage, 2 × 2 games

Yue Feng and Tarun Sabarwal

Journal of Economic Theory, 2020, vol. 190, issue C

Abstract: Strategic complements are well understood for normal form games, but less so for extensive form games. There is some evidence that extensive form games with strategic complementarities are a very restrictive class of games (Echenique (2004)). We study necessary and sufficient conditions for strategic complements (defined as increasing best responses) in 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 which payoffs satisfy these conditions has measure zero. Payoffs with these conditions require the player to be indifferent between their actions in two of the four subgames in stage two, eliminating any strategic role for their actions in these two subgames. In contrast, the set of games that exhibit strategic complements (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). The set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice. The results are easy to apply, and are robust to including dual payoff conditions and adding a third player. Examples with several motivations are included.

Keywords: Strategic complements; Extensive form game; Two stage game; Lattice (search for similar items in EconPapers)
JEL-codes: C60 C70 (search for similar items in EconPapers)
Date: 2020
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Related works:
Working Paper: Strategic complements in two stage, 2x2 games (2020)
Working Paper: Strategic Complements in Two Stage, 2 × 2 Games (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:190:y:2020:i:c:s0022053120301113

DOI: 10.1016/j.jet.2020.105118

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