Dynamic strategic complements in two stage, 2x2 games
Yue Feng and
Tarun Sabarwal ()
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Yue Feng: School of Business, Nanjing University, China and Center for Post-Doctoral Studies, Bank of Nanjing, China
No 202006, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics
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, 2x2 games. We find that the restrictiveness imposed by quasi-supermodularity 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, 2x2 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 (search for similar items in EconPapers)
JEL-codes: C60 C70 (search for similar items in EconPapers)
Pages: 46 pages
New Economics Papers: this item is included in nep-com, nep-gth and nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:kan:wpaper:202006
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