Fending off one means fending off all : evolutionary stability in submodular games - Wolfgang Leininger (Center for Economic Studies and ifo Institute (CESifo), 2004)
The implications of evolutionarily stable behavior in finite populations have recently been explored for a variety of aggregative games. This note proves an intimate relationship between submodularity and global evolutionary stability of strategies for these games, which -apart from being of independent interest - accounts for a number of results obtained in the recent literature: we show that any evolutionarily stable strategy (ESS) of a submodular aggregative game must also be globally stable. I.e. if one mutant cannot successfully invade a population, any number of mutants can even less do so.
Keywords: C79; D72; 330; Evolutionäre Spieltheorie; Theorie