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    <keywords>Evolutionary game theory; Public good games; Social dilemmas; Rewards; Punishment; Equilibrium selection</keywords>
    <abstract>Rewards and penalties are common practical tools that can be used to promote cooperation in  social institutions. The evolution of cooperation under reward and punishment incentives in joint  enterprises has been formalized and investigated, mostly by using compulsory public good games. Recently, Sasaki et al. (2012, Proc Natl Acad Sci USA 109:1165-1169) considered optional  participation as well as institutional incentives and described how the interplay between these  mechanisms affects the evolution of cooperation in public good games. Here, we present a full  classification of these cases of evolutionary dynamics. Specifically, whenever penalties are large  enough to cause the bi-stability of both cooperation and defection in cases in which participation in the public good game is compulsory, these penalties will ultimately result in cooperation if  participation in the public good game is optional. The global stability of coercion-based cooperation in this optional case contrasts strikingly with the bi-stability that is observed in the compulsory case We also argue that optional participation is not as effective under rewards as under punishment.</abstract>
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