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    <abstract>Evolutionary game theory describes systems where individual  success is based on the interaction with others. We consider a  system in which players unconditionally imitate more successful  strategies but sometimes also explore the available strategies  at random. Most research has focused on how strategies  spread via genetic reproduction or cultural imitation, but random exploration of the available set of strategies has  received less attention so far. In genetic settings, the latter  corresponds to mutations in the DNA, whereas in cultural  evolution, it describes individuals experimenting with new  behaviors. Genetic mutations typically occur with very small  probabilities, but random exploration of available strategies in  behavioral experiments is common. We term this phenomenon &quot;exploration dynamics&quot; to contrast it with the traditional focus  on imitation. As an illustrative example of the emerging  evolutionary dynamics, we consider a public goods game with  cooperators and defectors and add punishers and the option to  abstain from the enterprise in further scenarios. For small  mutation rates, cooperation (and punishment) is possible only if  interactions are voluntary, whereas moderate mutation rates  can lead to high levels of cooperation even in compulsory public goods games. This phenomenon is investigated through  numerical simulations and analytical approximations.</abstract>
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