Timing is crucial in situations ranging from currency attacks, to product introductions, to starting a revolution. These settings share the feature that payoffs depend critically on the timing of a few other key players—and their moves are uncertain. To capture this, we introduce the notion of clock games and experimentally test them. Each player’s clock starts on receiving a signal about a payoff relevant state variable. Since the timing of the signals is random, clocks are de-synchronized. A player must decide how long, if at all, to delay his move after receiving the signal. We show that (i) equilibrium is always characterized by strategic delay—regardless of whether moves are observable or not; (ii) delay decreases as clocks become more synchronized and increases as information becomes more concentrated; (iii) When moves are observable, players “herd ” immediately after any player makes a move. We then show, in a series of experiments, that key predictions of the model are consistent with observed behavior.

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A One-parameter Theory of Learning in Games Functional experience weighted attraction (fEWA) is a one-parameter theory of learning in games. It approximates the free parameters in an earlier model (EWA) with functions of experience. The theory was originally tested on seven different games and compared to four other learning and equilibrium theories, then four more games were added. Generally fEWA or parameterized EWA predict best out-of-sample, but one kind of reinforcement learning predicts well in games with mixed-strategy equilibrium. Of the learning models, belief learning models fit worst but fit better than noisy (quantal response) equilibrium models. The economic value of a theory is measured by how much more subjects would have earned if they followed the theory's recommendations. Most learning theories add value (though equilibrium theories often subtract value) and fEWA and EWA usually add the most value.

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