The ESP game belongs to the genre called Games With A Purpose (GWAP), which leverage people's desire to be entertained and also outsource certain steps of the computational process to humans. The games have shown promise in solving a variety of problems, which computer computation has been unable to resolve completely thus far. In this study, we consider generalized ESP games with two objectives. First, we propose an analytical model for computing the utility of generalized ESP games, where the number of players, the consensus threshold, and the stopping condition are variable. We show that our model can accurately predict the stopping condition that will yield the optimal utility of a generalized ESP game under a specific game setting. A service provider can therefore utilize the model to ensure that the hosted generalized ESP games produce high-quality labels efficiently. Second, we propose a metric, called system gain, for evaluating the performance of ESP-like GWAP systems, and also use analysis to study the properties of generalized ESP games. We believe that GWAP systems should be designed and played with strategies. To this end, we implement an optimal puzzle selection strategy (OPSA) based on our analysis. Using a comprehensive set of simulations, we demonstrate that the proposed OPSA approach can effectively improve the system gain of generalized ESP games, as long as the number of puzzles in the system is sufficiently large.
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