One of the main principles of gamification is the use of social comparison. Leaderboards are commonly used to allow players to compare their performance against others'. We sought to examine how leaderboard ranking affected satisfaction with a game and desire to play a game again. In our study, individuals in a second, fourth, or seventh position on the leaderboard reported higher satisfaction than individuals in other positions on the leaderboard. Our results support a potential mechanism that might contribute to game satisfaction from leaderboard position: counterfactual thinking. Future work and implications for the design of leaderboards are discussed.

We study the Cauchy problem involving non-local Ornstein-Uhlenbeck operators in finite and infinite dimensions. We prove classical solvability without requiring that the Lévy measure corresponding to the large jumps part has a first finite moment. Moreover, we determine a core of regular functions which is invariant for the associated transition Markov semigroup. Such a core allows to characterize the marginal laws of the Ornstein-Uhlenbeck stochastic process as unique solutions to Fokker-Planck-Kolmogorov equations for measures.

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