A Generalized Ky Fan Minimax Inequality on Finite-Dimensional Spaces

An existence result for a generalized inequality over a possible unbounded domain in a finite-dimensional space is established. The proof technique allows to avoid any monotonicity assumption. We adapt a weak coercivity condition introduced in Castellani and Giuli (J Glob Optim 75:163–176, 2019) for a generalized game which extends an older one proposed by Konnov and Dyabilkin (J Glob Optim 49:575–577, 2011) for equilibrium problems. Our main result encompasses and generalizes several existence results for equilibrium, quasiequilibrium and fixed-point problems.

Video Game Pursuit (VGPu) Scale Development: Designing and Validating a Scale With Implications for Game-Based Learning and Assessment

Background. Recent research on game-based assessment and training demonstrates growing interest in how individual differences affect game-based outcomes. However, there is still a lack of clarity about the variables that affect important game-based outcomes and issues with measurement approaches regarding these variables (e.g., no validation of scales). This study develops a model where video game pursuit (VGPu) is measured as an antecedent to entering the gaming cycle. We propose that VGPu-related antecedents lead to a feedback loop where engaging in the game cycle affects game-related outcomes which again affect the antecedents of re-entering the game cycle. Moreover, we validate a measure of VGPu and provide construct as well as criterion validity evidence. Methods. Within three studies ( N = 716) we develop and validate the VGPu scale - a psychometrically sound measure of intentions to pursue video games. Using Amazon’s MTurk (Studies 1, 2), participants responded to the VGPu items and we conducted exploratory and confirmatory factor analyses showing that VGPu consists of a general latent VGPu factor with four subfactors (Intentional Game Play, Generalized Game Self-Efficacy, Enjoyment of Games, Prone to Game Immersion). In Study 3, students responded to the VGPu items, to items examining construct validity, and played three video games from different genres to assess criterion-related validity of game performance and game reactions. Results. Results demonstrate construct and criterion-related validity showing that VGPu correlates with other game-related scales and predicts game performance and game reactions. Discussion. The findings demonstrate the value of the VGPu scale for research and practice because pursuing video games seems to be an important variable for predicting how individuals perform and react to game-based activities. Finally, we discuss implications for future research and practice in the realm of game-based assessment and training.

Maximum Genus of the Jenga Like Configurations

We treat the boundary of the union of blocks in the Jenga game as a surface with a polyhedral structure and consider its genus. We generalize the game and determine the maximum genus among the configurations in the generalized game.

High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering

How do large-scale participants in parimutuel wagering events affect the house and ordinary bettors? A standard narrative suggests that they may temporarily benefit the former at the expense of the latter. To approach this problem, we begin by developing a model based on the theory of large generalized games. Constrained only by their budgets, a continuum of diffuse (ordinary) players and a single atomic (large-scale) player simultaneously wager to maximize their expected profits according to their individual beliefs. Our main theoretical result gives necessary and sufficient conditions for the existence and uniqueness of a pure-strategy Nash equilibrium. Using this framework, we analyze our question in concrete scenarios. First, we study a situation in which both predicted effects are observed. Neither is always observed in our remaining examples, suggesting the need for a more nuanced view of large-scale participants.