Large Games: Robustness and Stability

This review focuses on properties related to the robustness and stability of Nash equilibria in games with a large number of players. Somewhat surprisingly, these equilibria become substantially more robust and stable as the number of players increases. We illustrate the relevant phenomena through a binary-action game with strategic substitutes, framed as a game of social isolation in a pandemic environment. Expected final online publication date for the Annual Review of Economics, Volume 13 is August 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Approximation and characterization of Nash equilibria of large games

We characterize Nash equilibria of games with a continuum of players in terms of approximate equilibria of large finite games. This characterization precisely describes the relationship between the equilibrium sets of the two classes of games. In particular, it yields several approximation results for Nash equilibria of games with a continuum of players, which roughly state that all finite-player games that are sufficiently close to a given game with a continuum of players have approximate equilibria that are close to a given Nash equilibrium of the non-atomic game.

The Relationships Between External and Internal Workloads During Basketball Training and Games

Purpose: To investigate the relationships between external and internal workloads using a comprehensive selection of variables during basketball training and games. Methods: Eight semiprofessional, male basketball players were monitored during training and games for an entire season. External workload was determined as PlayerLoad™: total and high-intensity accelerations, decelerations, changes of direction, and jumps and total low-intensity, medium-intensity, high-intensity, and overall inertial movement analysis events. Internal workload was determined using the summated-heart-rate zones and session rating of perceived exertion models. The relationships between external and internal workload variables were separately calculated for training and games using repeated-measures correlations with 95% confidence intervals. Results: PlayerLoad was more strongly related to summated-heart-rate zones (r = .88 ± .03, very large [training]; r = .69 ± .09, large [games]) and session rating of perceived exertion (r = .74 ± .06, very large [training]; r = .53 ± .12, large [games]) than other external workload variables (P < .05). Correlations between total and high-intensity accelerations, decelerations, changes of direction, and jumps and total low-intensity, medium-intensity, high-intensity, and overall inertial movement analysis events and internal workloads were stronger during training (r = .44–.88) than during games (r = .15–.69). Conclusions: PlayerLoad and summated-heart-rate zones possess the strongest dose–response relationship among a comprehensive selection of external and internal workload variables in basketball, particularly during training sessions compared with games. Basketball practitioners may therefore be able to best anticipate player responses when prescribing training drills using these variables for optimal workload management across the season.

Integrating Learning with Game Theory for Societal Challenges

Real-world problems often involve more than one decision makers, each with their own goals or preferences. While game theory is an established paradigm for reasoning strategic interactions between multiple decision-makers, its applicability in practice is often limited by the intractability of computing equilibria in large games, and the fact that the game parameters are sometimes unknown and the players are often not perfectly rational. On the other hand, machine learning and reinforcement learning have led to huge successes in various domains and can be leveraged to overcome the limitations of the game-theoretic analysis. In this paper, we introduce our work on integrating learning with computational game theory for addressing societal challenges such as security and sustainability.