Dynamics of Multi-Player Games

Abstract

We analyze the dynamics of competitions with a large number of players. In our model, n players compete against each other and the winner is decided based on the standings: in each competition, the mth ranked player wins. We solve for the long time limit of the distribution of the number of wins for all n and m and find three different scenarios. When the best player wins, the standings are most competitive as there is one-tier with a clear differentiation between strong and weak players. When an intermediate player wins, the standings are two-tier with equally-strong players in the top tier and clearly-separated players in the lower tier. When the worst player wins, the standings are least competitive as there is one tier in which all of the players are equal. This behavior is understood via scaling analysis of the nonlinear evolution equations.

8 pages, 8 figures

References in corpus (12)

• Simulating Dynamical Features of Escape Panic
• Dynamics of rumor propagation on small-world networks
• Statistical mechanics of money
• Wealth Distributions in Models of Capital Exchange
• Bifurcations and Patterns in Compromise Processes
• Inelastically scattering particles and wealth distribution in an open economy
• Simulation of Consensus Model of Deffuant et al on a Barabasi-Albert Network
• From Massively Parallel Algorithms and Fluctuating Time Horizons to Non-equilibrium Surface Growth
• Dynamics of Social Diversity
• On The Structure of Competitive Societies
• What is the most competitive sport?
• Power-law distributions from additive preferential redistributions

Cited by in corpus (6)

• Statistical physics of social dynamics
• Scaling in Tournaments
• Merger Dynamics in Three-Agent Games
• Nash equilibrium and evolutionary dynamics in semifinalists' dilemma
• Dynamics of Three Agent Games
• Quenched law of large numbers and quenched central limit theorem for multi-player leagues with ergodic strengths