The article explores the dynamics of the concave pro-rata game, identifying a unique symmetric pure strategy equilibrium where all players adopt the strategy x = (q/n)1. It highlights the critical role of the concavity of a function f in determining the existence of equilibria. If f does not meet specific concavity conditions, equilibria may not exist, or may only produce trivial solutions. The work offers detailed insights into the properties of equilibria within this framework, emphasizing the relationship between the structure of f and the players' strategic responses.
The study demonstrates that, under specific conditions, the concave pro-rata game has a unique, strict equilibrium where all players follow the symmetric strategy of x = (q/n)1.
The equilibrium is contingent on the concavity of the function f, where any deviation from strict concavity leads to trivial or nonexistent equilibria, thus emphasizing the conditions necessary for stable outcomes.
Collection
[
|
...
]