DeepAI AI Chat
Log In Sign Up

A Game of Random Variables

by   Artem Hulko, et al.
The University of Texas at Austin

This paper analyzes a simple game with n players. We fix a mean, μ, in the interval [0, 1] and let each player choose any random variable distributed on that interval with the given mean. The winner of the zero-sum game is the player whose random variable has the highest realization. We show that the position of the mean within the interval is paramount. Remarkably, if the given mean is above a crucial threshold then the unique equilibrium must contain a point mass on 1. The cutoff is strictly decreasing in the number of players, n; and for fixed μ, as the number of players is increased, each player places more weight on 1 at equilibrium. We characterize the equilibrium as the number of players goes to infinity.


page 1

page 2

page 3

page 4


The Parable of the Fruit Sellers Or, A Game of Random Variables

This paper analyzes a simple game with n players. Fix a mean in interval...

A Game of Martingales

We consider a two player dynamic game played over T ≤∞ periods. In each ...

Characterizing the interplay between information and strength in Blotto games

In this paper, we investigate informational asymmetries in the Colonel B...

Computing Shapley Values for Mean Width in 3-D

The Shapley value is a common tool in game theory to evaluate the import...

Playing Divide-and-Choose Given Uncertain Preferences

We study the classic divide-and-choose method for equitably allocating d...

Agent Failures in All-Pay Auctions

All-pay auctions, a common mechanism for various human and agent interac...

Stake-governed tug-of-war and the biased infinity Laplacian

We introduce a two-person zero-sum game that we call stake-governed tug-...