Gambling in contests with random initial law
Han Feng, David Hobson

TL;DR
This paper extends a contest model involving Brownian motions by allowing initial values to be random variables with a common law, establishing a unique symmetric Nash equilibrium characterized by a target law with specific properties.
Contribution
It introduces a variant of the contest model with random initial states and proves the existence and uniqueness of the equilibrium with a detailed characterization of the target law.
Findings
Existence and uniqueness of symmetric Nash equilibrium.
The equilibrium target law is greater than or equal to the initial law in convex order.
The target law has a specific structure with an atom at zero and a decreasing density on positive values.
Abstract
This paper studies a variant of the contest model introduced in Seel and Strack [J. Econom. Theory 148 (2013) 2033-2048]. In the Seel-Strack contest, each agent or contestant privately observes a Brownian motion, absorbed at zero, and chooses when to stop it. The winner of the contest is the agent who stops at the highest value. The model assumes that all the processes start from a common value and the symmetric Nash equilibrium is for each agent to utilise a stopping rule which yields a randomised value for the stopped process. In the two-player contest, this randomised value has a uniform distribution on . In this paper, we consider a variant of the problem whereby the starting values of the Brownian motions are independent, nonnegative random variables that have a common law . We consider a two-player contest and prove the existence and uniqueness of a…
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Taxonomy
TopicsAuction Theory and Applications · Experimental Behavioral Economics Studies · Game Theory and Voting Systems
