## Electronic Journal of Probability

### The compulsive gambler process

#### Abstract

In the  compulsive gambler process there is a finite set of agents who meet pairwise at random times ($i$ and $j$ meet at times of a rate-$\nu_{ij}$ Poisson process) and, upon meeting, play an instantaneous fair game in which one wins the other's money.  We introduce this process and describe some of its basic properties. Some properties are rather obvious (martingale structure;  comparison with Kingman coalescent) while others are more subtle (an "exchangeable over the money elements" property, and a construction reminiscent of the Donnelly-Kurtz look-down construction).  Several directions for possible future research are described. One - where agents meet neighbors in a  sparse graph - is studied here, and another - a continuous-space extension called the metric coalescent - is studied in Lanoue (2014).

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 35, 18 pp.

Dates
Accepted: 1 April 2015
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465067141

Digital Object Identifier
doi:10.1214/EJP.v20-3582

Mathematical Reviews number (MathSciNet)
MR3335826

Zentralblatt MATH identifier
1335.60141

Rights

#### Citation

Aldous, David; Lanoue, Daniel; Salez, Justin. The compulsive gambler process. Electron. J. Probab. 20 (2015), paper no. 35, 18 pp. doi:10.1214/EJP.v20-3582. https://projecteuclid.org/euclid.ejp/1465067141

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