Name
Title | ||
|---|---|---|
HOW TO DETECT A SALAMI SLICER: A STOCHASTIC CONTROLLER-AND-STOPPER GAME WITH UNKNOWN COMPETITION |
Abstract | ||
|---|---|---|
We consider a stochastic game of control and stopping specified in terms of a process X-t = -theta Lambda(t)+W-t, representing the holdings of Player 1, where W is a Brownian motion, theta is a Bernoulli random variable indicating whether Player 2 is active or not, and Lambda is a nondecreasing continuous process representing the accumulated "theft" or "fraud" performed by Player 2 (if active) against Player 1. Player 1 cannot observe theta or Lambda directly but can merely observe the path of the process X and may choose a stopping rule tau to deactivate Player 2 at a cost M. Player 1 thus does not know if she is the victim of fraud or not and operates in this sense under unknown competition. Player 2 can observe both theta and W and seeks to choose a fraud strategy Lambda that maximizes the expected discounted amount E [integral(tau)(0) e(-rs)d Lambda(s)vertical bar theta = 1], whereas Player 1 seeks to choose the stopping strategy tau so as to minimize the expected discounted cost E[theta integral(tau)(0) e(-rs)d Lambda(s) + e(-rr)MI({tau, infinity})]. This non-zero-sum game belongs to a class of stochastic dynamic games with unknown competition and continuous controls and is motivated by applications in fraud detection; it combines filtering (detection), stochastic control, optimal stopping, strategic features (games), and asymmetric information. We derive Nash equilibria for this game; for some parameter values we find an equilibrium in pure strategies, and for other parameter values we find an equilibrium by allowing for randomized stopping strategies. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1137/21M139044X | SIAM JOURNAL ON CONTROL AND OPTIMIZATION |
Keywords | DocType | Volume |
stochastic game theory, stochastic optimal control, fraud detection, optimal stopping | Journal | 60 |
Issue | ISSN | Citations |
1 | 0363-0129 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Erik Ekström | 1 | 0 | 0.34 |
| Kristoffer Lindensjö | 2 | 0 | 1.01 |
| Marcus Olofsson | 3 | 0 | 0.34 |