Publications

Dominion. A game exploring information exploitation

Hobbs, Jacob A.; Estrada, Trilce E.

FlipIt is a game theoretic framework published in 2012[1] to investigate optimal strategies for managing security resources in response to Advanced Persistent Threats. It is a two-player game wherein a resource is controlled by exactly one player at any time. A player may move at any time to capture the resource, incurring a move cost, and is informed of the last time their opponent has moved only upon completing their move. Thus, moves may be wasted and takeover is considered \stealthy", with regard to the other player. The game is played for an unlimited period of time, and the goal of each player is to maximize the amount of time they are in control of the resource minus their total move cost, normalized by the current length of play. Marten Van Dijk and others[1] provided an analysis of various player strategies and proved optimal results for certain subclasses of players. We extend their work by providing a reformulation of the original game, wherein the optimal player strategies can be solved exactly, rather than only for certain subclasses. We call this reformulation Dominion, and place it within a broader framework of stealthy move games. We de ne Dominion to occur over a nite time scale (from 0 to 1), and give each player a certain number of moves to make within the time frame. Their expected score in this new scenario is the expected amount of time they have control, and the point of the game is to dominate as much of the unit interval as possible. We show how Dominion can be treated as a two player, simultaneous, constant sum, unit square game, where the gradient of the bene t curves for the players are linear and possibly discontinuous. We derive Nash equilibria for a basic version of Dominion, and then further explore the roles of information asymmetry in its variants. We extend these results to FlipIt and other cyber security applications.