4 research outputs found
Desensitization and Deception in Differential Games with Asymmetric Information
Desensitization addresses safe optimal planning under parametric
uncertainties by providing sensitivity function-based risk measures. This paper
expands upon the existing work on desensitization to address safe planning for
a class of two-player differential games. In the proposed game, parametric
uncertainties correspond to variations in a vector of model parameters about
its nominal value. The two players in the proposed formulation are assumed to
have information about the nominal value of the parameter vector. However, only
one of the players is assumed to have complete knowledge of parametric
variation, creating a form of information asymmetry in the proposed game. The
lack of knowledge regarding the parametric variations is expected to result in
state constraint violations for the player with an information disadvantage. In
this regard, a desensitized feedback strategy that provides safe trajectories
is proposed for the player with incomplete information. The proposed feedback
strategy is evaluated in instances involving one pursuer and one evader with an
uncertain dynamic obstacle, where the pursuer is assumed to know only the
nominal value of the obstacle's speed. At the same time, the evader knows the
obstacle's true speed, and also the fact that the pursuer possesses only the
nominal value. Subsequently, deceptive strategies are proposed for the evader,
who has an information advantage, and these strategies are assessed against the
pursuer's desensitized strategy
Cops and Invisible Robbers: the Cost of Drunkenness
We examine a version of the Cops and Robber (CR) game in which the robber is
invisible, i.e., the cops do not know his location until they capture him.
Apparently this game (CiR) has received little attention in the CR literature.
We examine two variants: in the first the robber is adversarial (he actively
tries to avoid capture); in the second he is drunk (he performs a random walk).
Our goal in this paper is to study the invisible Cost of Drunkenness (iCOD),
which is defined as the ratio ct_i(G)/dct_i(G), with ct_i(G) and dct_i(G) being
the expected capture times in the adversarial and drunk CiR variants,
respectively. We show that these capture times are well defined, using game
theory for the adversarial case and partially observable Markov decision
processes (POMDP) for the drunk case. We give exact asymptotic values of iCOD
for several special graph families such as -regular trees, give some bounds
for grids, and provide general upper and lower bounds for general classes of
graphs. We also give an infinite family of graphs showing that iCOD can be
arbitrarily close to any value in [2,infinty). Finally, we briefly examine one
more CiR variant, in which the robber is invisible and "infinitely fast"; we
argue that this variant is significantly different from the Graph Search game,
despite several similarities between the two games
Pursuit–Evasion Games with incomplete information in discrete time
Pursuit–Evasion Games, Incomplete information, Zero-sum stochastic games, Recursive games, Nonnegative payoffs,