Surveillance Game Research Articles

Spoofing attack and surveillance game in geo‐location database driven spectrum sharing

The geo-location database (GDB) driven is the enforcement method for dynamic spectrum sharing in TV White Space and 3.5 GHz spectrum bands, as well as a preferred option for the other spectrum sharing applications. Although providing accurate and reliable spectrum information services, the GDB driven spectrum sharing suffers from a critical security threat of spoofing attack. Under a spoofing attack, an adversary could spoof either the identification (ID) or the location information in its request messages. This breaks the fairness and reduces the efficiency of the GDB driven spectrum sharing system. In order to counteract the location and ID spoofing attacks, we consider the location verification of request messages and the ID verification of communicating data. Because a resource manager and an adversary are independent and self-interested, we formulate two corresponding surveillance games to analyze the conflict interaction between spoofing attack and the countermeasures. By expressing the surveillance game on requests’ location in a strategic form and representing the surveillance game on data ID in a sequence form, we find out Nash equilibrium. The analytical and numerical results show that a resource manager can mitigate the spoofing attack by adequately adapting its penalty policy and surveillance strategy.

Maintaining strong mutual visibility of an evader moving over the reduced visibility graph

In this paper, we address the problem of determining whether a mobile robot, called the pursuer, is able to maintain strong mutual visibility (a visibility notion between regions over a convex partition of the environment) of an antagonist agent, called the evader. We frame the problem as a non cooperative game. We consider the case in which the pursuer and the evader move at bounded speed, traveling in a known polygonal environment with or without holes, and in which there are no restrictions as to the distance that might separate the agents. Unlike our previous efforts (Murrieta-Cid et al. in Int J Robot Res 26:233---253, 2007), we give special attention to the combinatorial problem that arises when searching for a solution through visiting several locations in an environment with obstacles. In this paper we take a step further, namely, we assume an antagonistic evader who moves continuously and unpredictably, but with a constraint over its set of admissible motion policies, as the evader moves in the shortest-path roadmap, also called the reduced visibility graph (RVG). The pursuer does not know which among the possible paths over the RVG the evader will choose, but the pursuer is free to move within all the environment. We provide a constructive method to solve the decision problem of determining whether or not the pursuer is able to maintain strong mutual visibility of the evader. This method is based on an algorithm that computes the safe areas (areas that keep evader surveillance) at all times. We prove decidability of this problem, and provide a complexity measure to this evader surveillance game; both contributions hold for any general polygonal environment that might or not contain holes. All our algorithms have been implemented and we show simulation results.

Connected surveillance game

The surveillance game [4] models the problem of web-page prefetching as a pursuit evasion game played on a graph. This two-player game is played turn-by-turn. The first player, called the observer, can mark a fixed amount of vertices at each turn. The second one controls a surfer that stands at vertices of the graph and can slide along edges. The surfer starts at some initially marked vertex of the graph, its objective is to reach an unmarked node before all nodes of the graph are marked. The surveillance number sn(G) of a graph G is the minimum amount of nodes that the observer has to mark at each turn ensuring it wins against any surfer in G. Fomin et al. also defined the connected surveillance game where the observer must ensure that marked nodes always induce a connected subgraph. They ask what is the cost of connectivity, i.e., is there a constant c>0 such that the ratio between the connected surveillance number csn(G) and sn(G) is at most c for any graph G. It is straightforward to show that csn(G)≤Δsn(G) for any graph G with maximum degree Δ. Moreover, it has been shown that there are graphs G for which csn(G)=sn(G)+1. In this paper, we investigate the question of the cost of the connectivity.We first provide new non-trivial upper and lower bounds for the cost of connectivity in the surveillance game. More precisely, we present a family of graphs G such that csn(G)>sn(G)+1. Moreover, we prove that csn(G)≤sn(G)n for any n-node graph G. While the gap between these bounds remains huge, it seems difficult to reduce it. We then define the online surveillance game where the observer has no a priori knowledge of the graph topology and discovers it little-by-little. This variant, which fits better the prefetching motivation, is a restriction of the connected variant. Unfortunately, we show that no algorithm for solving the online surveillance game has competitive ratio better than Ω(Δ). That is, while interesting, this variant does not help to obtain better upper bounds for the connected variant. We finally answer an open question [4] by proving that deciding if the surveillance number of a digraph with maximum degree 6 is at most 2 is NP-hard.

Cycles in extensive form perfect information games

We define and analyse a new class of perfect information games. The nodes of a directed graph G are partitioned into n player sets. Starting at a fixed node of G an infinite path is created as follows: If the current node belongs to player k, then player k chooses any successor node. A local reward n-vector is assigned to every arc. The payoff corresponding to the infinite path is the long term average of the local reward vectors. Such games are called DGA games. Negative and positive results are obtained for the existence of Nash equilibria in certain types of pure strategies (e.g., stationary and automated strategies). Applications to duopoly pricing models and “surveillance games” on graphs are given.

The isotropic rocket—A surveillance evasion game

In this paper the problem is considered of a vehicle, with bounded speed and the capability of instantaneous turns, that tries to escape from a circular region (such as from a radar) attached to a pursuer who has a bounded magnitude of acceleration, but who has the capability to direct the acceleration in any direction instantaneously. The central question is under what circumstances, i.e. for which parameter values and initial conditions, can the pursuer keep the vehicle (also called the evader) forever under surveillance. A subset of the state space will be given from where the evader cannot escape. The state space for this problem is three-dimensional and the problem has analogies with the famous isotropic rocket game treated by Isaacs and Bernhard. The efforts to locate the (permanent) region of surveillance will be described and the phenomena associated with this region, such as barriers, envelope barriers, leaking corners, as well as a correlation with the homicidal chauffer surveillance game, will be discussed.