On a Markov Game with One-Sided Incomplete Information

We apply the average cost optimality equation to zero-sum Markov games, by considering a simple game with one-sided incomplete information that generalizes an example of Aumann and Maschler (1995). We determine the value and identify the optimal strategies for a range of parameters.Repeated game with incomplete information, Zero-sum games, Partially observable Markov decision processes

On a Markov Game with One-Sided Incomplete Information

We apply the average cost optimality equation to zero-sum Markov games, by considering a simple game with one-sided incomplete information that generalizes an example of Aumann and Maschler (1995). We determine the value and identify the optimal strategies for a range of parameters

Handshaking Protocols and Jamming Mechanisms for Blind Rendezvous in a Dynamic Spectrum Access Environment

Blind frequency rendezvous is an important process for bootstrapping communications between radios without the use of pre-existing infrastructure or common control channel in a Dynamic Spectrum Access (DSA) environment. In this process, radios attempt to arrive in the same frequency channel and recognize each other’s presence in changing, under-utilized spectrum. This paper refines existing blind rendezvous techniques by introducing a handshaking algorithm for setting up communications once two radios have arrived in the same frequency channel. It then investigates the effect of different jamming techniques on blind rendezvous algorithms that utilize this handshake. The handshake performance is measured by determining the probability of a handshake, the time to handshake, and the increase in time to rendezvous (TTR) with a handshake compared to that without. The handshake caused varying increases in TTR depending on the time spent in each channel. Four different jamming techniques are applied to the blind rendezvous process: noise, deceptive, sense, and Primary User Emulation (PUE). Each jammer type is analyzed to determine how they increase the TTR, how often they successfully jam over a period of time, and how long it takes to jam. The sense jammer was most effective, followed by PUE, deceptive, and noise, respectively

Search-and-rescue rendezvous

We consider a new type of asymmetric rendezvous search problem in which player II needs to give player I a ‘gift’ which can be in the form of information or material. The gift can either be transfered upon meeting, as in traditional rendezvous, or it can be dropped off by player II at a location he passes, in the hope it will be found by player I. The gift might be a water bottle for a traveller lost in the desert; a supply cache for Captain Scott in the Antarctic; or important information (left as a gift). The common aim of the two players is to minimize the time taken for I to either meet II or find the gift. We find optimal agent paths and drop off times when the search region is a line, the initial distance between the players is known and one or both of the players can leave gifts. A novel and important technique introduced in this paper is the use of families of linear programs to solve this and previous rendezvous problems. Previously, the approach was to guess the answer and then prove it was optimal. Our work has applications to other forms of rendezvous on the line: we can solve the symmetric version (players must use the same strategy) with two gifts and we show that there are no asymmetric solutions to this two gifts problem. We also solve the GiftStart problem, where the gift or gifts must be dropped at the start of the game. Furthermore, we can solve the Minmax version of the game where the objective function is to minimize the maximum rendezvous time. This problem admits variations where players have 0, 1 or 2 gifts at disposal. In particular, we show that the classical Wait For Mommy strategy is optimal for this setting

Rendezvous-evasion search in two boxes with incomplete information

An agent (who may or may not want to be found) is located in one of two boxes. At time 0 suppose that he is in box B. With probability p he wishes to be found, in which case he has been asked to stay in box B. With probability p he tries to evade the searcher, in which case he may move between boxes A and B. The searcher looks into one of the boxes at times 1, 2, 3, ... . Between each search the agent may change boxes if he wants. The searcher is trying to minimise the expected time to discovery. The agent is trying to minimise this time if he wants to be found, but trying to maximise it otherwise. This paper nds a solution to this game (in a sense defined in the paper), associated strategies for the searcher and each type of agent, and a continuous value function v(p) giving the expected time for the agent to be discovered. The solution method (which is to solve an associated zero-sum game) would apply generally to this type of game of incomplete information