Tipsy Cop and Tipsy Robber

Viktoriya Bardenova, Vincent Ciarcia, and Dr. Erik Insko, Mathematics Department, Florida Gulf Coast University, 10501 FGCU Blvd. S., Fort Myers, FL 33965

In this project we look at interpretation of the game of cops and robbers. In the original game, both a cop and a robber alternate turns moving from vertex to adjacent vertex on a connected graph G with the cop trying to catch the robber and the robber trying to evade the cop. Harris et al. introduced a variant of the game-the tipsy cop and drunken robber. We generalize the work of Harris et al. using a slightly different interpretation to model the our game. We let the cop and robber be any amount of tipsy and use a spinner wheel to determine the probability of whether the next move will be a sober cop move, a sober robber move, or a tipsy move by either player.  
The questions we consider (given a specified set of initial conditions on the players' distance and tipsiness) are:

What is the probability P(i,j,M) that the game, beginning in state i, will be in state j after exactly M rounds?
What is the probability GM(d) that the game lasts at least M rounds and the expected number E(d) of rounds the game should last if they start distance d away?

We analyze the game on cycle, Petersen, friendship graphs, and toroidal grids using the theory of Markov chains. We provide an answer to questions from Harris et al. presenting a model for the game where players start off drunk and sober up as the game progresses and a model for the game where the players' tipsiness increases as a function of the distance between them.

Additional Abstract Information

Presenters: Viktoriya Bardenova, Vincent Ciarcia

Institution: Florida Gulf Coast University

Type: Poster

Subject: Mathematics

Status: Approved

Time and Location

Session: Poster 8
Date/Time: Tue 5:00pm-6:00pm
Session Number: 5576