Optimal strategy for avoiding capture in a multiple stage random walk on a cycle
Grzegorz Kubicki
University of Louisville, USA, and University of Opole, Poland
Ewa Kubicka
University of Louisville
Małgorzata Kuchta
Wroclaw University of Technology
Michal Morayne
Wroclaw University of Technology
PDF
Minisymposium: GENERAL SESSION TALKS
Content: We want to maximize the number of moves for a random walk on an even cycle before visiting the vertex opposite to the starting position. Our payoff is the number of moves but it is reduced to 0 if we are not able to avoid the opposite vertex. Optimal stopping time and the expected value of the payoff are determined for this random process as well as for the corresponding multistage process with $N$ stages. Asymptotic behavior of the expected payoff is determined as $N$ increases without bound.