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



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.

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