on a markov chain roulette-type game
01-12-2012 01:01
Abstract A Markov chain on non-negative integers which arises in a roulette-type game is
discussed. The transition probabilities are p 01= ρ, p Nj= δ Nj, pi, i+W= q, pi, i− 1= p= 1− q,
1≤ W< N, 0≤ ρ≤ 1, N− W< j≤ N and i= 1, 2,..., N− W. Using formulae for the determinant of
a partitioned matrix, a closed form expression for the solution of the Markov chain roulette-
type game is deduced. The present analysis is supported by two mathematical models from
tumor growth and war with bargaining.
discussed. The transition probabilities are p 01= ρ, p Nj= δ Nj, pi, i+W= q, pi, i− 1= p= 1− q,
1≤ W< N, 0≤ ρ≤ 1, N− W< j≤ N and i= 1, 2,..., N− W. Using formulae for the determinant of
a partitioned matrix, a closed form expression for the solution of the Markov chain roulette-
type game is deduced. The present analysis is supported by two mathematical models from
tumor growth and war with bargaining.