Abstract:
A multi-stage model with a finite horizon related to the gambler's ruin problem is considered. Two players compete against each other at each of the $n$ steps of the game. The probability that the player wins at the next step depends on the win/lose ratio in previous steps. The player's payoff is determined at the end of the game and is equal to the difference between wins and losses. The player's payoff also accounts for the cost $c$, which the player incurres at each step. It is assumed that the players are asymmetric and one of them can stop the game if the number of her losses exceeds the number of her wins by an amount $k$. The payoff of the player using such strategy is obtained. The numerical simulations of the player's payoffs for different values of the problem parameters are provided.
Keywords:gambler's ruin problem, random walk, optimal strategy, ruin probability.
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