Результаты исследований: Материалы конференций › материалы › Рецензирование
Optimal Stopping Strategies in Gambler’s Ruin Game. / Mazalov, Vladimir; Ivashko, Anna.
2024. 237-249 Работа представлена на 23 International Conference on Mathematical Optimization Theory and Operations Research , Омск, Российская Федерация.Результаты исследований: Материалы конференций › материалы › Рецензирование
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TY - CONF
T1 - Optimal Stopping Strategies in Gambler’s Ruin Game
AU - Mazalov, Vladimir
AU - Ivashko, Anna
N1 - Conference code: 23
PY - 2024/12
Y1 - 2024/12
N2 - We consider a game-theoretic version of the gambler’s ruin problem. In each of the n steps, two players with different capitals compete over a unit of capital. The players’ chances in each step are equal. Accordingly, the capital of each player can increase or decrease by one unit with equal probability. The player wins if the opponent runs out of capital. In this case, the player gets 1 as payoff. If the game has not ended within the time interval n, then the players gain nothing. At each step, the players are required to pay a value of c. Two variants of the game are examined: one where one player’s capital is infinite, and the other where both players’ capitals are infinite. The player’s strategy is the stopping time in the game in order to maximize the expected payoff. The players’ optimal stopping strategies and payoffs are determined. The numerical results of payoff simulation for different n are reported.
AB - We consider a game-theoretic version of the gambler’s ruin problem. In each of the n steps, two players with different capitals compete over a unit of capital. The players’ chances in each step are equal. Accordingly, the capital of each player can increase or decrease by one unit with equal probability. The player wins if the opponent runs out of capital. In this case, the player gets 1 as payoff. If the game has not ended within the time interval n, then the players gain nothing. At each step, the players are required to pay a value of c. Two variants of the game are examined: one where one player’s capital is infinite, and the other where both players’ capitals are infinite. The player’s strategy is the stopping time in the game in order to maximize the expected payoff. The players’ optimal stopping strategies and payoffs are determined. The numerical results of payoff simulation for different n are reported.
U2 - 10.1007/978-3-031-73365-9_16
DO - 10.1007/978-3-031-73365-9_16
M3 - Paper
SP - 237
EP - 249
T2 - XXIII International Conference Mathematical Optimization Theory and Operations Research
Y2 - 30 June 2024 through 6 July 2024
ER -
ID: 128691577