A Discrete-Time Homing Problem with Two Optimizers
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsNo comments. It is good to publish.
Author Response
See attached file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe article can be published in its current form
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsIn the studied stochastic difference game, one player strives to minimize the time that a controlled one-dimensional symmetric random walk, denoted as {Xn, n = 0, 1, ...}, stays within the continuation region C, characterized as {1, 2, ...}. On the other hand, the second player aims to extend the stay within region C. The game initiates with a value of X0 = x > 0 and terminates once Xn reaches a value less than or equal to 0. A detailed formula for the game's value function is presented, from which the optimal strategy is discerned, and particular challenges are explicitly resolved.
Page 1, line 19: Can you clarify the context in which "optimizers" are mentioned? As it appears, there is no direct optimization process described.
Page 1, line 24: The role of the parameter lambda is not clearly defined. Please elucidate its significance and application within the context.
Page 2, equation 6: Please describe how the DPE functions and its relevance.
Page 3, Remark 5: The parameter lambda is mentioned again without clear context. A more thorough explanation is needed to clarify its meaning and application.
Page 4, line 90: The origin of your boundary conditions is not specified. Could you detail their derivation or reference?
General Comment: The paper lacks a proper introduction to stochastic difference games and does not delve into the game-theoretic implications in the conclusion. It is essential to specify the nature of this game. What kind of equilibrium can be derived from it? Is the identified optimum also considered an equilibrium within the game's context? If so, how does this optimum function as a game equilibrium? Conversely, what qualifies it as a game if it is not an equilibrium? The audience, being keen on game theory, would greatly benefit from these clarifications.
Comments for author File: Comments.pdf
Author Response
See attached file.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
Comments and Suggestions for AuthorsThank you for the updates.
Comments on the Quality of English LanguageI have no comment.
