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A famous problem: a lady is in the center of the circular lake and a monster is on the boundary of the lake. The speed of the monster is $v_m$, and the speed of the swimming lady is $v_l$. The goal of the lady is to come to the ground without meeting the monster, and the goal of the monster is to meet the lady.

Under some conditions on $v_m,v_l$ the lady can always win. What if these conditions are not satisfied?

Edited: the monster cannot swim.

If the conditions are not satisfied, then monster can always perform a strategy such that the lady will not escape the lake. On the other hand this strategy is not desirable for both of them because they do not reach their goals.

As there was mentioned, this deals with undecidability of the problem. On the other hand, if you imagine yourself to be this lady/monster, you can be interested in the strategy which is not optimal. What is it? If there are such strategies in the game theory?

Edited2: My question is more general in fact. If we have a game with one parameter $v$ when two players $P_1, P_2$ are enemies and if $v>0$ then for any strategy of $P_2$ the player $P_1$ wins.

If $v\leq 0$ then for any strategy of $P_2$ there is a strategy of $P_1$ such that $P_2$ does not win and vice versa. I am interested in this case. From the mathematical point of view as I have understood the problem is undecidable since there is no an ultimate strategy neither for $P_1$ nor for $P_2$. But we are solving somehow these problem IRL.

Imagine that you are a lady in this game - then you would like to win anyway even while knowing that your strategy can be covered by the strategy of the monster. On the other hand, the monster knows that if he will cover all strategies of the lady she will never reach the shore and he will never catch her. I mean they have to develop some non-optimal strategies. I hope now it's more clear.

A famous problem:

A lady is in the center of the circular lake and a monster is on the boundary of the lake. The speed of the monster is $v_m$, and the speed of the swimming lady is $v_l$. The goal of the lady is to come to the ground without meeting the monster, and the goal of the monster is to meet the lady.

Under some conditions on $v_m,v_l$ the lady can always win. What if these conditions are not satisfied?

Edited: the monster cannot swim.

If the conditions are not satisfied, then monster can always perform a strategy such that the lady will not escape the lake. On the other hand this strategy is not desirable for both of them because they do not reach their goals.

As there was mentioned, this deals with undecidability of the problem. On the other hand, if you imagine yourself to be this lady/monster, you can be interested in the strategy which is not optimal. What is it? If there are such strategies in the game theory?

Edited2: My question is more general in fact. If we have a game with one parameter $v$ when two players $P_1, P_2$ are enemies and if $v>0$ then for any strategy of $P_2$ the player $P_1$ wins.

If $v\leq 0$ then for any strategy of $P_2$ there is a strategy of $P_1$ such that $P_2$ does not win and vice versa. I am interested in this case. From the mathematical point of view as I have understood the problem is undecidable since there is no an ultimate strategy neither for $P_1$ nor for $P_2$. But we are solving somehow these problem IRL.

Imagine that you are a lady in this game - then you would like to win anyway even while knowing that your strategy can be covered by the strategy of the monster. On the other hand, the monster knows that if he will cover all strategies of the lady she will never reach the shore and he will never catch her. I mean they have to develop some non-optimal strategies. I hope now it's more clear.

A famous problem: a lady is in the center of the circle lake, the monster is on the boundary of the lake. The speed of the monster is $v_m$, of swimming lady - $v_l$. The goal of the lady is to come to the ground without meeting the monster, the goal of the monster - to meet the lady.

Under some conditions on $v_m,v_l$ the lady can always win. What if this conditions are not satisfied?

Edited: the monster cannot swim.

If the conditions are not satisfied - then monster can always perform a strategy such that the lady will not escape the lake. On the other hand this strategy is not desirable for both of them because they do not reach their goals.

As there was mentioned, this deals with undecidability of the problem. On the other hand, if you imagine yourself to be this lady/monster, you can be interested in the strategy which is not optimal. What is it? If there are such strategies in the game theory?

Edited2: My question is more general in fact. If we have a game with one parameter $v$ when two players $P_1, P_2$ are enemies and if $v>0$ then for any strategy of $P_2$ the player $P_1$ wins.

If $v\leq 0$ then for any strategy of $P_2$ there is a strategy of $P_1$ such that $P_2$ does not win and vice versa. I am interested in this case. From the mathematical point of view as I have understood the problem is undecidable since there is no an ultimate strategy neither for $P_1$ nor for $P_2$. But we are solving somehow these problem IRL.

Imagine that you are a lady in this game - then you would like to win anyway even while knowing that your strategy can be covered by the strategy of the monster. On the other hand, the monster knows that if he will cover all strategies of the lady she will never reach the shore and he will never catch her. I mean they have to develop some non-optimal strategies. I hope now it's more clear.

A famous problem: a lady is in the center of the circular lake and a monster is on the boundary of the lake. The speed of the monster is $v_m$, and the speed of the swimming lady is $v_l$. The goal of the lady is to come to the ground without meeting the monster, and the goal of the monster is to meet the lady.

Under some conditions on $v_m,v_l$ the lady can always win. What if these conditions are not satisfied?

Edited: the monster cannot swim.

If the conditions are not satisfied, then monster can always perform a strategy such that the lady will not escape the lake. On the other hand this strategy is not desirable for both of them because they do not reach their goals.

As there was mentioned, this deals with undecidability of the problem. On the other hand, if you imagine yourself to be this lady/monster, you can be interested in the strategy which is not optimal. What is it? If there are such strategies in the game theory?

Edited2: My question is more general in fact. If we have a game with one parameter $v$ when two players $P_1, P_2$ are enemies and if $v>0$ then for any strategy of $P_2$ the player $P_1$ wins.

If $v\leq 0$ then for any strategy of $P_2$ there is a strategy of $P_1$ such that $P_2$ does not win and vice versa. I am interested in this case. From the mathematical point of view as I have understood the problem is undecidable since there is no an ultimate strategy neither for $P_1$ nor for $P_2$. But we are solving somehow these problem IRL.

Imagine that you are a lady in this game - then you would like to win anyway even while knowing that your strategy can be covered by the strategy of the monster. On the other hand, the monster knows that if he will cover all strategies of the lady she will never reach the shore and he will never catch her. I mean they have to develop some non-optimal strategies. I hope now it's more clear.

A famous problem: a lady is in the center of the circle lake, the monster is on the boundary of the lake. The speed of the monster is $v_m$, of swimming lady - $v_l$. The goal of the lady is to come to the ground without meeting the monster, the goal of the monster - to meet the lady.

Under some conditions on $v_m,v_l$ the lady can always win. What if this conditions are not satisfied?

Edited: the monster cannot swim.

If the conditions are not satisfied - then monster can always perform a strategy such that the lady will not escape the lake. On the other hand this strategy is not desirable for both of them because they do not reach their goals.

As there was mentioned, this deals with undecidability of the problem. On the other hand, if you imagine yourself to be this lady/monster, you can be interested in the strategy which is not optimal. What is it? If there are such strategies in the game theory?

A famous problem: a lady is in the center of the circle lake, the monster is on the boundary of the lake. The speed of the monster is $v_m$, of swimming lady - $v_l$. The goal of the lady is to come to the ground without meeting the monster, the goal of the monster - to meet the lady.

Under some conditions on $v_m,v_l$ the lady can always win. What if this conditions are not satisfied?

Edited: the monster cannot swim.

If the conditions are not satisfied - then monster can always perform a strategy such that the lady will not escape the lake. On the other hand this strategy is not desirable for both of them because they do not reach their goals.

As there was mentioned, this deals with undecidability of the problem. On the other hand, if you imagine yourself to be this lady/monster, you can be interested in the strategy which is not optimal. What is it? If there are such strategies in the game theory?

Edited2: My question is more general in fact. If we have a game with one parameter $v$ when two players $P_1, P_2$ are enemies and if $v>0$ then for any strategy of $P_2$ the player $P_1$ wins.

If $v\leq 0$ then for any strategy of $P_2$ there is a strategy of $P_1$ such that $P_2$ does not win and vice versa. I am interested in this case. From the mathematical point of view as I have understood the problem is undecidable since there is no an ultimate strategy neither for $P_1$ nor for $P_2$. But we are solving somehow these problem IRL.

Imagine that you are a lady in this game - then you would like to win anyway even while knowing that your strategy can be covered by the strategy of the monster. On the other hand, the monster knows that if he will cover all strategies of the lady she will never reach the shore and he will never catch her. I mean they have to develop some non-optimal strategies. I hope now it's more clear.