Walker and Texas Ranger are rational, self-interested bad guys (allegedly), who

Question

Walker and Texas Ranger are rational, self-interested bad guys (allegedly), who are imprisoned in separate cells of a dark and spooky dungeon. Naturally, it follows that they find themselves in a Prisoners’ Dilemma: Each may deny or confess to their crime. If both deny, each receives 1 year in the dungeon; if both confess, each receives 5 years in the dungeon. If their strategy choices differ, the confessor goes free while the denier receives 20 years in the dungeon. Suppose Walker is willing to pay $5,000 for each year by which he can reduce his sentence below 20 years. A corrupt jailer tells Walker that before he chooses his strategy, he can tell him exactly which strategy Texas Ranger will choose. How much is this information worth to Walker? Explain in a few sentences.

Explanation / Answer

Consider the given problem here there are two players “walker” and “Texas Ranger” both of them have two strategy choice. Now, let’s assume that both of the player don’t have any information about the other player, what the other player will choose. So, here if “walker” choose “confess”, then the optimum choice for “texas ranger” is “confess”, because (-5) > (-20). Similarly, if “walker” choose “deny”, then the optimum choice for “texas ranger” is “confess”, because 0 > (-1). So, here in both the cases “confess” is the best option for “texas”. Similarly, with the same logic we can show that “confess” is the best option for “walker” also.

So, under this case “confess, confess” is the solution of the game. So, here both the player will choose “confess” and the game end up.

Let’s assume that a corrupt jailer will give the information what “texas” will choose. So, here if “texas” choose “confess”, then the optimum choice for “walker” is “confess”, because (-5) > (-20). Similarly, if “texas” choose “deny”, then the optimum choice for “walker” is “confess”, because 0 > (-1). So, here in both the cases “confess” is the best option for “walker” it doesn’t matter what “texas” has chosen, => any information regarding “texas” is not worth full, because in both cases the optimum choice for “walker” is “confess”.

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