Benie and Leona were arrested for money laundering and were

Benie and Leona were arrested for money laundering and were interrogated separately by the police. Bernie and Leona were each presented with the following, independent offers. If one confesses and the other doesn\'t, the one who confesses will go free and the other will receive a 20-year prison sentence, and if both confess, each will receive a 10-year prison sentence. Bemie Leona both know that without any confessions, the police only have enough evidence to convict them of the lesser crime of tax evasion, and each would then receive a 2-year prison sentence. Use the above information to fill in the blanks in the payoff matrix for Bernie and Leona. Leona Confess Do Not Confess Confess Bernie Do Not Confess 2 years 20 years ree 10 years The dominant strategy is for ?A. Bernie and Leona to confess and receive a two-year sentence B. neither Bernie nor Leona to confess and they both receive a two-year sentence. O C. Bernie and Leona to confess and receive a ten-year sentence. O D. only Leona to confess and go free. while Bernie gets a sentence of 20 years.

Solution

As according to the given explaination of the game, The payoff matrix for Bernie and Leona :

Dominant strategy is the best respons of a player irrespective of what other play is doing.

IT means if we find a strategy which is best for a player and he will choose this strategy even if the other player chooses anything. So it means it is the dominant strategy for that player.

For Bernie :

IF Leona Confess - the best strategy for Bernie is to confess because if Bernie confess he will receive a 10 years sentence but if he do not confess, he will receive a 20 - years sentence. So best response of Bernie is to confess when Leona confesses.

If Leona Do not Confess - The best strategy for Bernie is to confess because if he confess he will go free, and if he do not confess he will receive a 2 years sentence. So the best response of Bernie is to confess when Leona do not confess.

It means the dominant strategy for Bernie is to confess because his best response is to confess irrespective of what Leona do.

Similalry, For Leona :

IF Bernie Confess - the best strategy for Leona is to confess because if she confess she will receive a 10 years sentence but if she do not confess, she will receive a 20 - years sentence. So best response of Leona is to confess when Bernie confesses.

If Bernie Do not Confess - The best strategy for Leona is to confess because if she confess she will go free, and if she do not confess she will receive a 2 years sentence. So the best response of Leona is to confess when Bernie do not confess.

It means the dominant strategy for Leona is to confess because his best response is to confess irrespective of what Bernie do.

So if both confesses both will receive a ten - year sentence.

Correct option is C. Bernie and Leona to confess and receive a ten - year sentence.

	Leona
		Confess	Do not Confess
Bernie	Confess		10 years		10 years
10 years		Free
Do not Confess		Free		2 years
20 years		2 years