Use the folllowing case for questions tow siblings brad and...

use the folllowing case for questions. tow siblings brad and mike are playing simultaneous hit and tell game. brad can hit mike or not and mike can tatttel o brad or not. relative to no hit or no tattel if brad hits mike and then tattels they both experince loss of 10. No telling gets mike loss of 5 but brad gains 5. if he tattels untruthfully mike gets a gain of 5 but brad loses 5. if they get al;iong no one gets anything. what would be the nash equilibrium? a. hit, tell, b. not hit, tell, c. hit, not tell, d. both B & C?

Transcript

00:01 Use the following normal form game to answer the questions below.

00:05 So here we have this table with player one and player two, the various strategies and their outcomes.

00:11 A, identify the one -shot nash equilibrium.

00:14 Choose one, b -c, ad, ac, or b -d.

00:20 B.

00:21 Suppose the players know this game will be repeated exactly three times.

00:26 Can they achieve payoffs that are better than the one -shot nash equilibrium? yes or no.

00:32 C.

00:34 Suppose this game is indefinitely repeated and the interest rate is 8%.

00:38 Can the players achieve payoffs that are better than the one -shot nash equilibrium? yes or no.

00:44 Suppose the players do not know exactly how many times the game will be repeated, but they do know that the probability the game will end after a given play is is sufficiently low.

00:56 Can players earn more than they could in the one -shot nash equilibrium.

01:00 Yes or no.

01:02 A, if player one chooses strategy a, then player two will be better off choosing strategy c.

01:08 Similarly, if player one chooses strategy b, player two will be better off choosing strategy c.

01:15 In both cases, player two will choose strategy c and therefore c is a dominant strategy for player two.

01:23 Similarly, if player two chooses strategy c, then player one will be better off choosing strategy a.

01:30 Similarly, if player two chooses strategy d, player one will be better off choosing strategy a.

01:37 In both cases, player one will choose strategy a, and therefore a is a dominant strategy for player one.

01:44 As the dominant strategy for player one is strategy a and for player two at strategy c, the one -shot nash equilibrium is a, c.

01:55 B, when both players know the game will be repeated exactly three times, they will still not be able to achieve payoffs that are better than the one -shot nash equilibrium because both the players will know that if the other person cooperates, they are better off if they will not.

02:11 Suppose that the game is initially at ac.

02:15 If player one knows that player two will cooperate and will play strategy d, then player one is better off by not cooperating and playing strategy c, where player one is getting an even higher payoff.

02:28 Similarly, if player one thinks of cooperating, then they will always fear that player two may not cooperate, and thus, player one will end up losing a higher amount.

02:39 This is more likely to happen in the game that happens for the third time...

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