The Von Neuman solution: Each player rolls a die each time. 1-2 Scissors, 3-4 Paper, 5-6 stone. If I do that, then whatever you do I will, on average, win 1/3rd of the time, lose 1/3rd, tie 1/3rd, for an expected payoff of 0. I cannot do better than that because you can hold my payoff to zero by playing that strategy, and you cannot do better because I can hold yours to zero by playing that strategy. So we have a mixed strategy that is the VN solution
First Step
Second Step
At the bottom of the tree, player 2 on the second round knows that he is better off confessing, so we can eliminate the "don't confess" option (grey on First Step figure), and similarly for player 1. After eliminating those branches, we are left with the Second Step figure, and each party, knowing what will happen at the second play, can calculate he is better off confessing. An example of subgame perfect equilibrium.
B. Base punishment upon what the court believes the criminal thought the risks were.
C. Base punishment upon what happens.
VII. Regulation of Sex. Why do we do it? Adultery laws, fornication laws, ...
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No Liability |
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Care by Tank |
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No |
Yes |
Yes |
Yes |
Tank Act Level |
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No |
Yes |
No |
Yes |
Care by Car |
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Yes |
No |
Yes |
Yes |
Car Act Level |
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Yes |
No |
Yes |
No |