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| 1 | +EFG 2 R "Princess Bride signaling game (from Watson)" { "Wesley" "Prince" } |
| 2 | +"This game is Exercise 29.6 from Watson [^Wat13], based on a scene from |
| 3 | +the Rob Reiner film, _The Princess Bride_: |
| 4 | + |
| 5 | +Wesley (the protagonist) confronts the evil prince Humperdinck. Wesley |
| 6 | +is one of two types: weak or strong. Wesley knows whether he is weak or |
| 7 | +strong, but the prince only knows that he is weak with probability 1/2 and |
| 8 | +strong with probability 1/2. Wesley is lying in a bed in the prince's |
| 9 | +castle when the prince enters the room. Wesley decides whether to get out |
| 10 | +of bed or stay in bed. The prince observes Wesley's action but does not |
| 11 | +observe Wesley's type. The prince then decides whether to fight or |
| 12 | +surrender to Wesley. The payoffs are such that the prince prefers to fight |
| 13 | +only with the weak Wesley, because otherwise the prince is an inferior |
| 14 | +swordsman. Also, the weak Wesley must pay a cost to get out of bed. |
| 15 | + |
| 16 | +In the game in this file, the cost the weak Wesley pays to get out of bed |
| 17 | +is set to 2. |
| 18 | + |
| 19 | +[^Wat13]: Watson, Joel. (2013) Strategy: An Introduction to Game Theory, |
| 20 | + third edition. W. W. Norton & Company. |
| 21 | +" |
| 22 | + |
| 23 | +c "" 1 "" { "Strong" 1/2 "Weak" 1/2 } 0 |
| 24 | +p "" 1 1 "" { "Up" "Stay" } 0 |
| 25 | +p "" 2 1 "" { "Surrender" "Fight" } 0 |
| 26 | +t "" 1 "Outcome1" { 1, 0 } |
| 27 | +t "" 2 "Outcome2" { 0, -2 } |
| 28 | +p "" 2 2 "" { "Surrender" "Fight" } 0 |
| 29 | +t "" 3 "Outcome3" { 1, 0 } |
| 30 | +t "" 4 "Outcome4" { 0, -2 } |
| 31 | +p "" 1 2 "" { "Up" "Stay" } 0 |
| 32 | +p "" 2 1 "" { "Surrender" "Fight" } 0 |
| 33 | +t "" 5 "Outcome5" { -1, 0 } |
| 34 | +t "" 6 "Outcome6" { -3, 1 } |
| 35 | +p "" 2 2 "" { "Surrender" "Fight" } 0 |
| 36 | +t "" 7 "Outcome7" { 1, 0 } |
| 37 | +t "" 8 "Outcome8" { -1, 1 } |
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