SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Games

berit avatar
berit
13 diapositives · 552 Views · Sep 11, 2014

Games. Game 1 Each pair picks exactly one whole number The lowest unique positive integer wins Game 2: Nim Example: Player A picks 5, Player B picks 6, Player A picks 13, Player B picks 19, etc. Game 3 Each pair picks exactly one number The number closest to half the average wins. LUPI.

Games - slide 1
01 / 13Games
1 / 17

Télécharger la présentation

Games
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Games • Game 1 • Each pair picks exactly one whole number • The lowest unique positive integer wins • Game 2: Nim • Example: Player A picks 5, Player B picks 6, Player A picks 13, Player B picks 19, etc. • Game 3 • Each pair picks exactly one number • The number closest to half the average wins

  2. LUPI • Lowest unique positive integer game • The winner is the person that meets the following criteria • Exactly one person picked the number • There is no smaller number in which exactly one person picked that number

  3. LUPI • Example with 20 participants • 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 8, 10, 50, 99, 100 • 0 does not win (three people guessed this) • 1 does not win (six people guessed this) • 2 does not win (two people guessed this) • 3 does not win (two people guessed this) • 4 wins (exactly one person guessed this)

  4. LUPI • Analysis about NE is too complicated for this class • We will not analyze this game, but many of you probably tried to guess the number that others would choose

  5. Nim • Recall rules • Each person must add a whole number from 1 to 10 when it is her/his turn • The person that hits the winning number wins

  6. Nim • If each person plays optimally, the winning number determines who wins • How do we do this? • A method called backward induction • Suppose, for example, we play to 11

  7. Nim to 11 • The first person picks a number between 1-10 • The second person picks 11  winner

  8. Nim to 22 • The first person picks a number between 1-10 • Suppose I act second • How should I act? • If I pick 11, then I know I can win, because I can repeat the same set of steps to guarantee victory • Example  3, 11, 19, 22

  9. Nim, working backwards • Based on the previous logic, if I can pick numbers that are multiples of 11 less than the winning number, I can guarantee victory • This is what I will call the “path to victory”

  10. Nim, working backwards • Examples of paths to victory • 99  88  77  66  55  44  33  22  11 • 100  89  78  67  56  45  34  23  12  1 • In the first game, the first person to act cannot guarantee victory if the other player knows the path to victory • In the second game, the first player can guarantee victory by choosing 1 and then following the path to victory

  11. Pick half the average • Rules: • Each person picks a number from 0 to 100 • The person that picks the number closest to half of the average wins • In case of a tie, the winners split the prize

  12. Pick half the average • If you assume that each player picks a number randomly between 0 and 100, then I know the average is 50, and I should pick 25 • However, it would be irrational for anyone to pick a number over 50, since it cannot win  Should I pick a number over 25?

  13. Pick half the average • I can repeat this thinking an infinite number of times to reach the NE • Everybody should pick 0 • How many people picked… • 0? • A number over 50?