What is the optimal strategy for the Dictionary Game?












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In the Dictionary Game, $n$ players take turns saying English words. The first player starts by choosing any word, which splits the dictionary in two parts. The next player chooses a part and picks a word in that part which will split that part into two smaller parts. This continues until one player is no longer able to find a word.



Note that the players do not actually use a dictionary, they can only say words they know. Additionally, when a player says a word the other player doesn't know, the other players will learn the word and be able to use it in a future round.




  • What is the optimal strategy, assuming the game is played once?

  • What is the optimal strategy, assuming the game is played $m$ times?






game-theory






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    0












    $begingroup$


    In the Dictionary Game, $n$ players take turns saying English words. The first player starts by choosing any word, which splits the dictionary in two parts. The next player chooses a part and picks a word in that part which will split that part into two smaller parts. This continues until one player is no longer able to find a word.



    Note that the players do not actually use a dictionary, they can only say words they know. Additionally, when a player says a word the other player doesn't know, the other players will learn the word and be able to use it in a future round.




    • What is the optimal strategy, assuming the game is played once?

    • What is the optimal strategy, assuming the game is played $m$ times?






    game-theory






    share









    $endgroup$















      0












      0








      0





      $begingroup$


      In the Dictionary Game, $n$ players take turns saying English words. The first player starts by choosing any word, which splits the dictionary in two parts. The next player chooses a part and picks a word in that part which will split that part into two smaller parts. This continues until one player is no longer able to find a word.



      Note that the players do not actually use a dictionary, they can only say words they know. Additionally, when a player says a word the other player doesn't know, the other players will learn the word and be able to use it in a future round.




      • What is the optimal strategy, assuming the game is played once?

      • What is the optimal strategy, assuming the game is played $m$ times?






      game-theory






      share









      $endgroup$




      In the Dictionary Game, $n$ players take turns saying English words. The first player starts by choosing any word, which splits the dictionary in two parts. The next player chooses a part and picks a word in that part which will split that part into two smaller parts. This continues until one player is no longer able to find a word.



      Note that the players do not actually use a dictionary, they can only say words they know. Additionally, when a player says a word the other player doesn't know, the other players will learn the word and be able to use it in a future round.




      • What is the optimal strategy, assuming the game is played once?

      • What is the optimal strategy, assuming the game is played $m$ times?






      game-theory




      game-theory





      share












      share










      share



      share










      asked 4 mins ago









      StefanStefan

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      4446






















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