The Smokers

To make a cigar, one needs three ingredients: paper, matches, tobacco.

  • Alice has an infinite supply of paper.
  • Bob has an infinite supply of matches.
  • Carol has an infinite supply of tobacco.

The dealer arbitrarily puts two ingredients on the table and the agents take them and combine with their own supplies to make a cigar and smoke it. The dealer again puts two arbitrary ingredients on the table when one of the agents has finished smoking.

Which of the two following ways should the agents desirably behave in?

(A)

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Alice:
    1. Wait until there are matches on the table - grab them.
    2. Wait until there is tobacco on the table - grab it.
    3. Make cigar. Smoke.
    4. Loop

Bob:
    1. Wait until there is paper on the table - grab it.
    2. Wait until there is tobacco on the table - grab it.
    3. Make cigar. Smoke.
    4. Loop

Carol:
    1. Wait until there are matches on the table - grab them.
    2. Wait until there is paper on the table - grab it.
    3. Make cigar. Smoke.
    4. Loop

(B)

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Alice:
    1. Wait until there are both matches and tobacco on the table - grab them both.
    2. Make cigar. Smoke.
    3. Loop.

Bob:
    1. Wait until there are both paper and tobacco on the table - grab them both.
    2. Make cigar. Smoke.
    3. Loop.

Carol:
    1. Wait until there are both matches and paper on the table - grab them both.
    2. Make cigar. Smoke.
    3. Loop.

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