During a recent deep-think, I have refined a previously posted idea.
Suppose we sharpen the information game to the following:
A group of 20 players posts a list of characteristics about themselves
along with their game-identities. From this group of twenty,
three players, Alpha, Bravo and Charlie, with an all-knowing,
all-seeing, no-talking referee Delta, conduct a friendly competition
under the following conditions, after each ante-ing up 100 dollars:
0) Alpha tries to send Charlie a piece of information, working
only thru their mutual friend Bravo, without knowing the identity
of Charlie. Alpha is simultaneously attempting to ascertain the
identity of Charlie.
1) Charlie attempts to ascertain the information while denying
it to Bravo, who is also trying to get the information.
2) Messages passed from Alpha to Charlie or back again
pass unchanged thru Bravo. Alpha and Charlie may query
each other, however Charlie wishes to hide her identity from
Alpha, as part of the game.
3) This works like the popular board game "Clue" in which
any of the three players may appeal to Delta at any time to
adjudicate the outcome. In general, the first player to submit
a correct piece of information to Delta wins 200, and the other two
players split the remaining 100. If any player submits an incorrect
piece of information, she wins nada and the remaining two players
split the 300 clams.
4) The exception is thus: as previously stated, Alpha is sending
a piece of info to an unknown Charlie thru known Bravo without
Bravo discovering the info. If Alpha successfully passes the
info to Charlie and Charlie submits same to Delta and is
found to be correct, Charlie wins 150 and Alpha gets 150.
If Bravo intercepts the info and submits before Charlie, then
Bravo gets 200 and Alpha and Charlie get 50 each.
5) Any player may choose to end the round at any time, at
which time each player receives their ante 100 back.
With these six rules, is there a means of encoding or some
winning strategy? Is it clear that any of the three players has
an advantage? How can the ante/payoff matrix be modified to
make the game equitable? spike
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