info game

From: Spike Jones (
Date: Fri Feb 25 2000 - 23:15:29 MST

In the info game, where Alpha (A) is trying to send message (I)
Charlie (C) without Bravo (B) getting the message, and
simultaneously attempting to ascertain the identity of Charlie
from a list of 20 possible randomly chosen players.

label ending condition
u. A knows C
v. A knows not C
w. B knows I
x. B knows not I
y. C knows I
z. C knows not I

With this code, if the round ends and Alpha manages to send the
info to Charlie without Bravo figuring it out, and Alpha has not
managed to ascertain the identity of Charlie, then ending conditions
v and x and y are true, called vxy. Then the following outcomes
are possible:

1) uwy
2) uwz
3) uxy
4) uxz
5) vwy
6) vwz
7) vxy
8) vxz

Nowthen, condition 8 is the starting position and is listed as an
ending possiblity because any of the players can stop the round at
any time. First lets agree that these are all the possible outcomes,
then we can perhaps write a sim to determine the logical payoffs
with each. The logical payoff for ending condition 8 would be
100 to each of the three players.

So this is my first guess at a payoff matrix:

outcome A gets B gets C gets

1) uwy 100 100 100
2) uwz 150 150 0
3) uxy 150 0 150
4) uxz 200 50 50
5) vwy 0 150 150
6) vwz 50 200 50
7) vxy 50 50 200
8) vxz 100 100 100

Nowthen, if each outcome is equally likely, does this
payoff matrix look about right?


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