Consider the following game:
N people each hold a different weighted M-sided die. They each
truthfully declare the weighting of their die, then play the following
game:
1. Each player contributes $1.00 to a pot of winnings
2. Each player rolls their die
3. Whoever rolls the highest number wins. If more than one person rolls
the same highest number, the pot is split between them.


Given the number of players, and the weighting of each player's die,
is there a polynomial-time algorithm to determine each player's
expected value for the game (and if so, what is it)?

Example: 3 players, 2-sided die
Player 1 rolls a '1' with probability 1.0
Player 2 rolls a '2' with probability 1.0
Player 3 rolls a '2' with probability 1.0

In this case, players 2 and 3 always tie when they roll a '2', and
player 1 always loses when he rolls a '1'.

Total pot is $3.00 (each player contributed $1.00)

Expected Value for player 1 is 0
Expected Value for player 2 is 1.5
Expected Value for player 3 is 1.5