My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I was sure that such game has well-known name. But my question on math.stackexchange, where I was trying to find any directions for future research, have died without acceptable answer. This makes me suspicious about accidentially stepping on new grounds, so I decided to try again here. Quoting myself Formulating game model more formally per @usul advice:
- Number of players: $N \ge 3$
- Simultaneous moves, each player have full information on previous rounds
- Number of rounds: variable with geometric distribution, not known to the players
- Possible moves: $R$ (bet on red), $B$ (bet on black), $R'$ (fold), $B'$ (fold)
Round outcomes:
$N_R$ - number of $R$ moves, $N_B$ - number of $B$ moves
\begin{array}{c|cccc} & R & B & R' & B' \\ \hline N_R \gt N_B & N_B / N_R & -1 & 0 & 0 \\ N_R \lt N_B & -1 & N_R / N_B & 0 & 0 \\ N_R = N_B & 0 & 0 & 0 & 0 \end{array}
EDIT: Please, take note - I have simplified game description:
- only bets of value $1$ are allowed now
- two different folds have replaced "players can communicate between rounds" requirement
Does anyone know, if this or similar game have been researched already? If yes, any references are welcome. If no, any advices on how to crack this open are welcome too.