We used to have a general mafia thread if I'm not wrong. I can't seem to find it so I decided to post this here.
@Osman, @Alen, @Fred, @Klin, @Ocelot, @Voller, @X, @Quetzzzzz, @ALC, @Enron, @Tevez10, @Ragazza, @j0ker, @piotrr (and anybody else who may be interested)
Following our discussion about whether the bodyguard should protect the detective no matter what or he/she should be unpredictable and try to read the Gs' game, I thought perhaps we can model it with game theory. So anybody who knows a little about game theory and is enthusiastic about mafia is more than welcome to contribute
So my opinion was that protecting the detective is a must. I backed it by saying that it takes balls for Gs to go after the bodyguard because chances are the BG is protecting him/herself. Well, this is contradictory to my initial suggestion, because if you, as the BG, always protect the D, Gs will figure it out (in multiple iterations of the game) and will go after you. So I want to see, using game theory, what the best strategy is (for both sides) and where an equilibrium will occur (if there's an equilibrium at all). First I need some help with the payoffs. For this you don't need economics, you just have to love mafia
BG's strategies: {protect the D, protect him/herself}
Gs' strategies: {go after D, go after BG, go after a random player}
Assumption: Gs know who the BG and D are. BG knows that Gs know who the BG and D are.
Civilians' payoffs after Gs' attack:
- Both BG and D are alive. No normal civilian has been killed either (i.e., Gs had gone after a protected target): I thought I'd give a 2 for detective, a 1 for BG, a .5 for both of them being alive at the same time and another .5 for a waste of whacking option for Gs. It's a payoff of 2+1+.5+.5=
4.
- Both BG and D are alive. A normal civilian has been killed: Again a 2 for the D, a 1 for the BG, a .5 for both of them being alive at the same time and a -.5 for a whacked C. It's a payoff of 2+1+.5-.5=
3.
- D is alive, BG is dead: 2 for the D, -1 for the killed BG. It's a payoff of 2-1=
1.
- BG is alive, D is dead: -2 for the killed D, 1 for the BG. It's a payoff of 1-2=
-1.
Gangsters' payoffs after their attack:
- Detective is dead:
4
- BG is dead:
2
- A random C is dead:
1
- No one is dead:
-1
Any idea?