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02/24/2020 12:48 PM by name withheld; Help needed with game theory project about simple-ish hand game

I am trying to do an analysis/examination of a hand game (like rock-paper-scissors) called 007. Here are the rules: Two players count by saying "double-o-seven" and simultaneously do an action when they say "seven". They continue [View full text and thread]

02/23/2020 08:13 PM by name withheld; Help needed with game theory project about simple-ish hand game

I am trying to do an analysis/examination of a hand game (like rock-paper-scissors) called 007. Here are the rules: Two players count by saying "double-o-seven" and simultaneously do an action when they say "seven". They continue [View full text and thread]

02/23/2020 05:05 PM by name withheld; Help needed with game theory project about simple-ish hand game

I am trying to do an analysis/examination of a hand game (like rock-paper-scissors) called 007. Here are the rules:

Two players count by saying "double-o-seven" and simultaneously do an action when they say "seven". They continue doing this (i.e. saying "double-o-seven" and doing an action) until a player wins, or there is a tie. Three actions exist:
Reload (R): You make a thumbs up and point it over your shoulder. Your gun must be reloaded before shooting. Reloads can be accumulated (i.e. you can reload twice in a row to be able to shoot twice in a row).
Shoot (S): You point finger guns at your opponent. You have to have reloaded at least once to do this action. If you shoot at someone who is reloading, they "die" and you won the game.
Block (B): You make an "X" formation with your arms across your chest. If you shoot your opponent while they are blocking, they are safe and the game continues.
The first action players must take is to reload.

My issue with analyzing this game using what I know from game theory basics/fundamentals is that it is a simultaneous and continuous game. I tried making a payoff matrix:

P1/P2 r b s
R (1,1) (1,0) (-5,5)
B (0,1) (0,0) (0,-1)
S (5,-5) (-1,0) (-2,-2)

However, I don't feel this is completely accurate, due to the fact that how many reloads you have is a property that carries over in between actions. This matrix only seems accurate if both players were to only take one action. Using best responses I found that (R,r). (R,b), (B,r) and (B,b) are Nash equilibria, but I'm hesitant to accept this since
Reloading only has utility if you eventually shoot, unlike other example games I've seen where outcomes have a utility (such as a monetary gain) on their own.

The expected utility seems like it should change depending on how many reloads you already have (i.e. reloading is more valuable if you have no reloads, compared to if you already have reloaded 20 times).

My next guess was to use a game tree to represent this game, but I don't think you can since both players act simultaneously.

Any and all help would be much appreciated [Manage messages]