I'm familiar with Game Theory concepts (I took one course at College, but it was rather superficial), but my mathematical skills aren't at the best level though. However, I'd like to hear from more Game Theory savvy people if my idea could be realised.
(1) Is it possible to build a Cake Cutting setting with 3 players wherein 2 have static strategies and goals (called dummies if I'm not mistaken) but the remaining one player is the game-maker - he/she can amend the initial strategy and goals, he/she can choose with whom to cooperate and against whom to play in an iterating game?
(2) Is it possible to build a setting in which the outcome (gain) of one player gets worse with every turn unless that player changes his/her strategy (a race against the clock)?
Thanks in advance!