“The mathematical analysis is simple: Player 2 should always accept”—that is incorrect. As the game is defined, players are equal. Player Two wields the obvious veto power by not accepting a proposal he doesn’t like. Player One has a no less effective veto power by not advancing a proposal he doesn’t like in the first place. Players communicate about the proposals before the match, which effectively turns it into a infinitely repeated game.
Asymmetry only arises if there is no prior communication. Only in that case Player One has an advantage, even if we ignore any “feelings”, play rationally, and not allow taking future rounds into consideration (i.e. only play once).
“The mathematical analysis is simple: Player 2 should always accept”—that is incorrect. As the game is defined, players are equal. Player Two wields the obvious veto power by not accepting a proposal he doesn’t like. Player One has a no less effective veto power by not advancing a proposal he doesn’t like in the first place. Players communicate about the proposals before the match, which effectively turns it into a infinitely repeated game.
Asymmetry only arises if there is no prior communication. Only in that case Player One has an advantage, even if we ignore any “feelings”, play rationally, and not allow taking future rounds into consideration (i.e. only play once).