Abstract
We study a recently introduced extension of normal form
games with a phase before the actual play of the game, where each player
can make binding offers for payments of utility to the other players after
the play of the game, contingent on the recipient playing the strategy
indicated in the offer. Such offers transform the payoff matrix of the
original game and allow for some degree of cooperation between rational
players while preserving the non-cooperative nature of the game. We
focus on 2-player negotiations games arising in the preplay phase when
offers for payments are made conditional on a suggested matching offer of
the same kind being made in return by the receiver.We study and analyze
such bargaining games, obtain results describing their possible solutions
and discuss the degrees of efficiency and fairness that can be achieved in
such negotiation process depending on whether time is valuable or not.