  We consider an extension of strategic normal form games with a phase of
negotiations before the actual play of the game, where players can make binding
offers for transfer of utilities to other players after the play of the game,
in order to provide additional incentives for each other to play designated
strategies. Such offers are conditional on the recipients playing the specified
strategies and they effect transformations of the payoff matrix of the game by
accordingly transferring payoffs between players. We introduce and analyze
solution concepts for 2-player normal form games with such preplay offers under
various assumptions for the preplay negotiation phase and obtain results for
existence of efficient negotiation strategies of the players. Then we extend
the framework to coalitional preplay offers in N-player games, as well as to
extensive form games with inter-play offers for side payments.
