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This paper analyses the role of transfer payments and strategic contracting within two-person strategic form games with monetary payoffs. First, it introduces the notion of transfer equilibrium as a strategy combination for which individual stability can be supported by allowing the possibility of transfers of the induced payoffs. Clearly, Nash equilibria are transfer equilibria, but under common regularity conditions the reverse is also true. This result typically does not hold for finite games without the possibility of randomisation, and transfer equilibria for this particular class are studied in some detail. The second part of the paper introduces, also within the setting of finite games, contracting on monetary transfers as an explicit strategic option, resulting in an associated two-stage contract game. In the first stage of the contract game, each player has the option of proposing transfer schemes for an arbitrary collection of outcomes. Only if the players fully agree on the entire set of transfer proposals, the payoffs of the game to be played in the second stage are modified accordingly. The main results provide explicit characterisations of the sets of payoff vectors that are supported by Nash equilibrium and virtual subgame perfect equilibrium, respectively. [ABSTRACT FROM AUTHOR]