In the previous chapter, we assumed that the players were able to collect their payoff values to a common basket, and this common payoff was distributed among the players. There are, however, many cases when this is impossible. First, if the payoffs of the different players are not transferable, second, if the players are unable to agree on the mechanism of side payments. In this chapter, solution concepts are introduced in which each player earns his own payoff and receives it directly. In finding any such solution a negotiation process has to take place before reaching an agreement. In order to give sufficient incentive to the players to negotiate and to reach an agreement, very unfavorable payoff values are assigned to the players in case if no agreement is reached. Instead of negotiating on specific strategies, the subject of the negotiation is the received payoff value of each player. For mathematical simplicity we will discuss only two-person conflicts , and the general N-person case will be briefly discussed later.