Nash Bargaining

A Nash bargaining game is another application of the simultaneous-move, one-shot game. In Nash bargaining, two competitors or players "bargain" over some item of value. In a simultaneous-move, one-shot game, the players have only one chance to reach an agreement.

For example, suppose the board of directors specifies a $1 million profit-sharing pool provided that both management and workers can come to agreement concerning how such profits are to be distributed. For simplicity, assume that this pool can only be distributed in amounts of $0, $500,000, and $1 million. If the sum of the amounts requested by each party totals more than $1 million, neither party receives anything. If the sum of the amounts requested by each party totals no more than $1 million, each party receives the amount requested.

Table 11.3 shows the nine possible outcomes from such a profit-sharing bargaining game. If the workers request $1 million, the only way that they would get any money at all is if management requests nothing. Similarly, if management requests $1 million, the only way they get money is if workers request nothing. If either party requests nothing, Nash equilibrium solutions are achieved when the other party requests the full $1 million. Thus, the ($1 million, $0) and ($0, $1 million) solutions are both Nash equilibriums. However, suppose the workers

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