The Nash Bargaining Game is a simple two player game used to model bargaining interactions. In the Nash Bargaining Game two players demand a portion of some good (usually some amount of money). If the two proposals sum to less than the total good, then both players get their demand. Otherwise, both get nothing. This game was first suggested by John Nash in his (1950)
Equilibrium Analysis
Strategies are represented in the Nash Bargaining Game by an pair (x, y). x and y are selected from the interval [0, z], where z is the total good. If x+y is equal to or less than z, the first player receives x and the second y. Otherwise both get 0.
There are many Nash equilibria in the Nash Bargaining Game. Any x and y such that x+y=z is a Nash equilibrium. If either player increases her demand, both players receive nothing. If either reduces her demand she will receive less than had she demanded x or y. There is also a Nash equilibrium where both players demand the entire good. Here both players receive nothing, but neither player can increase her return by unilaterally changing her strategy.
Applications
Recently the Nash Bargaining Game has been used by some philosophers and economists in order to explain the emergence of human attitudes toward distributive justice (Alexander 2000; Alexander and Skyrms 1999; Binmore 1998, 2005). These authors primarily use evolutionary game theory in order to explain how individuals come to believe that proposing a 50-50 split is the only just solution to the Nash Bargaining Game.
See Also
References
Alexander, Jason McKenzie (2000) "Evolutionary Explanations of Distributive Justice." Philosophy of Science 67: 490-516.
Alexander, Jason and Brian Skyrms (1999) "Bargaining with Neighbors: Is Justice Contagious" Journal of Philosophy 96(11): 588-598.
Binmore, Ken (1998) Game Theory and The Social Contract Volume 2: Just Playing Cambridge: MIT Press.
Binmore, Ken (2005) Natural Justice
Nash, John (1950) "The Bargaining Problem" Econometrica 18: 155-162.