Vikings Agnes and Bjorn have just pillaged a village and collected $100 worth of

Question

Vikings Agnes and Bjorn have just pillaged a village and collected $100 worth of loot that they have to decide how to split. They play the following game: each Viking simultaneously announces a demand, a for Agnes and b for Bjorn, where a and b must be real numbers in [0,100]. If a+b 100, then they have an agreement: Agnes takes a, Bjorn takes b, and they leave town. Any leftover money stays with the villagers. On the other hand, if they make incompatible demands (i.e., if a+b > 100), then their disagreement leaves enough time for help to arrive from the next village, forcing Agnes and Bjorn to leave with zero.

If each Viking's payoff is just the amount of loot that he or she gets, find all pure strategy Nash equilibria of the bargaining game between Agnes and Bjorn.

Now suppose that Bjorn is soft-hearted and doesn't want to leave the villagers destitute. Now his payoff is

b+10                if a+b 99

b if a+b > 99 and a+b 100

0                      if a+b > 100

(That is, Bjorn gets a `warm glow' benefit of +10 if at least $1 is left for the villagers.) Agnes' payoff doesn't change -- she still gets a if a+b 100 and 0 otherwise. Calculate Bjorn's best response function BRB(a) and determine all pure strategy Nash equilibria of this new game.

c. In part (b), the only way for Bjorn to donate to the villagers was to leave money on the bargaining table. If we gave him the option to collect b in the bargaining game and then leave $1 behind on his way out of town, would the outcome change? Explain briefly.

Explanation / Answer

a free market is an idealized system in which the prices for goods and services are determined by the open market and by consumers. In a free market the laws and forces of supply and demand are free from any intervention by a government, by a price-setting monopoly, or by other authority. Proponents of the concept of free market contrast it with a regulated market, in which a government intervenes in supply and demand through various methods - such as tariffs - used to restrict trade and to protect the local economy. In an idealized free-market economy, prices for goods and services are set freely by the forces of supply and demand and are allowed to reach their point of equilibrium without intervention by government policy.

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