Game Theory

The neo Luddites and the pro Technologists have publicly agreed to a halt in developing weapons and have cosigned a treaty to that effect. However, they are both engaged in a covert arms race in which each group is assumed to have two possible strategies: develop a new weapon or maintain the status quo. In the vernacular of game theory, the “cooperative action” is to maintain the status quo by honoring the treaty.

This game is based on the assumption that if only one group develops a new weapon then the group with the new weapon will conquer the other. In this case, the conquering group earns a reward of 20 units and the conquered group looses 100 units. It is also assumed that the cost of developing a new weapon is 10 units.

(a) What is the reward matrix for this problem?

(b) Is this a “true prisoner’s dilemma game”? Why or why not?

(c) Is there an equilibrium point for this game? If so, what is this point? If not, explain why.

(d) Does this problem provide any insight into how maintaining the balance of power may lead to an arms race? Discuss your answer.