Question

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.

Answer 1

This is a popular strategy (Game Theory), being applied to a lot of economic models

I will make you understand the problem easily

As there are two groups here making a decision to build a weapon or not it is there decision to maintain status quo by honoring the treaty.But you can't make a decision in the present state as You don't know whether the other group making a weapon or not.

So the calculations are as follows ->

If you are building weapon you will get a victory and win 20 points but as building weapon costs you 10 units the total gain of yours is 10 units

when none of the group build weapon they neither lose or gain so that total will be 0.

If both are building weapons they will only lose money to build the weapon and neither of gain anything so for both of them total will be -10.

and the conquered unit will lose 100 units.This rule applies to the other group too.Now we will build the reward matrix

the right side value shows for the Pro technologists and the left side values show for the neo Luddites

		Pro Technologist
	Strategy	No weapon	Build Weapon
Neo Luddites	No weapon	0,0	-100,10
	Build weapon	10,-100	-10,-10

b) This is a prisoners dilemma because regardless of what the other group does its always in the individual groups interest to build. See if pro technology builds then the neo luddites will build as well as you can see from the matrix when pro is building neo is having -100 and below it when neo builds it has -10 so obviously -10 is greater than -100 so when Pro is Building Neo should build too and this case is also applicable similar way to Pro too.

c) there is no nash equilibrium point possible for this result.

d)Yes this problem discuss that signing treaty for maintaining peace may lead to arm race as we can see from the table that for both the groups when the opponent group is not building weapon the building weapon group gaining profit which may lead them to think of making weapon as well as winning a reward. This will lead the groups to think of making arms deal and building weapons as both are not sure of opponent's strategy