# Nash Equilibrium (Pure Strategy) and Prisoner's Dilemma

Below is a payoff matrix for Intel and AMD. In each cell, the first number refers to AMD's profit, while the second is Intel's.

a. Is there a Nash Equilibrium(s)? Why or why not?

b. Is this an example of the Prisoner's Dilemma? Why or why not?

Intel

AMD Lower Price Same Price Higher Price

Lower Price -2, -6 6, -2 12,-15

Same Price 6,14 9, 8 15, 4

Higher Price -13,7 3, 9 16,20

https://brainmass.com/economics/game-theory/nash-equilibrium-pure-strategy-and-prisoner-s-dilemma-539544

#### Solution Preview

Nash equilibrium can be defined as set of strategies from which no player has incentive to unilaterally change its action because doing so would reduce the player's earnings.

In the payoff matrix below, each cell is in format AMD's Payoff , Intel's Payoff

Hence, in first cell of the Payoff Matrix, [-2,-6], -2 represents AMD's Payoff and -6 represents Intel's Payoff

Intel

AMD Lower Price (L) Same Price (S) Higher Price (H)

Lower Price (L) ...

#### Solution Summary

Solution assumes pure strategy Nash Equilibrium. It provides step by step explanation of Nash Equilibrium then moves on to Prisoner's Dilemma establishing relation between the two along with the example.

Competition, Coordination & Equilibrium

1. Suppose Microsoft can produce a new sophisticated software product. However, it wants to do so only if Intel produces high-speed microprocessors. Otherwise, the software will not sell. Intel, in turn, wants to produce high-speed microprocessors only if there is popular software on the market that requires high-speed processing. Is this a game of competition or coordination? What is the equilibrium?

2. What is the relation between a dominant strategy and a Nash equilibrium?

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