Question

on and Vlad are two players in an indefinitely repeated Prisoners Dilemma Game. Let the

probability that the game continues one more round be “q”. Assume both players are risk neutral

and have a common per-period discount rate of “d”.

1. From this information alone, what must be true about the range of possible values for d and q?

2. Is mutual defection a Nash Equilibrium (NE)? If so, under what conditions is mutual

defection a NE? (HINT: Consider Don’s best response when Vlad’s strategy is “always defect”).

3. Identify the mathematical conditions under which mutual cooperation is a NE. State this

condition in an intuitive and easy to understand sentence. (HINT: assume both players use the

“Grim Trigger” strategy).

Answer #1

2. Nash Equilibrium is one of the most important concepts of game theory developed by John Nash which was an American mathematician. It is an important concept within game theory where optimum consequence of a game is there when no incentive to depart from their preliminary strategy.

Mutual defection is a Nash Equilibrium of Prisoner's Dilemma which is a common situation analyzed in game theory.

In Prisoner's Dilemma game two players (as criminals) are arrested and each prisoner get a chance to either betray the other by appearing that the other committed the crime or collaborate by remaining silent. If both prisoners betray each other then they get five years in prison. In the mentioned question if Don and Vlad betray each other then it can be claimed Mutual Defection as Nash Equilibrium.

Let α1, α2 ∈ R. Consider the following version of
prisoners’ dilemma (C
means “Confess” and N means “Do not confess”):
2
C N
1
C 0, 0 α1, −2
N −2, α2 5, 5
Suppose that the two players play the above stage game infinitely
many times. Departing
from our in-class discussion, however, we assume that for each i ∈
{1, 2}, player i discounts
future payoffs at rate δi ∈ (0, 1), allowing δ1 and δ2 to
differ....

Consider a two-player game between Child’s Play and Kid’s
Korner, each of which produces and sells wooden swing sets for
children. Each player can set either a high or a low price for a
standard two-swing, one-slide set. The game is given as below:
Kid’s korner
High price
Low price
Child’s play
High price
64, 64
20, 72
Low price
72, 20
57, 57
a. Suppose the players meet and make price decisions only once.
What is the Nash equilibrium...

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INNOVATION
Deep Change: How Operational Innovation Can Transform Your
Company
by
Michael Hammer
From the April 2004 Issue
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8.95
In 1991, Progressive Insurance, an automobile insurer based in
Mayfield Village, Ohio, had approximately $1.3 billion in sales. By
2002, that figure had grown to $9.5 billion. What fashionable
strategies did Progressive employ to achieve sevenfold growth in
just over a decade? Was it positioned in a high-growth industry?
Hardly. Auto insurance is a mature, 100-year-old industry...

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