There are two competing companies in the car sector, say Suzuki
and Nissan, that have chosen to offer a new car model. Each should
decide whether to offer payment facilities to its customers, an
action that will increase its market share, but at the same time
will generate a cost for the company. Both companies prefer not to
offer such payment facilities, but each company fears that if its
rival offers them, then it will lose many customers. In particular,
each of these two companies’ profits will be 400 if both offer
payment facilities and 600 if none offers them. If a company does
not offer payment facilities and its rival offers them, then it
will obtain a profit of 300, while its rival will obtain a profit
of 800. Suzuki and Nissan decide simultaneously whether to offer
payment facilities or not to their customers.
a) Represent this game in matrix form and find its Nash
equilibrium.
b) Characterize the type of the game and argue why the equilibrium
in (a) is also equilibrium in strictly dominant strategies.
c) Now Suzuki decides first whether to offer payment facilities or
not and then Nissan takes its decision. Represent the game in
extensive form and find its subgame perfect Nash equilibrium. d) If
the game in which Suzuki and Nissan decide simultaneously whether
to offer payment facilities or not is repeated two times, do you
think that these companies will obtain higher profits per period?
Argue why or why not.
e) If the game in (d) is repeated instead for an infinite number of
times and both companies have a discount factor ?=0.8, will your
answer in (d) be the same? Explain in detail.
I NEED ONLY QUESTION e, thank you
Payoff matrix
Suzuki/ Nissan | Offer | don't offer |
Offer | (400*,400•) | (800*,300) |
Don't offer | (300,800•) | (600,600) |
D) in simultaneous Game
NE: both firms offer payment facilities
E) infinitely repeated game ;
using Grim Trigger strategy
if both Firms Cooperate & decide dont offer payments, then both could earn higher payoff, as compared to NE
so if both Cooperate, the present discount value of payoffs
Vc = 600 + 600d + 600d2 + 600d3 + ...
( Let d is discount factor )
Vc = 600/(1-d)
= 600/.2
Vc = 3000
if any one deviates , while other is Cooperating, then it gets 800,
Next punishment starts from next period onwards, where both will play only NE of stage game, next period onwards
So present discount value of cheating payoff
Vd = 800 + 400d + 400d2 + 400d3 +....
= 800 + 400d/(1-d)
= 800 + 400*.8/.2
= 800 + 1600
= 2400
Now as Vc > Vd
so Cooperation is possible,
a new eqm , where both ;dont offer payment , could be sustained as SPNE of infinitely repeated game
There are two competing companies in the car sector, say Suzuki and Nissan, that have chosen...
There are two competing companies in the car sector, say Suzuki and Nissan, that have chosen to offer a new car model. Each should decide whether to offer payment facilities to its customers, an action that will increase its market share, but at the same time will generate a cost for the company. Both companies prefer not to offer such payment facilities, but each company fears that if its rival offers them, then it will lose many customers. In particular,...
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please answer all questions!
it
should be no problem with 1st question.
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