1.) Consider the discrete Bertrand game described in the Oligopoly lecture notes/video. According to the rules...

1.) Consider the discrete Bertrand game described in the Oligopoly lecture notes/video. According to the rules of this game each student selects a number from the set {0,1,2, 3, 4, 5, 6, 7, 8, 9, 10} and is randomly matched with another student. Whoever has the lowest number wins that amount in dollars and whoever has the high number wins zero. In the event of ties, each student receives half their number in dollars. What number would you select if you played this game in our online class? Explain your reasoning.

2.) Continue to consider this discrete Bertrand model, but now assume that each student has a constant cost of 5 that is deducted from all payoffs. So whoever has the low number wins their number, minus 5. Whoever has the high number loses 5 total. In the event of a tie, each student wins an amount equal to their number divided by two, then minus five. Find any Nash equilibria in this game. Explain your reasoning. Hint: It is perfectly fine for both players to have losses in equilibrium! There are more than 1 Nash equilibria.

Expert Solution

Rahul Sunny answered 2 years ago

1.) Consider the discrete Bertrand game described in the Oligopoly lecture notes/video. According to the rules...

1.) Consider the discrete Bertrand game described in the Oligopoly lecture notes/video. According to the rules of this game each student selects a number from the set {0,1,2, 3, 4, 5, 6, 7, 8, 9, 10} and is randomly matched with another student. Whoever has the lowest number wins that amount in dollars and whoever has the high number wins zero. In the event of ties, each student receives half their number in dollars. What number would you select if...

Consider the discrete Bertrand game. According to the rules of this game each student selects a...

Consider the discrete Bertrand game. According to the rules of this game each student selects a number from the set {0,1,2, 3, 4, 5, 6, 7, 8, 9, 10} and is randomly matched with another student. Whoever has the lowest number wins that amount in dollars and whoever has the high number wins zero. In the event of ties, each student receives half their number in dollars. What number would you select if you played this game? Explain your reasoning.

Consider this discrete Bertrand model, but assume that each student has a constant cost of 5...

Consider this discrete Bertrand model, but assume that each student has a constant cost of 5 that is deducted from all payoffs. So whoever has the low number wins their number, minus 5. Whoever has the high number loses 5 total. In the event of a tie, each student wins an amount equal to their number divided by two, then minus five. Find any Nash equilibria in this game. Explain your reasoning. Hint: It is perfectly fine for both players...

As in Example 2.20 of the 01-29 version of the lecture notes, consider the Markov chain...

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1.) Consider the discrete Bertrand game described in the Oligopoly lecture notes/video. According to the rules...

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