***** CLEAR ANSWERS AND GRAPHS IF NEEDED******** 1.) Consider the discrete Bertr

Question

***** CLEAR ANSWERS AND GRAPHS IF NEEDED********

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.

Explanation / Answer

Answer-In the above numbers of set {0,1,2,3,4,5,6,7,8,9,10}

Nash equilibrium will be attained when each candidate selects number 10 because in that case, each will recieve 5 dollars. But since, under Bertrand game each candidate selects the number simultaneously so one cannot observe the outcome of other and vice-versa.

While taking decision on number each student will calculate its return. For example : If first student selects 8 and second student selects 3 then, second student gains 3 dollars while first student wins zero. So, selection should be like that in which student have certainity of some winning. In the above scenario, if first student selects 1 by taking into account that (1) other cannot selects 0 then winning will be zero and (2) if student selects more than 1 then, he will earn 1$ and (3) in the case of tie, each willl earn $0.5. That means in all situations, he will win something.

If student selects number 2 then, it will be the case when other student selects 1 then, first student earns zero. Similarly, for every number from 2 to 10 there is uncertainity of earning any amount.

So, If I would be the player of this game then, I will definately select number 1 as outcome of selecting this number is somewhere certain rather than choosing any other number.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.