Hello This assignment is a little bit different than some of

Hello! This assignment is a little bit different than some of the previous ones we’ve seen. In this particular assignment, what’s different is I’m asking you to place yourself within a hypothetical experiment. The experiment is concerning a game that I describe in the lecture video as well as in the slides. It’s technically a discrete Bertrand oligopoly pricing game. Anyway, I’m asking you to select a number, and to imagine being hypothetically randomly matched with another student. Whoever has the lowest number of that pair wins. If you tie, you each get a value equal to half your number. If you have the high number you get zero. So now tell me: What would be your strategy? Which number would you pick, and why? In the second part, I ask you to consider a variation on the formal game in the lecture slides and video. Here the game has the same general format, but I’ve adjusted the cost structure. Your job is to determine: How does it change? How do the payoffs change? How does the strategy change if at all? Most importantly, I need you to find the Nash equilibria of the new game. To help you, recall the definition of a Nash equilibrium. A Nash equilibrium is a strategy profile, in this case a selection of numbers from each player, such that no one has a profitable unilateral deviation—so no one would want to select a different number!

Solution

The number that I would pick in such a scenario would be equal to 0. Since any number that is higher than 0 might give me 0 anyway as there are chances of some pair picking up a lower number. Hence 0 will be my optimal strategy.

The Nash equilibrium in a discrete bertrand oligopoly game is when prices equal to the marginal cost of the firms involved because any price above that will lose all customer and below it will yield losses

For perfect comparison, please provide the game in your lecture slides as well