Assignment - Hicksian Demand and Game Theory
Problem 1 - Consider an agent with utility function u(q1, q2) = q12 + aq22, where q1 is the quantity of good 1, q2 is the quantity of good 2, and a > 0 is a parameter. The agent has income Y > 0 and faces prices p1 > 0 and p2 > 0 of goods 1 and 2 respectively.
Consider only the case 1/p1 > √a/p2. Establish that (a) h(p, u¯) = q(p, E(p, u¯)), (b) find Hicksian demand h(p, u¯) of this agent and (c) her expenditure function E(p, u¯) (in any order).
You do not need to set up a Lagrangian (in fact, I would prefer if you do not), but you have to explain how you have obtained your solution.
Problems 2 and 3 - In Problems 2 and 3, I ask you to formally model a game. "Formally model" means that:
1. You need to argue that this game can be thought of as a simultaneous move game (since we have not studied sequential games, you must find the best arguments for the game being simultaneous move even if you think it is better to model it as a sequential game);
2. Identify players and justify your choice;
3. Identify strategies and justify your choice;
4. Identify payoffs and justify your choice.
The descriptions are intentionally kept close to how the situation would be described by a non-economist (that is, too vague for an economist). You need to make choices and justify them; choices are not unique. Make the choices that would keep the game simple, but capture the story presented to you.
In other words, you can simplify the actual game. For example, in Problem 2, you need to decide how many players you would like to have, how many fingers those players can extend, etc. In Problem 3, you have even larger latitude in making decisions, as you can focus on the decision inside the submarine or the game between the US and Soviet forces. Please keep justifications short and to the point; longer justification is more likely to hurt you than to help you.
You will not need to solve any of those games.
Problem 2 - The problem is based on the game of Morra
Morra is a hand game that dates back thousands of years to ancient Roman and Greek times. Each player simultaneously reveals their hand, extending any number of fingers, and calls out a number. Any player who successfully guesses the total number of fingers revealed by all players combined scores a point.
Formally model the game of Morra (one round only).
Problem 3 - The problem is based on the following story, cited from the Guardian
On 27 October 1962, Vasili Alexandrovich Arkhipov was on board the Soviet submarine B-59 near Cuba when the US forces began dropping non-lethal depth charges. While the action was designed to encourage the Soviet submarines to surface, the crew of B-59 had been incommunicado and so were unaware of the intention. They thought they were witnessing the beginning of a third world war.
Two of the vessel's senior officers - including the captain, Valentin Savitsky - wanted to launch a [ten kiloton nuclear torpedo they had on board].1 According to a report from the US National Security Archive, Savitsky exclaimed: "We're gonna blast them now! We will die, but we will sink them all we will not become the shame of the fleet."
But there was an important caveat: all three senior officers on board had to agree to deploy the weapon. As a result, the situation in the control room played out very differently. Arkhipov refused to sanction the launch of the weapon and calmed the captain down. The torpedo was never fired.
The whole story is too complex to model. Pick some aspect of the story, briefly describe it in your own words (so that the marker knows what you are modeling) and model it as a formal simultaneous move game.
Some of you may find the story horrifyingly similar to the story "Red Alert" by Peter George, written in 1958, which Stanley Kubric turned into a film "Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb", which was completed in 1963.
Attachment:- Assignnment File.rar