This question is about the game theory in economics. Please can anyone answer the following question step by step elaborately? Exercise IV.5.) - Imperfect informationLobbyist 1 considers whether to spend money for lobbying for a new bill in favor ofhis interest group or not. If he invests, lobbyist 2 from the opposite interest groupwill also join in investing into lobbying. If lobbyist 1 chooses not to lobby, the gameends, and both groups receive a payoff of 2. If he decides to lobby, both lobbyistssimultaneously decide between spending a high or a low amount of money. If bothchoose a high amount or both choose a low amount, the bill will not be passed andboth groups end up with a payoff of zero. If lobbyist 1 chooses a high amount andlobbyist 2 a low amount, the bill will be passed in favour of lobbyist 1, leaving himwith a payoff of 3, while lobbyist has a payoff of 1 (a bill is better than no bill).Iflobbyist 1 chooses a low amount and lobbyist 2 a high amount, then lobbyist 1 hasa payoff of 1 and lobbyist 2 a payoff of 3.(a) Represent this game as a normal-form and an extensive-form game(b) Solve for all subgame perfect Nash equilibria in pure and mixed strategies

Given, Two Players : Lobbyist1 and Lobbyist 2 Lobbyist1's Strategies : To Spend and Not to Spend…

Answered: Lobbyist 1 considers whether to spend…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.15P

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This question is about the game theory in economics. Please can anyone answer the following question step by step elaborately?

Exercise IV.5.) - Imperfect information
Lobbyist 1 considers whether to spend money for lobbying for a new bill in favor of
his interest group or not. If he invests, lobbyist 2 from the opposite interest group
will also join in investing into lobbying. If lobbyist 1 chooses not to lobby, the game
ends, and both groups receive a payoff of 2. If he decides to lobby, both lobbyists
simultaneously decide between spending a high or a low amount of money. If both
choose a high amount or both choose a low amount, the bill will not be passed and
both groups end up with a payoff of zero. If lobbyist 1 chooses a high amount and
lobbyist 2 a low amount, the bill will be passed in favour of lobbyist 1, leaving him
with a payoff of 3, while lobbyist has a payoff of 1 (a bill is better than no bill).If
lobbyist 1 chooses a low amount and lobbyist 2 a high amount, then lobbyist 1 has
a payoff of 1 and lobbyist 2 a payoff of 3.
(a) Represent this game as a normal-form and an extensive-form game
(b) Solve for all subgame perfect Nash equilibria in pure and mixed strategies

Definition Definition Economic decision-making framework that analyzes how different players optimize their outcomes with given pay-offs corresponding to their available strategies. The assumptions of game theory are: The number of players or competitors are finite/limited; All participants are rational The rules of the game are known to every player; and Each participant has a finite set of actions. A common way in which game theory is presented as an ( m x n ) matrix in which m represents the strategies of row player and n represents the strategies of column player. There are several limitations of game theory: Many businesses have a large number of competitors, and selecting an optimal strategy in these circumstances is difficult; Real-life business operating environments are full of uncertainty and difficult to model as a game theory; and The assumption of rationality and utility maximization isn't always an accurate portrayal of human nature.

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