Two firms are planning to sell 10 or 20 units of their goods...

Name: Problem 1, Chapter 14: Microeconomics
Uploaded: 2022-02-11T21:20:08-08:00
Duration: 5 min
Channel: Niamat Khuda
Description: Two firms are planning to sell 10 or 20 units of their goods and face the following profit matrix: a. What is the Nash equilibrium if both firms make their decisions simultaneously? b. Draw the game tree if Firm 1 can decide first. What is the outcome? Why? c. Draw the game tree if Firm 2 can decide first. What is the outcome? Why?

Two firms are planning to sell 10 or 20 units of their goods and face the following profit matrix: a. What is the Nash equilibrium if both firms make their decisions simultaneously? b. Draw the game tree if Firm 1 can decide first. What is the outcome? Why? c. Draw the game tree if Firm 2 can decide first. What is the outcome? Why?

Two firms are planning to sell 10 or 20 units of their goods and face the following profit matrix: a. What is the Nash equilibrium if both firms make their decisions simultaneously?
b. Draw the game tree if Firm 1 can decide first. What is the outcome? Why?
c. Draw the game tree if Firm 2 can decide first. What is the outcome? Why?

Key Concepts

Subgame Perfect Equilibrium

Subgame perfect equilibrium refines Nash equilibrium for sequential games by requiring that players’ strategies constitute a Nash equilibrium in every subgame of the original game. This concept ensures that the strategies are credible and optimal at every point in the game, eliminating non-credible threats.

Nash Equilibrium

A Nash equilibrium is a strategy profile where no player can improve their payoff by unilaterally deviating from their chosen strategy. It captures the idea that each player’s decision is optimal given the other players’ decisions, ensuring that every player’s decision is a best response to the others.

Simultaneous Games

Simultaneous games are those in which all players choose their strategies at the same time without knowing the actions chosen by the other players. In a simultaneous move setup, the strategic challenge is to anticipate the opponents’ choices while committing to the strategy that maximizes one’s own payoff based on these expectations.

Sequential Games

Sequential games involve players making decisions one after the other, with later players having some knowledge of the earlier players’ actions. This structure introduces timing into the strategic analysis, allowing the first mover to potentially influence the subsequent choices of the other players.

Game Trees

Game trees are graphical representations of sequential or extensive-form games. They illustrate the order of moves, the choices available at each decision point, and the payoffs received at the end of each branch of the game, helping to analyze strategic decision-making step by step.

Transcript

00:04 Hey guys, let's two problem one.

00:06 In this problem, we need to find out what is the nash equilibrium.

00:11 If both the firms make their decision simultaneously, we need to draw the game tree if one can decide first and what is the outcome.

00:21 And we need to draw the game tree if one two decides first.

00:25 Then what is the outcome? now the nash equilibrium of the simultaneous game in the given matrix are 1020 and 2010.

00:35 Which means that when firm 1 sells 10 units, farm 2 is going to sell 20 units, and vice versa.

00:45 The next one is we need to draw the game tree if firm 1 decides first.

00:50 So we have our game tree here where firm 1 is at the top and it is going to decide first.

00:57 It can decide to sell 10 units or it can decide to sell 20 units.

01:02 When farm 1 decides to sell 10 units, then firm 2 at point b, it can either sell 10 units or 20 units and this is the values that we get.

01:13 And when form 2 at point b, it can either choose 10 or 20, and this is what the values we get.

01:23 Now what is the outcome? here at point a, the firm 2 will choose 20 units.

01:33 The reason is 35 is greater than 30.

01:41 Because 35 is greater than 30, therefore farm 2 is going to choose 20 units.

01:48 And at point b here, firm 2 is going to choose 10 units because now 40 is greater than 20.

01:59 Therefore, we have either 20 or we have 10.

02:04 If firm 2 is at point a, it will choose 20.

02:08 If it is at point b, it will choose point 10.

02:12 Now we need to move backward.

02:14 When we move backward, we have this one.

02:18 Form 1 is going to choose 10 and the outcome is 50 -30 or firm 1 is going to choose 20...

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