Thank you! I have not uploaded any videos lately because I do these during my free time, and lately my job hasn't allowed me much of that. More videos to come soon, though!

Thank you for the compliment - I am glad these videos are helpful to you! Thank you for watching!

I am glad this video was helpful to you! Thank you for watching!

Thank you for your feedback - and thank you for watching!

Thank you for the compliment and thank you for watching!

Thank you for watching!

I am glad this was helpful! Thank you for watching and good luck on your exam!

Thank you for watching!

You're welcome! Thank you for watching!

You are correct! Thank you for catching that typo. That's what I get from copying and pasting the equation when I was making the slide!

Thank you for the compliment - and thank you for watching!

Thank you for watching!

You're welcome! Thank you for watching!

Thank you! And thank you for watching!

Ha! Fortunately for you my videos are free (except for the ads - which are not my choice)! Thank you for watching!

Thank you for the sweet compliment! And thank you for watching!

Thank you Frances, you made me smile! I'm glad this video was helpful to you, and thank you for watching!

Thank you for watching - I'm glad it was helpful!

I'm glad you found it helpful, Christopher! Thank you for watching!

Thank you Francis I am glad it was helpful. Thank you for watching!

Thank you for your comment and for watching!

I am glad this video was helpful to you! Thank you for watching!

Hi Sofia - thank you for your question. D is simply a constant in firm 2's cost function. It can be any positive number. Hope this helps. Thank you for watching!

No. We are assuming that player 2 plays A with probability 1. Thus, Player 2's expected payoff from playing A is their payoff if Player 3 plays C multiplied by the probability that Player 3 plays C, which is 8q, plus their payoff if Player 3 plays D multiplied by the probability that Player 3 plays D, which is 10(1-q). Thus, E(A) is 8q + 10(1-q). This is consistent with other videos when you set p equal to 1. Hope this helps!

Glad to hear it! Thank you for watching!

Well, it's part of the equilibrium, but it's player 2's beliefs about Player 1's type when Player 1 engages in off equilibrium play, so you could call it an off equilibrium belief.

Wow! Thank you for the compliment! And thank you for watching!

Glad I could help! Thank you for watching!

If you give me an email address I'll be happy to send them your way.

Thank you for watching!

Thank you!

Thank you for watching!

I'm glad it was helpful. Thank you for watching!

Thank you for the compliment, and thank you for watching!

I am glad this video was helpful! Thank you for watching!

I am glad that you like it. Thank you for watching!

Hi Ignacio - Sorry for the delayed reply. I assume your question refers to about 8:06 minutes into the video. To solve for a2, I need to get all the expressions with a2 on one side of the equals sign, and everything else on the other side. The first step is to add 1/4(a2) to both sides of the equation. On the right hand side, these two terms cancel. Since there is already an a2 on the left hand side, I have 1*a2, which is the same as (4/4)*a2 plus (1/4)*a2, which gives me (5/4)* a2 on the left hand side. Hope this helps! Thank you for watching!

Thank you for watching, Subodh!

I am happy that this was helpful for you! Thank you for watching!

I'm glad it was helpful! Thank you for watching!

Thank you for your comment, and thank you for watching!

Glad that you found it helpful. Thank you for watching!

Thank you!

Hi Irma. We know this because when q < 2/5, (see 5:28 or so in the video), the red line is higher than the blue line, which means that player 1's expected payoff from bottom is greater than their expected payoff from top. When q > 2/5, the the blue line is above the red line, meaning that player 1's expected payoff from top is greater than their expected payoff from bottom. You find q = 2/5 by finding where the red line and the blue line cross. To do this, set 3q = 2(1-q) and solve for q. Hope this helps! Thank you for watching!

Great question! Really, all the numbers tell you are how each player rank orders each of the possible outcomes in the game. Larger numbers mean better outcomes. Any set of numbers that generates the same rank ordering for a player are equally good. So in this sense, the numbers are definitely made up. However, for a real-world game, it is definitely possible to apply some reasoning to why a player might prefer Outcome A to Outcome B. The numbers that one uses for the payoffs from A and B are completely arbitrary, as long as the payoff from A is larger than the payoff from B. Hope this helps!

@@KatherineSilzCarson Katherine thanks for the prompt response to a question asked in frustration. So far I haven't managed to find a game theory/prisoner dilemma/nash equilibrium explanation for dummies that I can understand. All I'm looking for looks something like this... Hi today we're looking at game theory and how it's applied to businesses, who use it to justify financial strategies against competitors. It can be represented in a table. Here's a real life example with actual figures. This is what these two companies did and this is how you can do it too, check it out... Draw a table like so, add company A and Company B here and here like so. Add this number here if this and add that number there if that. *Then proceeds to fill in each cell with a number - not examples of numbers - while explaining exactly what they represent* That's all I'm looking for really.

​@@KatherineSilzCarson I struggle to follow your top/bottom left/right analogy, and how does top equal 1? What does top even mean in this scenario? Everyone in the comments gets it and seems to understand perfectly, what am I missing? Im not following the logic of anything yet everything sounds so well expained..

@@120201atta Try to think of it this way. Suppose that there are two business who are competing in the same market. They can either collude to keep prices high, or undercut each other. If one firm undercuts the other, then the firm that undercuts gets a larger market share, and thus, more profits. If they both undercut, their profits would be small. This is analogous to the prisoner's dilemma game. Make the row player firm 1, and the column player firm 2. Top, Left might be both colluding, with each player getting profits of 4. Top Right would be firm 1 colluding and firm 2 undercutting. In that case, firm 1's profits might be zero (because they lose their market share), and firm 2's might be 6 (because they get the whole market). Bottom Left would be the same, except the firms' actions and payoffs are reversed. Bottom right has both firms undercutting, in which perhaps they each make profits of 1. Each firm has a dominant strategy to undercut, even though if they could figure out a way to work together and collude, total profits to both firms would be higher. At that outcome, though, each still has an incentive to undercut their opponent and try to get 6. This happens in real life with OPEC sometimes (or with non-member countries reneging on their agreements with OPEC). Hope this helps put some more business context on the prisoner's dilemma for you. Thank you for your questions and for watching!