This video goes over the strategies and rules of thumb to help figure out where the Nash equilibrium will occur in a 2×2 payoff matrix. Generally you need to figure out what the dominant strategy is for each player and then use the dominant strategy of each player to see if a final cell ends up being the choice for both players.

This is generally something that is reviewed during the oligopoly section of a course or perhaps during the game theory segment.

You can find more information about this topic at:

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This was very helpful. Thank you. 🙂

sorry but is dominut supposed to be dominant

Be careful. Nash equilibrium can exist without dominant strategies being present. For example, the Battle of the Sexes scenario: https://en.wikipedia.org/wiki/Battle_of_the_sexes_(game_theory)

Hi.Thank you for this excellent presentation.I have watched all the videos and find them super useful.Unfortunately, there 2 exercises about game theory that I can't solve.Pleaseee could you help me? Pleasee

This is the exercise:

A). Consider a duopoly with differentiated products. The two firms are denoted 1 and 2, and their

products q1 and q2 with prices p1 and p2, respectively. There is a representative consumer whose net

utility from purchasing the two goods is U=q1+q2-1/2(q1 ^2 + q2^2)-yq1q2-p1q1-p2q2

The parameter y, which ranges in between 0 and 1, is the degree of product differentiation (products

are perfect substitutes when y= 1, while they are independent when y= 0. Firms have symmetric

and constant marginal cost c 1.

1. Derive the direct and indirect demand functions (i.e., quantities as function of prices, and prices as

function of quantities)

2. Consider then the case of quantity competition (Cournot). Derive the best response functions and

the Nash equilibrium, as a function of the parameters y and c.

3. Do the same for the case of price competition (Bertrand).

4. Compare the two equilibria. Which one is preferred by the firms? And by the consumer?

B. Consider a sealed‐bid first‐price auction. There are two bidders, 1 and 2, with valuations for the good

of v1 and v2, respectively. Each buyer’s valuation is his/her own private information. v1 is uniformly

distributed on include (0,1) and v2 is uniformly distributed on include (0,2). So player 1, for instance, knows v1 exactly

but regarding v2 he/she knows only that it is uniformly distributed between 0 and 2.

1. Define the Bayesian equilibrium for this game.

2. Find a Bayesian equilibrium.

3. Discuss uniqueness.

Wow. This was a great explanation. Thank you!

thank u

thanks

What's wrong with your voice?!

Thank you so much! This helps a lot for my test tomorrow

By far the best video I've seen for helping me understand this concept, thank you very much for the detailed explanation.