 # How to find Nash Equilibrium in a 2X2 payoff matrix 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.

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• This was very helpful. Thank you. 🙂 Anna S. June 22, 2020 7:00 pm
• sorry but is dominut supposed to be dominant Brody Reardon June 22, 2020 7:00 pm
• 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) Michael Aronow June 22, 2020 7:00 pm
• 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. Ulvi Mustafayev June 22, 2020 7:00 pm
• Wow. This was a great explanation. Thank you! Lilybeth Chavez June 22, 2020 7:00 pm
• thank u kishan soni June 22, 2020 7:00 pm
• thanks Nik Theodoro June 22, 2020 7:00 pm
• What's wrong with your voice?! Cha Ris Se June 22, 2020 7:00 pm
• Thank you so much! This helps a lot for my test tomorrow Claudia Ashe June 22, 2020 7:00 pm
• By far the best video I've seen for helping me understand this concept, thank you very much for the detailed explanation. Lorelai M June 22, 2020 7:00 pm