How do you find Nash equilibrium with best response function?

Find the firms’ best response functions. To find the best response of firm 1 to any action a2 of firm 2, fix a2 and solve. maxa1a1(c + a2 a1).
A Nash equilibrium is a pair (a1*,a2*) such that a1* = b1(a2*) and a2* = b2(a1*). Thus a Nash equilibrium is a solution of the equations a1* = (c + a2*)/2. a2* = (c + a1*)/2.

How do I find the best response function?

To find best response function of firm 1, look at its payoff as a function of its output, given output of firm 2. Any price greater than p2 is a best response to p2: B1(p2) = {p1 : p1 > p2}. Note: a price between p2 and c is a best response!

How do I find the best response curve?

A reaction curve (or best-response curve) is a graph which shows profit-maximizing output of one firm in a duopoly given the output of the other firm. We can obtain a firm’s reaction curve using the MRR = MCR condition. The equation above expresses the output of Reach in terms of output of Dorne.

Is best response the same as Nash equilibrium?

The concept of a best response is central to John Nash’s best-known contribution, the Nash equilibrium, the point at which each player in a game has selected the best response (or one of the best responses) to the other players’ strategies (Nash 1950). …

Is Nash equilibrium the best outcome?

Unlike dominant strategy, the Nash equilibrium doesn’t always lead to the most optimal outcome, it just means that an individual chooses the best strategy based on the information they have.

Which is an example of a Nash equilibrium?

Example. A Nash equilibrium is a pair ( a 1 *, a 2 *) such that a 1 * = b 1 ( a 2 *) and a 2 * = b 2 ( a 1 *). Thus a Nash equilibrium is a solution of the equations a 1 * = ( c + a 2 *)/2 a 2 * = ( c + a 1 *)/2. Substituting the second equation in the first equation, we get ( a 1 *, a 2 *) =…

How to find a Nash equilibrium using Cournot’s model?

To find a Nash equilibrium of Cournot’s model for a specific cost function and demand function we follow the general procedure for finding a Nash equilibrium of a game using best response functions. Each of two firms has the cost function TC(y) = 30y; the inverse demand function for the firms’ output is p = 120 Q, where Q is the total output.

How to find the firm’s best response function?

Find the firms’ best response functions. To find the best response of firm 1 to any action a 2 of firm 2, fix a 2 and solve max a 1a 1(c + a 2 a 1). The derivative is c + a 2 2a 1, so the maximizer is a 1 = (c + a 2)/2. Thus firm 1’s best response function is given by b 1(a 2) = (c + a 2)/2.

How to find the best response function of player I?

Denote the best response function of player i by bi . Find the pair ( a 1 , a 2) of actions with the property that player 1’s action is a best response to player 2’s action, and player 2’s action is a best response to player 1’s action: a 1 = b 1 ( a 2) and a 2 = b 2 ( a 1 ). the players are two firms

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