IGNOU MEC 1 2012 - Explain the concept of Nash equilibrium. How it is related to (a) Domi

Question

Explain the concept of Nash equilibrium. How it is related to (a) Dominant strategy equilibrium and (b) Sub-game perfection?

25 Oct 2017

Answer :

Word Count : 540

In a ‘n’ player normal form game G = {S₁, S₂,…..……,S_n; u₁, u₂,..……….,u_n}, the strategies (s^*₁,s^*₂,…….,s^*_n) constitute a Nash equilibrium if, for each player I, s_i is player i’s best response to the strategies specified for the (n-1) other players, (s^*_1,s^*_2,………, s^*_i-1, s^*_i+1,…….,s^*_n) :

U₁ (s^*_1,s^*_2,………, s^*_i-1, s^*_i, s^*_i+1,…….,s^*_n) ≥ U₁ (s^*_1,s^*_2,………, s^*_i-1, s^*_i, s^*_i+1,…….,s^*_n) where i = 1,2,…,n

or, for every feasible strategy s_i in S_i; that is s^*_i solves

max U₁ (s^*_1,s^*_2,………, s^*_i-1, s^*_i, s^*_i+1,…….,s^*_n)

s^*₂Ð„S^*_i

Nash equilibrium is strategically stable and self-enforcing because no single player wants to deviate from her predicted strategy.

Dominant Strategy – A player in a simultaneous move game may have nay finite number of pure strategies at her disposal. One of these strategies called as dominant strategies if it outperforms all of her other strategies, no matter what any other

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