Programme Code : MEC
Course Code : MEC -001
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Year : 2012 Views: 1494 Submitted By : Abhijit Ghoshal On 19th November, 2012

Do you have solution for this Question. If yes    I aslo want solution.

Q.


Explain the concept of dominant strategy equilibrium. Discuss the concept of Nash equilibrium. Is every

dominant strategy equilibrium a Nash equilibrium? What do you understand by subgame-perfect

equilibrium?



Write short notes on the following

a) Inter-temporal utility maximization


Catch The Solution

By neeraj rawat


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 player does.

In the normal form game G = {S1, S2,…..……,Sn; u1, u2,..……….,un}, let s1i and s11i be feasible strategies for the player I (i.e s1i and s11i are members of Si). Strategy s11i strictly dominates strategy s1i, if for each possible combination of other players’ strategies, i’s payoff from playing s1i is strictly less than i's payoff from playing s11i. Symbolically,



U1 (s1,s2,………, si-1, s1i, si+1,…….,sn) < U1 (s1,s2,………, si-1, s11i, si+1,…….,sn)

for each (s1,s2,………, si-1, si+1,…….,sn) that can be constructed from other players’ strategy spaces (S1,S2,………, Si-1, Si+1,…….,Sn). Strategy s11i is called strictly dominant strategy for player i. The dominance is said to be weak when there is a weak inequality (≤ rather than <) in the above equality.

 



In a ‘n’ player normal form game G = {S1, S2,…..……,Sn; u1, u2,..……….,un}, the strategies (s*1,s*2,…….,s*n) constitute a Nash equilibrium if, for each player I, si 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) :



or 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 si in Si; that is s*i solves



max U1 (s*1,s*2,………, s*i-1, s*i, s*i+1,…….,s*n)

s*2ЄS*i



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



 



Yes dominant strategy equilibria always Nash equilibria.  In a dominant strategy Nash equilibrium the players all play strategies that are their best responses to their rivals regardless of which strategies their rivals play



 



Sub-game perfection – A sub-game is a part of the game, which starts from a singleton information set and stretches up to the end of the game. A configuration of strategies, which induces Nash equilibrium in every sub-game of a game, is called sub-game perfect Nash equilibrium. This is explained in the example given below:



































Coke will always play Accommodating, and as Pepsi can foresee this. Pepsi will also play accommodating as well. Therefore the Nash equilibrium of the sub-game is (Accommodating, Accommodating) and PSNE (Enter- Accommodating, Accommodating) is the only SPNE (sub-game perfect Nash equilibrium) of the game. Thus, the concept of SPNE is able to eliminate non-credible threat.




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