Game Theory - 12 Game without Saddle Point - 6 Dominance Rule

#OperationsResearch #Math #Statistics #Game #GameTheory #SaddlePoint #DominanceRule #FreeLecture #FreeStudy #Solution

Also visit and subscribe
https://www.youtube.com/c/PrashantPuaar/playlists

"Puaar Academy’ provides video lectures on various subjects like statistics, operations research, costing, management accounting etc.

Prof. Prashant Puaar is M. Com - Gold medalist, Fellow of Insurance Institute of India and NET (UGC) Qualified having experience of more than two decades in teaching the subjects like Statistics, Costing, Accountancy, Finance Management, Operations Research, Management Accounting, Taxation, Economics, Research Methodology, Business Maths and various topics/subjects of competitive exams.

Dominance Rule:
'Dominance Rule' is a bunch of rules used to reduce the order of the game (i.e. the size of the pay-off matrix). These rules are helpful in deleting some rows and columns (i.e. strategies) of the pay-off matrix which are less attractive as compared to at least one of the remaining rows and columns (i.e. strategies) in terms of pay-offs to both the players. The rows and columns once deleted in such a way can never be used for the determination of the optimal strategy in case of both the players.

IMPORTANT NOTE:
Students need not to show the workings /partial workings, which I have shown while explaining, as a part of their answer. I have shown that just to make the thing easy for the students while watching this lecture. These workings are actually the thought process to be followed to select the row /column to be deleted. Of course, for your own satisfaction, and safety, you can write it.

These rules are generally used for the solution of two-player zero-sum games. The rules are as follows:

(1) For Player-A (gainer) if each element in a row (Rr) is less than or equal to the corresponding element in another row (Rs) in the pay-off matrix, then row (Rr) is said to be dominated by the row (Rs) and, hence, (Rr) can be deleted from the pay-off matrix. It means, Player-A would never use the strategy corresponding to row (Rr) because he would gain less by choosing such a strategy.

(2) For Player-B (loser) if each element in a column (Cr) is less than or equal to the corresponding element in another column (Cs) in the pay-off matrix, then column (Cr) is said to be dominated by the column (Cs) and, hence, (Cr) can be deleted from the pay-off matrix. It means, Player-B would never use the strategy corresponding to column (Cr) because he would gain less by choosing such a strategy.

(3) A strategy (k) can also be dominated if it is less attractive to the average of two or more other pure strategies. In such case, strategy (k) can be deleted.

A game, after reducing it up to 2x2 applying dominance rule. can be solved by any of the suitable methods already discussed in earlier videos. I have left it to the students to select the method to solve game here in this case. I suggest to solve the game by more than one methods, as that will provide a good practice of methods.

Here...
A2 - A4: You can see that at B1, A2 dominates A4 but at B4, A4 dominates A2 and, thus, neither A2 dominates A4 nor A4 dominates A2. The similar thing happens in case of B2 - B4.
B2 - B4: B2 dominates at B4, but at A4, B4 dominates B2 and, hence, neither B2 dominates B4 nor B4 dominates B2.
You can see that the value '8' at A4-B4 becomes the reason of terminating the dominance of A2 and B2 over A4 and B4 respectively.

When all values are equal we obviously select any only (and any) one at a time. If all the values are equal, we don't need to have both the alternatives with us forever and we may select any one and drop the other.

Remember the term "Greater than or equal to" for the 'gainer' and "Less than or equal to" for the 'loser' in the game while using the dominance principle.

Game Theory, Saddle Point, Game without Saddle Point, Dominance Rule, Operations Research, MBA, MCA, BE, CA, CS, CWA, CMA, CPA, CFA, BBA, BCom, MCom, BTech, MTech, CAIIB, FIII, Graduation, Post Graduation, BSc, MSc, BA, MA, Diploma, Production, Finance, Management, Commerce, Engineering , Grade-11, Grade- 12

- www.prashantpuaar.com

Видео Game Theory - 12 Game without Saddle Point - 6 Dominance Rule канала PUAAR Academy