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Snoogins47
08-04-2005, 05:54 PM
Hey ya'll, I recently picked up a game theory textbook, out of personal interest. I've spent a whopping 15 minutes on it so far, and I'm already quite confused. I'm fairly sure it's because I'm reading/interpreting something incorrectly.

Basically, it's about dominated strategies. Here's the normal form game that's outlined in the problem that stumped me.

<font class="small">Code:</font><hr /><pre>
N C J
N 73,25 57,42 66,32

C 80,26 35,12 32,54

J 28,27 63,31 54,29

</pre><hr />

Now, assuming I typed that correctly, the first thing I noticed when I looked at the game is that, according to whatever probably flawed definition of Nash Equilibria that's formed in my head, J,C would be an NE, since either player, were they aware of the other player's action, would still pick that (So, J is the best response to player 2s C, and vice versa) Obviously it still hasn't quite made perfect sense in my head, but this seems to be the optimum strategy then, and thus, the solution.

If that's incorrect, go ahead and fill me in, but that's not the issue I'm having. The issue is that this particular problem is given with the instructions being "solve this game by eliminating dominated strategies." To give the book definitions:

"Suppose Si and Si(1) are two strategies for player i in a normal form game. We say that Si(1) is strictly dominated by s(i) if, for every choice of strategies of the other players, i's payoff from choosing s(i) is strictly greater than i's payoff from choosing s(i1). "

Weakly dominated is defined as a minor alteration, saying that the payoffs in the dominating strategy are all AT LEAST as great as the payoffs in the dominated strategy.

Now, my problem here is that for the life of me, based on the way I've interpreted this definition, I cannot find any dominated strategies for either player.

Player 1 choosing N cannot dominate C or J, because C is superior to N if player 2 plays J, and J is superior to N if player 2 plays C. You can reason this out to show that therefore, C or J cannot dominate N. This leaves C and J, and C is superior to J when player 2 plays J.

For player 2, C is superior to N when player 1 plays N. J is superior to N when player 1 plays C or J. J beats out C when player 1 plays C.

I am willing to wager that my misunderstanding comes from a flawed definition of 'strategy' or a flawed definition of what a dominated strategy truly is. But hey, cut me some slack: I've only been studying game theory for 20 minutes. Is there anybody out there who could recognize the (most likely) very obvious flaws I'm operating under, and possibly elucidate these basic concepts for me? It would be greatly appreciated.

Anticipating your questions: no, I'm not a student looking for help with my homework. I'm not even a student, period.

gergery
08-05-2005, 07:40 PM
For player 2 (across the top), N is a dominated strategy.

His payouts are respectively, 25, 26, 27 going down the N column. But if he were to pick J, then his payouts are 32, 54, 29.

So player 2 needs to ask himself, “if player 1 chooses N, am I better off choosing J or N”? So he compares the first numbers, and sees that 32&gt;25. he then repeats, 54&gt;26, and 29&gt;27.

So no matter what Player 1 picks, Player 2 will always prefer J over N. Thus its dominated. Spank that option, baby!

--Greg