I'd like some input here..

"Two players, Jack and Jill are put in seperate rooms. Then each is told the rules of the game. Each is to pick one of six letters: G, K, L, Q, R or W.
If they happen to chose the same letter, both get prizes as follows:

Letter| G | K | L | Q | R | W |
Jacks'| 3 | 2 | 6 | 3 | 4 | 5 |
Jills'..| 6 | 5 | 4 | 3 | 2 | 1 |

If they chose different letters, each of them gets zero. This whole schedule is revealed to both of them, and both are told that both know the schedule, and so on.

a ) Draw the table for this game. What are the Nash Equilibria in pure strategies?
b ) Can one of the equilibria be a focal point? Which one? Why?



So.. here's my thoughts..
All of the results of this game are nash equlibria, meaning (G,G) (K,K) (L,L) (Q,Q) (R,R) (W,W) are all equilibria?? Given their opponents pick, neither of the players would then regret their own picks, am i right?
When drawing the table, should I add all the (0,0) outcomes of this game?

As for the focal point, Im not sure how to solve this one? Im thinking maybe (Q,Q) since it seems "fair" to both players that they will receive the same payout?

All input is appreciated

I don't have time to think about the whole thing right now, but I will comment on one detail.

There is no "fair" solution in game theory. Every player is always going to choose the highest revenue solution for him. Whatever the end game.

You need to understand this before you go into game theory.

If you start bringing in psychological input, outside market data, etc then you can start talking about "fair" or "optimized" decisions. Unless you do that, then you need to remain concentrated on the fact that each player will choose what is the best result for him.

This means that the choice of your payers will most likely always be (L,G)

I know, but i havent worked with focal points before, so i did a little research and found this



edit: (L,G) is not a real solution, as the payout there will be (0,0)
how about (L,L)?

This post was edited by Simens on Sep 8 2010 04:45am

I'm not sure what to say. I might not understand what you're after.

Because here's the deal. What your "quote" is referring to is a little more complicated than a simple payoff table.

In a situation where you must coordinate with a partner without the ability to communicate, or with a competitor to try and level market prices, it's usually a step by step process.

Both will make a starting move. The other will analyze that move. If the move induces a level of trust, he will send out a message through his next move. If message is received and perceived, the other player will adjust accordingly. You could have a game with 8 teams, where each must choose the price of their product 10, 20 or 30. Teams compete 4 vs 4, A1 vs B1, A2 vs B2, etc.
Allow them 8 rounds, considering that they have a table that shows them the payoffs according to what they choose and what their opponent chooses.

In such a scenario, players will not be allowed to communicate with other teams (no price fixing), so you need to send messages through the choices you make. And this is where the "TRUST" component comes into play on the market.

So, to go back to your initial problem, unless there is more than one round of decisions, unless the game is more than just a one time decision, the equilibrium you are talking about cannot be reached. A one time round will come out as (L,G) and no other choice. More than one round, well you'd have to imagine curves of decisions.

Then the payout will be (0,0)

Game theory rarely results in the best payout. The initial theory with the dual prisoner dilemma results in a 3,3 year sentence. It's a terrible choice but it's the rational one.

(L,G) is a solution. You just do not see it as one because you are concentrating on dual payoff. In game theory, you need to concentrate on single payoff.

Player 1 wants 6, he chooses L.
Player 2 wants 6, he chooses G.

Game over, so to speak ^^

this is not a sequential game, is simultaneous
meaning there are no steps, both players make their choise at the same time

and no, L,G is no Nash Equilibrium
both players would regret their choise

This post was edited by Simens on Sep 8 2010 04:56am

Ok, I'll read your starting post again, and see if I can give you a more precise answer to your specific question.

I need to go to the hairdresser, but I'l be back because I love economics and debating the Game Theory is one of the most entertaining thing there is in economics.

I will be back but not under the same name probably since this account will most likely be banned in an hour or less.

lol

ok

Have you done the payoff matrix ?

You need it to see Nash's more clearly. That's a basic "rule" or "idea".

Edit : But yes, you are right. In this strategy there are no other payoffs but for both payers choosing the same letter.

So all the solutions G,G L,L etc are Nash equilibriums.

This actually bothers me :( from an intellectual point of view. There are not enough solutions, because other choices do not payoff.

This post was edited by Volmondo on Sep 8 2010 05:02am

well yes i have, buts its just (0,0) for all other solutions than (G,G), (K,K), (L,L), (Q,Q), (R,R), (W,W)

btw, im no "noob" in game theory

btw2: i dont think there is just one right solution to the focal point question


This post was edited by Simens on Sep 8 2010 05:06am