An Economics Experiment (test your intuition)

[almostbusto]

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I think if all 5 players were very clever and rational they could get it to the max point. this is because they could all determine each other's pay offs without ever stating them... for example player 4 could tell player 5 that he could bribe him X amount of dollars to move the location to (50,30)(Player 4's max payoff).

each player would try to bribe/solicit bribes to increase there payoff. so there would be two ways to increase you payoff, get more bribe money or move the location. now the math might get hairy but after enough offers 5 smart people should be able to solve it perfectly after a bunch of bids.

this, as i understand it, would not be breaking the rules.


also noteworthy is the fact that they will finish at the max total payoff, but each player is unlikely to recieve their payoff based on the grid number and formule. ie player 2 will probably get paid some money for accepting that postion

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Do they have to wink when they ask?

[/ QUOTE ]no but obviously the guy with the 10$ to work with will be able to bribe higher amounts, whereas the five dollar guys won't be able to offer as much. the players will pick up on this and as a result they will decide they need to move the final position closer to the 10$ guy than the arthimatic center of all five positions.

[almostbusto]

here is one way you could tell people your payoff number legally. iff you know the formula. pick a point there is no way you can get a yes vote on (like -100, -100 or something way out there). calculate how much you would get if that position won. then offer all of the money(you don't tell him that) to one of the players. if every player does that, then everyone knows AT LEAST how much money everyone has to gain.

this i guess potentially opens things up to lying. but by lying all the other players will want to move the final position further away from you because you won't be able to give them as much bribe money. so it doesn't seem that there is a gain from lying(this would require a proof, i am not sure i could do it). if that is true, you want to look like you get as big a payout as possible. and you can't promise more money than you'll make so being honest is the only way to go.

[madnak]

That assumption may or may not be true. Part of the reason I haven't actually said anything about the game itself is that it lacks context. From a game theory perspective it would be trivial, but if it's an actual human game played by human players with a relevant outside context, then it depends on many factors. Who are the players? How much money is involved? What kind of "meta-game" influence is allowed (for instance, the "after it's over I'll give you a buck")? In what environment is it being played, and with what expectations (This game played as part of a business course would have different results than if played in a research study or as a party game)? What kinds of communications are allowed between players?

[Sephus]

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I think if all 5 players were very clever and rational they could get it to the max point. this is because they could all determine each other's pay offs without ever stating them... for example player 4 could tell player 5 that he could bribe him X amount of dollars to move the location to (50,30)(Player 4's max payoff).

each player would try to bribe/solicit bribes to increase there payoff. so there would be two ways to increase you payoff, get more bribe money or move the location. now the math might get hairy but after enough offers 5 smart people should be able to solve it perfectly after a bunch of bids.

this, as i understand it, would not be breaking the rules.


also noteworthy is the fact that they will finish at the max total payoff, but each player is unlikely to recieve their payoff based on the grid number and formule. ie player 2 will probably get paid some money for accepting that postion

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in general when you're doing problems like this, you can't assume that the players have things outside the game to barter with.

it looks like the answer is player 1's point, simply because when you're at any other point there are alternate points that at least 3 of the 5 would prefer to be at.

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you don't need anything outside of the game to barter with. they are bartering with the profits that they would gain if everyone votes for the game to end. its like saying "hey player 1 if you vote for the position i pick, ill toss you a buck when its all over"

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they can't do this, because when the game is over there is no way for them to force each other to pay up. when the game ends, it's over. these aren't "real people" playing the game, they're theoretical players whose only motivation is maximizing their own payoffs.

[Sephus]

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From a game theory perspective it would be trivial

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if it is, it is. it's posed as a game theory problem so that's the only perspective necessary.

[almostbusto]

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I think if all 5 players were very clever and rational they could get it to the max point. this is because they could all determine each other's pay offs without ever stating them... for example player 4 could tell player 5 that he could bribe him X amount of dollars to move the location to (50,30)(Player 4's max payoff).

each player would try to bribe/solicit bribes to increase there payoff. so there would be two ways to increase you payoff, get more bribe money or move the location. now the math might get hairy but after enough offers 5 smart people should be able to solve it perfectly after a bunch of bids.

this, as i understand it, would not be breaking the rules.


also noteworthy is the fact that they will finish at the max total payoff, but each player is unlikely to recieve their payoff based on the grid number and formule. ie player 2 will probably get paid some money for accepting that postion

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in general when you're doing problems like this, you can't assume that the players have things outside the game to barter with.

it looks like the answer is player 1's point, simply because when you're at any other point there are alternate points that at least 3 of the 5 would prefer to be at.

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you don't need anything outside of the game to barter with. they are bartering with the profits that they would gain if everyone votes for the game to end. its like saying "hey player 1 if you vote for the position i pick, ill toss you a buck when its all over"

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they can't do this, because when the game is over there is no way for them to force each other to pay up. when the game ends, it's over. these aren't "real people" playing the game, they're theoretical players whose only motivation is maximizing their own payoffs.

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dude is says anything goes. i see nothing in the rules that would suggest that modifying the payouts is illegal. the goal is still to maximize payoffs they are just trading payoffs. if players can't contract there this is definitely not an anything goes game. property rights and enforcement of contracts are two of the more fundamental and basic properties of markets. to say they don't exist in the context of the game makes the game far from a free for all

[madnak]

Really? Then it would be up and to the right of Player 1. That's the point representing the Nash Equilibrium, isn't it?

[madnak]

To expand on that, I'm thinking the information issues and moves and all that would be superfluous with perfectly rational players. But maybe I'm wrong; maybe a player could successfully bluff. Intuitively, it seems like the point would end up being the Nash equilibrium point if it were a simple game of unanimous agreement with full information. I'm not really sure who would have the informational advantage give than the players can't see each others payoff grids. I just assumed no advantage and that eventually they'd reach the same equilibrium as if they all knew each other's points. But that assumption really didn't have a basis.

[madnak]

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anything goes

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I kill them all and take the money.

I think it's clear on re-reading it that it's not meant to be a game theory problem. It's meant to be a psychological problem. I don't like economics experiments like this, because depending on the personalities of those at the table there can be dramatically different results. I assume diddle's probably looking for the most common solution in his quiz.

[almostbusto]

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To expand on that, I'm thinking the information issues and moves and all that would be superfluous with perfectly rational players. But maybe I'm wrong; maybe a player could successfully bluff. Intuitively, it seems like the point would end up being the Nash equilibrium point if it were a simple game of unanimous agreement with full information. I'm not really sure who would have the informational advantage give than the players can't see each others payoff grids. I just assumed no advantage and that eventually they'd reach the same equilibrium as if they all knew each other's points. But that assumption really didn't have a basis.

[/ QUOTE ]there is no way to hit the max total payout(i assume this is what you met by equillibrium) unless you share the information. how would they know they need to more the final position closer to the 10$ payout guy otherwise?



another idea to share information. all players could hypothetically offer every other player some sum of money to be able to control their vote for the entire game. obviously, each person would be more willing to buyout the guy further from him, and the players with higher payouts would be able to offer more money to control votes. seems like that gets a fair amount of info out there. i imagine they would use this bidding just as a way to get information out and they would never actually sell their votes(the votes are more valuable that what anyone can offer for one reason). i haven't thought much about the implications of that bidding but its something for someone to think about perhaps.

EDIT: i am almost certain this way works now.the other way i suggested most likely works but it would be harder to prove it seems