University question

    • germany5590
      germany5590
      Basic
      Joined: 02.12.2011 Posts: 50
      Hi friends,

      I am doing an assignment for University that I have pretty much done, but I need to do a case study on it and ask other people about the opinion and choices. This assignment is for Game Theory (Economics). This is the question...

      You are in a game show. You and two other players have been selected for this game and you are each moved into seperate rooms. You do not know each other. All you know is that these players are rational thinking.

      The game host explains the rules to all three of you.

      "I will offer the first player (that is you) a deal to either accept my offer of $200 or decline it, if you choose to accept you get $200 and the other 2 players get $400 each and the game is over! If you choose to decline I move on to the second player and over him the same deal. If he chooses to accept you, as player 1, get nothing, Player 2 get $200 and the final player gets $400. If player 2 chooses to decline the game show host moves into the third room and gives the final player a similar over. This time the third player chooses to accept he will receive $200 and the rest will go home with nothing, if he chooses to decline though everyone will go home with $400."

      The players can not discuss a strategy once the game has been explained.

      The question I ask you now is what is your best strategy? Accept the deal and take home $200 or decline and hope the other players decline aswell?

      It would be good if you could state the reasoning behind your choice. There is no right or wrong answer to this question so do not be afraid to give it a shot. If you are interested in the solution (the most probable outcome) let me know.

      Thanks.

      P.S. No one is actually getting money from me ;)


      Edits:


      -Does each player know that if every player declines the deal they walk away with $400?
      Yes, all the players have the same information on the outcomes. None of the players has more information then the other.
  • 15 replies
    • Castle93
      Castle93
      Bronze
      Joined: 06.06.2011 Posts: 1,452
      Does each player know that if every player declines the deal they walk away with $400?
    • germany5590
      germany5590
      Basic
      Joined: 02.12.2011 Posts: 50
      Yes, they all know the rules. The know all outcomes.
    • i5bet72o
      i5bet72o
      Bronze
      Joined: 17.06.2010 Posts: 1,615
      Assuming all players are logical and rationale and believe that the other players are logical and rational

      Player 3 has an incentitive to not accept the deal
      Player 2 knows thats player 3 has an incentitive to not accept the deal so he also has an incentitive to not accept the deal
      Player 1 knows that both other players have an incentitive to not accept the deal so he will also have an incentive to not accept the deal

      Therefore all three players will not accept the deal
    • germany5590
      germany5590
      Basic
      Joined: 02.12.2011 Posts: 50
      spot on
    • i5bet72o
      i5bet72o
      Bronze
      Joined: 17.06.2010 Posts: 1,615
      Originally posted by germany5590
      spot on
      I was always pretty good at econ.
    • PokerPPP
      PokerPPP
      Bronze
      Joined: 29.10.2009 Posts: 494
      Guys, don't worry. I GOT THIS :D


      First off, I suspect this is your Intermediate micro homework or part of it.
      Secondly, this is the infamous Prisoners' Dilemma game altered with 3 people.
      Third, not really a good answer so far.

      There are 2 equilibria in this game as in most game theory games. 1 equilibrium is Nash equilibrium and the second equilibrium is the Pareto one.
      Information is important in these games as everything alters the outcome.
      Must be noted that this is a FULL information game as players know all outcomes possible. However, your question does not say whether this is a game repeated to infinity or a one-shot game - this would also alter the outcome. Say it is a one-shot game - pareto efficiency equilibrium is - all players decline, so that there is no room for Pareto improvement for either player ( as per Pareto efficiency definition). The Nash equilibrium, however will be all players accept, suspecting one of the others accepted & therefore ensuring a piece of the pie. However, if this was a game repeated to infinity in the long term all players will convert to the pareto equilibrium and the Nash and Pareto equilibrium will be the same - everybody declines and extracts maximum value.
    • Krishjanis
      Krishjanis
      Bronze
      Joined: 04.01.2010 Posts: 977
      In a perfect world with rational thinkers I'm declining and waiting for my 400$ from the third guy.
      But in a real world I would snap take the 200$, why? Because people are idiots, I'm not taking the risk that the other two are not overweight, sweaty, god believing, television brain washed idiots. And it's not just internet or television where people are stupid, in my every day life someone pops up that does something completely illogical, there are idiots all around us.
      One other deciding factor is the amount of money, for 400$ I could risk losing them by declining 200$, but if you increase the amount of money by like 10 times then it's 200$x10 every time.
    • i5bet72o
      i5bet72o
      Bronze
      Joined: 17.06.2010 Posts: 1,615
      Originally posted by PokerPPP
      Guys, don't worry. I GOT THIS :D


      First off, I suspect this is your Intermediate micro homework or part of it.
      Secondly, this is the infamous Prisoners' Dilemma game altered with 3 people.
      Third, not really a good answer so far.

      There are 2 equilibria in this game as in most game theory games. 1 equilibrium is Nash equilibrium and the second equilibrium is the Pareto one.
      Information is important in these games as everything alters the outcome.
      Must be noted that this is a FULL information game as players know all outcomes possible. However, your question does not say whether this is a game repeated to infinity or a one-shot game - this would also alter the outcome. Say it is a one-shot game - pareto efficiency equilibrium is - all players decline, so that there is no room for Pareto improvement for either player ( as per Pareto efficiency definition). The Nash equilibrium, however will be all players accept, suspecting one of the others accepted & therefore ensuring a piece of the pie. However, if this was a game repeated to infinity in the long term all players will convert to the pareto equilibrium and the Nash and Pareto equilibrium will be the same - everybody declines and extracts maximum value.
      This situation is different from the prisioners dilema. In the prisioners dilema prisioners are making desisions simultaniaously while in this case people are making desisions one person at a time.

      Unlike the prisioners dilema, Player 3 will ONLY have a desision if the first two players reject the deal.
      The superior option for him would be to reject the deal.
      Rejects:+$400
      Accepts:+$200

      Also unlike the prisioners dilema, Player 2 will ONLY have a desion if the first player rejects the deal.
      Player 2 knows that if he rejects the deal, player 3 will reject the deal therefore the superior option for him is to reject the deal

      Player 1 would know that the superior option for both of the second two players is to reject the deal therefore he would also reject the deal

      Therefore BOTH the pareto and the nash equilibrium are for all players to reject the deal.

      I also took imediate econ and got an A
    • i5bet72o
      i5bet72o
      Bronze
      Joined: 17.06.2010 Posts: 1,615
      I could change the question to make it a three way prisioners dilema.
      Three contestants are put into three seperate rooms, and are asked simultaniously whether they want to accept a deal for $200 or not.
      If any one (or more) of them accept the deal, everyone who accepts the deal get $200 and everyone else gets nothing,
      If none of them accept the deal, everyone gets $400

      In my question, in one shot would be everyone accepts and in infinity trials would be everyone declines
    • PokerPPP
      PokerPPP
      Bronze
      Joined: 29.10.2009 Posts: 494
      Okay disregard my first post as I did not fully read the question. Pareto is obv - all decline ofc. Stated this way the game way too easy as the game ends if P1 says yes. Would have been way different if it were simultaneous. In this game:
      P3 is always the winner no matter what.
      P1 knows that if he declines, action goes to P2, that is, P2 will know that P1 did not accept as the game is still running. P2 will choose to decline as he wants to maximize. Action goes to P3, again, because the action goes to P3 he already knows that P1 & 2 declined so he declines as well - all players decline Nash = Pareto.

      This game is rigged towards P3 who is always a winner, while P1 is always in the worst spot. The game does NOT contain any strategy whatsoever and either player will act as above no matter how dumb he is. The game would have a different outcome if P2 is asked the question REGARDLESS of P1's answer. Strategy will apply then and the outcome would be different.
    • Castle93
      Castle93
      Bronze
      Joined: 06.06.2011 Posts: 1,452
      Yeah in short each player has a mutual interest to decline the deal as they are all rational thinkers, if they assure the other is too.


      Have you ever come across the prisoners dilemma in game theory?
    • thazar
      thazar
      Bronze
      Joined: 14.09.2009 Posts: 6,560
      to some extent I guess:

      1) if the board is a split and the pot is small enough, if one of the players goes all in calling could sometimes cost more more rake than the actual pot

      if you are first to act: shoving should be the best as the best play for your opponent is to fold however if your opponent call you will end up losing more :) , if you check however and your opponent shove you will have to fold to minimise loss.

      2) in a tournaments, there are situation where the best situation for all players will be for the pot to be checked down to show down to have more chance to eliminate the bubble player and all be guaranteed a good amount but the first person betting could get extra chips in pot for example.
    • germany5590
      germany5590
      Basic
      Joined: 02.12.2011 Posts: 50
      Well I finished my assignment and I came to the conclusion that there are 2 mixed strategy equilibria and 1 Nash Equilibrium. The Nash Equilibrium is the one pointed out in the first response by ibet72o. All players reject. You get to this solution by using backward induction (start with player 3). Then there are the two mixed strategy equilibria (I might have screwed this part of my answer up a bit, but thats fine).
      The expected outcome for player one could be: 200 (by accepting)+0 (reject/accept)+0(reject/reject/accept)+400 (rej/rej/rej) giving him an EMV of 600/4 = 150. Hence he is better of accepting the deal because the initial offer of 200 exceeds his EMV of 150.
      For player 2 the expected monetary value is (accept) 200+ 0 (acc/rej)+ 400 (rej/rej) =600/3 = 200.

      Hence this player is indifferent because when gets the chance to accept his initial offer of 200 it balances out with his EMV, hence he can mix up his strategy by accepting or rejecting.
    • BObamaJr
      BObamaJr
      Bronze
      Joined: 29.01.2012 Posts: 232
      This is the archetypal question of university theory.

      It is called the prisoner's dilemma. There is no answer to your question. Logically, all players should co-operate to achieve the most mutually beneficial outcome for themselves and all participants. However, as all parties are distrustful and uncertain over the other's action they choose the option that will maximize their self-interest even if it isn't the most logical option.

      I did International Relations Theory at uni and this was one of the first examples our lecturer used. In IR theory it is used to explain why states preference their national interest over other nations even it produces a less beneficial outcome.
    • andreibalint
      andreibalint
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      Joined: 11.04.2009 Posts: 872
      The equilibrium is for the first two players to decline and wait for the third to decline so that everybody gets 400. They know C will decline since this is the way he makes the most money.

      B won't accept either since he knows the same thing. Remember they are supposed to be rational, so they all think this way.