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I'm currently writing my thesis in econ and have encountered a bit of game theory which im not too well acquainted with. The problem is as follows:

Suppose there are two players, In the first round each player can invest in information for some cost C. In the second round players choose if they which to enter the contest or not. What of player j's choice in the first round has to be known to player i (for there to be a solution to the model)? his set of strategies or which strategy he actually chose to play?

Thanks in advance.

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    $\begingroup$ It's impossible to know without more details. There are many types of games. Sometimes the opponent's action space is completely known, sometimes not. Sometimes the opponent's strategy is knowable, sometimes not. I'd argue that your task is to make arguments for setting up the model by factoring in different levels of uncertainty for however is appropriate. Fully-generalized games are exceptionally complicated. $\endgroup$
    – Emily
    May 9, 2014 at 18:06

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What's usually required is that each player must know the set of strategies. It is a game of imperfect information, also known as a Bayesian game. What is unkown is the random state of nature, which is often thought of as the types of the other players. Put another way, you can get an equilibrium if you don't know the other player's choice,--do you go to the symphony or the wrestling match, but generally not if you don't even know how many differ spots the other player is considering.

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  • $\begingroup$ Thanks for taking you time to answer, much appreciated. If we proceed on your example. Suppose I can go either to the symphony or the wrestling match today, and my opponent has the same choice. However, we will have to make another decision tomorrow. Does my first decision of symphony versus wrestling have to be known to my opponent (and vice versa) when he makes his decision in the second round for there to be an equilibrium? EDIT: to clarify, im not interested in unknown strategy spaces, only in having the actual strategies executed unknown. $\endgroup$
    – Winston
    May 10, 2014 at 19:09
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    $\begingroup$ No, although it is now a different sort of game, imperfect as opposed to incomplete info. Kreps' work on Sequential equilibrium is one of the big solution concepts. Take a look at Osborne and Rubinstein's books for more details, and more equilibrium concepts. $\endgroup$
    – Trurl
    May 11, 2014 at 15:20
  • $\begingroup$ Thank you very much, sir. I accepted your original answer, so this topic can be viewed as complete. $\endgroup$
    – Winston
    May 11, 2014 at 15:27

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