<p><span class="math-container">$\epsilon_i$</span> is distributed uniformly on <span class="math-container">$[-\phi, \phi] $</span> where <span class="math-container">$\phi&gt;1$</span>. My working so far is as follows: <span class="math-container">$$\mathbb{E}U_1[I]=1+\epsilon_1\\\mathbb{E}U[N]=0\\$$</span> Therefore, the optimal strategy for player 1 is for all <span class="math-container">$\epsilon_1&gt;-1$</span> to play <span class="math-container">$I$</span> and for all <span class="math-container">$\epsilon_2&lt;-1$</span> to play <span class="math-container">$U$</span>. This strategy specification is the same for player 2. In terms of pinning-down a BNE, I am lost beyond this point. Thank you.   <a href="https://i.sstatic.net/FlseF.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FlseF.png" alt="enter image description here"></a> </p>

CC BY-SA 4.0
2020-06-04T08:48:57.127Z
Why do you think that $\mathbb{E}U_1[I]=1+\epsilon_1$? And what does the LHS even mean - there is no indication of what strategy player 2 plays...?
VARulle
CC BY-SA 4.0
2020-06-04T08:54:33.453Z
@VARulle Because if player 1 plays $I$ then player 2 will respond by playing N, and so player 1 gets $1+\epsilon_1$.
Charles
CC BY-SA 4.0
2020-06-04T08:56:54.820Z
Are you saying that player 1 moves first?
VARulle
CC BY-SA 4.0
2020-06-04T08:57:31.433Z
@VARulle No; it is a simultaneous move game.
Charles
CC BY-SA 4.0
2020-06-04T09:00:08.783Z
Then how can player 2 "respond by playing N", if he doesn't observe player 1's choice of I?
VARulle
CC BY-SA 4.0
2020-06-04T09:01:28.617Z
@VARulle The payoff structure is common knowledge, so he knows that player 2 will play N if he plays $I$.
Charles
CC BY-SA 4.0
2020-06-04T09:08:53.683Z
But they choose simultaneously. So how should player 1 know that he played $I$?
VARulle
CC BY-SA 4.0
2020-06-04T09:11:02.843Z
Or, on a more technical level: In a game, $U_i$ is always a function of the chosen strategy *profile*, not of player $i$'s chosen strategy alone!
VARulle
CC BY-SA 4.0
2020-06-04T09:15:51.620Z
@VARulle I understand that but am entirely lost in my approach to this problem. How would you suggest I approach it? Thank you.
Charles
CC BY-SA 4.0
2020-06-04T12:30:50.057Z
First, in the question you should clarify who knows which $\epsilon_i$ at what point in time.
VARulle
<microeconomics><game-theory>
Grab the dollar Bayesian game
Charles
# Grab the dollar Bayesian game

(Asked by: username_0 on 2020-06-04)

$\epsilon\_i$ is distributed uniformly on $[-\phi, \phi] $ where $\phi>1$. My working so far is as follows: $$\mathbb{E}U\_1[I]=1+\epsilon\_1\\\mathbb{E}U[N]=0\\$$ Therefore, the optimal strategy for player 1 is for all $\epsilon\_1>-1$ to play $I$ and for all $\epsilon\_2<-1$ to play $U$. This strategy specification is the same for player 2. In terms of pinning-down a BNE, I am lost beyond this point. Thank you. [![enter image description here](https://i.sstatic.net/FlseF.png)](https://i.sstatic.net/FlseF.png)

**Tags:** microeconomics, game-theory

> **Comments:**
> **username_1**: Why do you think that $\mathbb{E}U_1[I]=1+\epsilon_1$? And what does the LHS even mean - there is no indication of what strategy player 2 plays...?  
> **username_0**: @username_1 Because if player 1 plays $I$ then player 2 will respond by playing N, and so player 1 gets $1+\epsilon_1$.  
> **username_1**: Are you saying that player 1 moves first?  
> **username_0**: @username_1 No; it is a simultaneous move game.  
> **username_1**: Then how can player 2 "respond by playing N", if he doesn't observe player 1's choice of I?  
> **username_0**: @username_1 The payoff structure is common knowledge, so he knows that player 2 will play N if he plays $I$.  
> **username_1**: But they choose simultaneously. So how should player 1 know that he played $I$?  
> **username_1**: Or, on a more technical level: In a game, $U_i$ is always a function of the chosen strategy *profile*, not of player $i$'s chosen strategy alone!  
> **username_0**: @username_1 I understand that but am entirely lost in my approach to this problem. How would you suggest I approach it? Thank you.  
> **username_1**: First, in the question you should clarify who knows which $\epsilon_i$ at what point in time.  

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## 0 answers

