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There are two players called 1 and 2. Player 1 can be of two types t E {0,1} with Pr (t=1) = n E (0,1). [Here, a is a symbol] The actions and payoffs of the game are given by: left right 0,4|1,1 up down 1,2 t,4 where the row player is player 1. We will use the following notation: 01(t): probability that player 1 plays up if she is of type t; 02: probability that player 2 plays left.

There are two players called 1 and 2. Player 1 can be of two types t E {0,1} with Pr (t=1) = n E (0,1). [Here, a is a symbol] The actions and payoffs of the game are given by: left right 0,4|1,1 up down 1,2 t,4 where the row player is player 1. We will use the following notation: 01(t): probability that player 1 plays up if she is of type t; 02: probability that player 2 plays left.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 33EQ
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If type-0 player 1 is mixing, what condition must be satisfied in this equilibrium?

There are two players called 1 and 2. Player 1 can be of two types t E {0,1} with Pr (t=1) = T. E (0,1). [Here, a is a symbol] The actions and payoffs of the game are given by: |left right up 0,4 1,1 down 1,2 t,4 where the row player is player 1. We will use the following notation: 01(t): probability that player 1 plays up if she is of type t; 02: probability that player 2 plays left.
Transcribed Image Text:There are two players called 1 and 2. Player 1 can be of two types t E {0,1} with Pr (t=1) = T. E (0,1). [Here, a is a symbol] The actions and payoffs of the game are given by: |left right up 0,4 1,1 down 1,2 t,4 where the row player is player 1. We will use the following notation: 01(t): probability that player 1 plays up if she is of type t; 02: probability that player 2 plays left.
We want to know whether and when it is possible that in a Bayes Nash equilibrium player 1 mixes between up and down whenever she is of type t = 0, i.e. 01(0) E (0,1). We therefore proceed to construct such an equilibrium and then verify for which values of t this equilibrium exists.
Transcribed Image Text:We want to know whether and when it is possible that in a Bayes Nash equilibrium player 1 mixes between up and down whenever she is of type t = 0, i.e. 01(0) E (0,1). We therefore proceed to construct such an equilibrium and then verify for which values of t this equilibrium exists.
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We can immediately conclude that in this equilibrium type-1 player 1 must play...? State your answer as a value for σ1(1).

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