Bayes Nash Equilibria in Battle of SexesIs this equivalent to the game of chicken?Strategic form: mixed...

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Bayes Nash Equilibria in Battle of Sexes

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Bayes Nash Equilibria in Battle of Sexes


Is this equivalent to the game of chicken?Strategic form: mixed strategy nash equilibria?Bayesian Nash Equilibrium - Mixed StrategiesMonotone transformation of a gameComparing Nash equilibriaBayesian-Nash equilibrium in a first-price auctionGame Theory; Finding the Nash EquilibriaComputing pure strategy Nash equilibria in finite gamesBayesian Nash Equilibria: Strong and Weak TypesDefinition of Bayesian Nash equilibrium













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$begingroup$


Consider the static Bayesian game as described above. $ t_1$ and $ 𝑡_2$enter image description here are the types of the row and column player respectively, which are both uniformly distributed on the interval [0,1]. The first part of the question is asking us to find a Bayesian Nash Equilibrium. Trivially, don't the the top left and bottom right corners correspond to equilibrium outcomes? Unless I've misunderstood the definition of a BNE.










share|improve this question









$endgroup$

















    1












    $begingroup$


    Consider the static Bayesian game as described above. $ t_1$ and $ 𝑡_2$enter image description here are the types of the row and column player respectively, which are both uniformly distributed on the interval [0,1]. The first part of the question is asking us to find a Bayesian Nash Equilibrium. Trivially, don't the the top left and bottom right corners correspond to equilibrium outcomes? Unless I've misunderstood the definition of a BNE.










    share|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      Consider the static Bayesian game as described above. $ t_1$ and $ 𝑡_2$enter image description here are the types of the row and column player respectively, which are both uniformly distributed on the interval [0,1]. The first part of the question is asking us to find a Bayesian Nash Equilibrium. Trivially, don't the the top left and bottom right corners correspond to equilibrium outcomes? Unless I've misunderstood the definition of a BNE.










      share|improve this question









      $endgroup$




      Consider the static Bayesian game as described above. $ t_1$ and $ 𝑡_2$enter image description here are the types of the row and column player respectively, which are both uniformly distributed on the interval [0,1]. The first part of the question is asking us to find a Bayesian Nash Equilibrium. Trivially, don't the the top left and bottom right corners correspond to equilibrium outcomes? Unless I've misunderstood the definition of a BNE.







      game-theory bayesian-game






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 4 hours ago









      StudentStudent

      486




      486






















          1 Answer
          1






          active

          oldest

          votes


















          2












          $begingroup$

          Yes, you are correct. All types $t_{1}$ choose O (B) and all types $t_{2}$
          choose O (B) are both Bayesian equilibria.



          Note that there are other Bayesian equilibrium in this game, if you are interested this is explained in detail here (p. 10, see reference below) for this particular battle of the sexes with two-sided incomplete information. The basic idea is to note that in this game, each player has a continuum of types, and so the set of types is infinite. You can look for a Bayesian equilibrium in which player 1 goes to the $Opera$ if $t_{1}$ exceeds some critical value $x_{1}$ and chooses $Fight$ otherwise, and player 2 chooses to $Fight$ if $t_{2}$ exceeds some critical value $x_{2}$ and goes to the $Opera$ otherwise. To find the values $x_{1}$, $x_{2}$ that make these strategies a Bayesian equilibrium you can calculate each player's expected payoffs given the other player's strategy and find the optimal values based on this.



          Game Theory: Static and Dynamic Games of Incomplete Information
          Branislav L. Slantchev Department of Political Science, University of California – San Diego






          share|improve this answer











          $endgroup$









          • 2




            $begingroup$
            Ideally you would post a short description of the linked content, because links break over time. You can give a name that people can google, quote, etc.
            $endgroup$
            – Giskard
            3 hours ago










          • $begingroup$
            Fantastic. I must point out that the question had a hint about threshold values which is what confused me. Perhaps that is covered in your link.
            $endgroup$
            – Student
            3 hours ago










          • $begingroup$
            I have modified it to include the idea and reference @Giskard, thanks for the tip
            $endgroup$
            – user20105
            3 hours ago






          • 1




            $begingroup$
            @Student yes, there is a Bayesian equilibrium with threshold values. I included a quick hint here but it is very well explained in the link.
            $endgroup$
            – user20105
            3 hours ago












          Your Answer








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          1 Answer
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          1 Answer
          1






          active

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          active

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          active

          oldest

          votes









          2












          $begingroup$

          Yes, you are correct. All types $t_{1}$ choose O (B) and all types $t_{2}$
          choose O (B) are both Bayesian equilibria.



          Note that there are other Bayesian equilibrium in this game, if you are interested this is explained in detail here (p. 10, see reference below) for this particular battle of the sexes with two-sided incomplete information. The basic idea is to note that in this game, each player has a continuum of types, and so the set of types is infinite. You can look for a Bayesian equilibrium in which player 1 goes to the $Opera$ if $t_{1}$ exceeds some critical value $x_{1}$ and chooses $Fight$ otherwise, and player 2 chooses to $Fight$ if $t_{2}$ exceeds some critical value $x_{2}$ and goes to the $Opera$ otherwise. To find the values $x_{1}$, $x_{2}$ that make these strategies a Bayesian equilibrium you can calculate each player's expected payoffs given the other player's strategy and find the optimal values based on this.



          Game Theory: Static and Dynamic Games of Incomplete Information
          Branislav L. Slantchev Department of Political Science, University of California – San Diego






          share|improve this answer











          $endgroup$









          • 2




            $begingroup$
            Ideally you would post a short description of the linked content, because links break over time. You can give a name that people can google, quote, etc.
            $endgroup$
            – Giskard
            3 hours ago










          • $begingroup$
            Fantastic. I must point out that the question had a hint about threshold values which is what confused me. Perhaps that is covered in your link.
            $endgroup$
            – Student
            3 hours ago










          • $begingroup$
            I have modified it to include the idea and reference @Giskard, thanks for the tip
            $endgroup$
            – user20105
            3 hours ago






          • 1




            $begingroup$
            @Student yes, there is a Bayesian equilibrium with threshold values. I included a quick hint here but it is very well explained in the link.
            $endgroup$
            – user20105
            3 hours ago
















          2












          $begingroup$

          Yes, you are correct. All types $t_{1}$ choose O (B) and all types $t_{2}$
          choose O (B) are both Bayesian equilibria.



          Note that there are other Bayesian equilibrium in this game, if you are interested this is explained in detail here (p. 10, see reference below) for this particular battle of the sexes with two-sided incomplete information. The basic idea is to note that in this game, each player has a continuum of types, and so the set of types is infinite. You can look for a Bayesian equilibrium in which player 1 goes to the $Opera$ if $t_{1}$ exceeds some critical value $x_{1}$ and chooses $Fight$ otherwise, and player 2 chooses to $Fight$ if $t_{2}$ exceeds some critical value $x_{2}$ and goes to the $Opera$ otherwise. To find the values $x_{1}$, $x_{2}$ that make these strategies a Bayesian equilibrium you can calculate each player's expected payoffs given the other player's strategy and find the optimal values based on this.



          Game Theory: Static and Dynamic Games of Incomplete Information
          Branislav L. Slantchev Department of Political Science, University of California – San Diego






          share|improve this answer











          $endgroup$









          • 2




            $begingroup$
            Ideally you would post a short description of the linked content, because links break over time. You can give a name that people can google, quote, etc.
            $endgroup$
            – Giskard
            3 hours ago










          • $begingroup$
            Fantastic. I must point out that the question had a hint about threshold values which is what confused me. Perhaps that is covered in your link.
            $endgroup$
            – Student
            3 hours ago










          • $begingroup$
            I have modified it to include the idea and reference @Giskard, thanks for the tip
            $endgroup$
            – user20105
            3 hours ago






          • 1




            $begingroup$
            @Student yes, there is a Bayesian equilibrium with threshold values. I included a quick hint here but it is very well explained in the link.
            $endgroup$
            – user20105
            3 hours ago














          2












          2








          2





          $begingroup$

          Yes, you are correct. All types $t_{1}$ choose O (B) and all types $t_{2}$
          choose O (B) are both Bayesian equilibria.



          Note that there are other Bayesian equilibrium in this game, if you are interested this is explained in detail here (p. 10, see reference below) for this particular battle of the sexes with two-sided incomplete information. The basic idea is to note that in this game, each player has a continuum of types, and so the set of types is infinite. You can look for a Bayesian equilibrium in which player 1 goes to the $Opera$ if $t_{1}$ exceeds some critical value $x_{1}$ and chooses $Fight$ otherwise, and player 2 chooses to $Fight$ if $t_{2}$ exceeds some critical value $x_{2}$ and goes to the $Opera$ otherwise. To find the values $x_{1}$, $x_{2}$ that make these strategies a Bayesian equilibrium you can calculate each player's expected payoffs given the other player's strategy and find the optimal values based on this.



          Game Theory: Static and Dynamic Games of Incomplete Information
          Branislav L. Slantchev Department of Political Science, University of California – San Diego






          share|improve this answer











          $endgroup$



          Yes, you are correct. All types $t_{1}$ choose O (B) and all types $t_{2}$
          choose O (B) are both Bayesian equilibria.



          Note that there are other Bayesian equilibrium in this game, if you are interested this is explained in detail here (p. 10, see reference below) for this particular battle of the sexes with two-sided incomplete information. The basic idea is to note that in this game, each player has a continuum of types, and so the set of types is infinite. You can look for a Bayesian equilibrium in which player 1 goes to the $Opera$ if $t_{1}$ exceeds some critical value $x_{1}$ and chooses $Fight$ otherwise, and player 2 chooses to $Fight$ if $t_{2}$ exceeds some critical value $x_{2}$ and goes to the $Opera$ otherwise. To find the values $x_{1}$, $x_{2}$ that make these strategies a Bayesian equilibrium you can calculate each player's expected payoffs given the other player's strategy and find the optimal values based on this.



          Game Theory: Static and Dynamic Games of Incomplete Information
          Branislav L. Slantchev Department of Political Science, University of California – San Diego







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 1 hour ago









          Giskard

          13.7k32348




          13.7k32348










          answered 3 hours ago









          user20105user20105

          35010




          35010








          • 2




            $begingroup$
            Ideally you would post a short description of the linked content, because links break over time. You can give a name that people can google, quote, etc.
            $endgroup$
            – Giskard
            3 hours ago










          • $begingroup$
            Fantastic. I must point out that the question had a hint about threshold values which is what confused me. Perhaps that is covered in your link.
            $endgroup$
            – Student
            3 hours ago










          • $begingroup$
            I have modified it to include the idea and reference @Giskard, thanks for the tip
            $endgroup$
            – user20105
            3 hours ago






          • 1




            $begingroup$
            @Student yes, there is a Bayesian equilibrium with threshold values. I included a quick hint here but it is very well explained in the link.
            $endgroup$
            – user20105
            3 hours ago














          • 2




            $begingroup$
            Ideally you would post a short description of the linked content, because links break over time. You can give a name that people can google, quote, etc.
            $endgroup$
            – Giskard
            3 hours ago










          • $begingroup$
            Fantastic. I must point out that the question had a hint about threshold values which is what confused me. Perhaps that is covered in your link.
            $endgroup$
            – Student
            3 hours ago










          • $begingroup$
            I have modified it to include the idea and reference @Giskard, thanks for the tip
            $endgroup$
            – user20105
            3 hours ago






          • 1




            $begingroup$
            @Student yes, there is a Bayesian equilibrium with threshold values. I included a quick hint here but it is very well explained in the link.
            $endgroup$
            – user20105
            3 hours ago








          2




          2




          $begingroup$
          Ideally you would post a short description of the linked content, because links break over time. You can give a name that people can google, quote, etc.
          $endgroup$
          – Giskard
          3 hours ago




          $begingroup$
          Ideally you would post a short description of the linked content, because links break over time. You can give a name that people can google, quote, etc.
          $endgroup$
          – Giskard
          3 hours ago












          $begingroup$
          Fantastic. I must point out that the question had a hint about threshold values which is what confused me. Perhaps that is covered in your link.
          $endgroup$
          – Student
          3 hours ago




          $begingroup$
          Fantastic. I must point out that the question had a hint about threshold values which is what confused me. Perhaps that is covered in your link.
          $endgroup$
          – Student
          3 hours ago












          $begingroup$
          I have modified it to include the idea and reference @Giskard, thanks for the tip
          $endgroup$
          – user20105
          3 hours ago




          $begingroup$
          I have modified it to include the idea and reference @Giskard, thanks for the tip
          $endgroup$
          – user20105
          3 hours ago




          1




          1




          $begingroup$
          @Student yes, there is a Bayesian equilibrium with threshold values. I included a quick hint here but it is very well explained in the link.
          $endgroup$
          – user20105
          3 hours ago




          $begingroup$
          @Student yes, there is a Bayesian equilibrium with threshold values. I included a quick hint here but it is very well explained in the link.
          $endgroup$
          – user20105
          3 hours ago


















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