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VARulle
VARulle
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Bimatrix I was given these two bimatrices, for two different versions of a Bayesian-form game.

In the first version of the game, a player named The Nature chooses between $A$ or $B$ with probability $1/2$ each. The players don't know what The Nature chose. After that, players 1 and 2 play simultaneously, with utilities given by the bimatrix on the rightleft if The Nature chooses $A$, or the leftright one if The Nature chooses $B$. In this game I found a Nash equilibrium when player 1 chooses $Z$ and player 2 chooses $V$, with expected utilities $5$ and $1$, respectively.

In the second version of the game, player 1 knows what The Nature played, but player 2 doesn’t. Then they play the respective game simultaneously. Here I found a Nash equilibrium when player 1 chooses $(X_A, Y_B)$, and player 2 chooses W, i.e. if The Nature plays $A$ player 1 chooses $X$, and if The Nature plays $B$, player 2 chooses $Y$. However here the expected utilities of the players are $4$ and $1$ respectively, which seems counterintuitive since player 1 had more information, but gets a worst expected utility.

I want to know why this might be the case, and examples of games in real life (not necessarily related to economics) where this kind of things may happen.

Bimatrix I was given these two bimatrices, for two different versions of a Bayesian-form game.

In the first version of the game, a player named The Nature chooses between $A$ or $B$ with probability $1/2$ each. The players don't know what The Nature chose. After that, players 1 and 2 play simultaneously, with utilities given by the bimatrix on the right if The Nature chooses $A$, or the left one if The Nature chooses $B$. In this game I found a Nash equilibrium when player 1 chooses $Z$ and player 2 chooses $V$, with expected utilities $5$ and $1$, respectively.

In the second version of the game, player 1 knows what The Nature played, but player 2 doesn’t. Then they play the respective game simultaneously. Here I found a Nash equilibrium when player 1 chooses $(X_A, Y_B)$, and player 2 chooses W, i.e. if The Nature plays $A$ player 1 chooses $X$, and if The Nature plays $B$, player 2 chooses $Y$. However here the expected utilities of the players are $4$ and $1$ respectively, which seems counterintuitive since player 1 had more information, but gets a worst expected utility.

I want to know why this might be the case, and examples of games in real life (not necessarily related to economics) where this kind of things may happen.

Bimatrix I was given these two bimatrices, for two different versions of a Bayesian-form game.

In the first version of the game, a player named The Nature chooses between $A$ or $B$ with probability $1/2$ each. The players don't know what The Nature chose. After that, players 1 and 2 play simultaneously, with utilities given by the bimatrix on the left if The Nature chooses $A$, or the right one if The Nature chooses $B$. In this game I found a Nash equilibrium when player 1 chooses $Z$ and player 2 chooses $V$, with expected utilities $5$ and $1$, respectively.

In the second version of the game, player 1 knows what The Nature played, but player 2 doesn’t. Then they play the respective game simultaneously. Here I found a Nash equilibrium when player 1 chooses $(X_A, Y_B)$, and player 2 chooses W, i.e. if The Nature plays $A$ player 1 chooses $X$, and if The Nature plays $B$, player 2 chooses $Y$. However here the expected utilities of the players are $4$ and $1$ respectively, which seems counterintuitive since player 1 had more information, but gets a worst expected utility.

I want to know why this might be the case, and examples of games in real life (not necessarily related to economics) where this kind of things may happen.

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unconscious statistician
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Bayesian form games, situations in real life for which having more information is not necessarily better

Bimatrix I was given these two bimatrices, for two different versions of a Bayesian-form game.

In the first version of the game, a player named The Nature chooses between $A$ or $B$ with probability $1/2$ each. The players don't know what The Nature chose. After that, players 1 and 2 play simultaneously, with utilities given by the bimatrix on the right if The Nature chooses $A$, or the left one if The Nature chooses $B$. In this game I found a Nash equilibrium when player 1 chooses $Z$ and player 2 chooses $V$, with expected utilities $5$ and $1$, respectively.

In the second version of the game, player 1 knows what The Nature played, but player 2 doesn’t. Then they play the respective game simultaneously. Here I found a Nash equilibrium when player 1 chooses $(X_A, Y_B)$, and player 2 chooses W, i.e. if The Nature plays $A$ player 1 chooses $X$, and if The Nature plays $B$, player 2 chooses $Y$. However here the expected utilities of the players are $4$ and $1$ respectively, which seems counterintuitive since player 1 had more information, but gets a worst expected utility.

I want to know why this might be the case, and examples of games in real life (not necessarily related to economics) where this kind of things may happen.