Two workers independently choose how much effort to put in their jobs. If worker 1 chooses e₁ ≥ 0 and worker 2 chooses e₂ ≥ 0, their payoffs are given by u₁(e1, €2,01,02) = 0101 + ße1e2− −e² 2 u₁(e₁, €2,01,0₂) = 0₂e2+ Be₁ €2-1/2e2²2 where 0 <ß < 1 and 0 ≤ 0; ≤ 1 for i = 1,2. Assume that 0; is player i̇'s private information: each player knows her own and believes that the other player's is drawn from the uniform distribution over [0, 1]. Find the Bayesian Nash equilibria of this game

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Chapter1: Making Economics Decisions
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Two workers independently choose how much effort to put in their jobs. If worker 1 chooses
e₁ ≥ 0 and worker 2 chooses e2 ≥ 0, their payoffs are given by
u₁(e₁,e2,01,02) = 0₁e₁ + ße₁e₂ ·
- 1/²
u₁ (e₁,e₂,0₁,0₂) = 0₂ €₂ + ßе₁e₂. = ²2
where 0 <ß < 1 and 0 ≤ 0; ≤ 1 for i:
=
1,2. Assume that 0; is player i's private information: each player
knows her own 0 and believes that the other player's 0 is drawn from the uniform distribution over [0, 1].
Find the Bayesian Nash equilibria of this game.
Transcribed Image Text:Two workers independently choose how much effort to put in their jobs. If worker 1 chooses e₁ ≥ 0 and worker 2 chooses e2 ≥ 0, their payoffs are given by u₁(e₁,e2,01,02) = 0₁e₁ + ße₁e₂ · - 1/² u₁ (e₁,e₂,0₁,0₂) = 0₂ €₂ + ßе₁e₂. = ²2 where 0 <ß < 1 and 0 ≤ 0; ≤ 1 for i: = 1,2. Assume that 0; is player i's private information: each player knows her own 0 and believes that the other player's 0 is drawn from the uniform distribution over [0, 1]. Find the Bayesian Nash equilibria of this game.
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