Consider the game Ms. Bennet and Mr. Darcy play in ‘First Impressions’, Selected Set V. Suppose that Ms. Bennet prefers to meet Mr. Darcy (a = 0) with probability p. Further suppose that: - The ‘meeting Ms. Bennet’ plays Ball with probability q (and Dinner with probability 1 − q); - ‘avoiding Ms. Bennet’ plays Ball with probability r (and Dinner with probability 1 − r); M - r. Darcy plays Ball with probability s (and Dinner with probability 1 − s). Write down the strategic form game and find for all values of p ∈ (0, 1) the Bayesian-Nash equilibria in mixed strategies.
Consider the game Ms. Bennet and Mr. Darcy play in ‘First Impressions’, Selected Set V. Suppose that Ms. Bennet prefers to meet Mr. Darcy (a = 0) with probability p. Further suppose that:
- The ‘meeting Ms. Bennet’ plays Ball with probability q (and Dinner with probability 1 − q);
- ‘avoiding Ms. Bennet’ plays Ball with probability r (and Dinner with probability 1 − r); M
- r. Darcy plays Ball with probability s (and Dinner with probability 1 − s).
Write down the strategic form game and find for all values of p ∈ (0, 1) the Bayesian-Nash equilibria in mixed strategies.
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Is it possible that Step. 3 contains a contradiction? As "If Player 1 plays Ball (B): Player 2 meets (M) if the expected payoff of meeting is greater than the expected payoff of avoiding." and then, "If Player 1 has Dinner (D): Player 2 meets (M) if the expected payoff of meeting is greater than the expected payoff of avoiding." The same arises in the one for player 2. Is for both the second sentence meant to be "smaller than"? If not, please elaborate.
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