Two individuals are involved in a synergistic relationship. More effort is better for the relationship, but...

 

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Two individuals are involved in a synergistic relationship. More effort is better for the relationship, but effort is costly to each individual. Specif- ically, an effort level is a non-negative number, and player 1's payoff function is e1(1+e2 - e1), where ei is player I's effort level and ez is player 2's effort level. For player 2 the cost of effort is either the same as that of player 1, and hence her payoff function is given by 2(1+€1-e2) or effort is very costly for her in which case her payoff function is given by 2 (1+e1-22). Player 2 knows player 1's payoff function and if the cost of effort is high for herself or not. Player 1, however, is uncertain about player 2's cost of effort. He believes that the cost of effort is low with probability p, and high with probability 1-p, where 0 < p < 1. All of this is common knowledge. Find the Bayesian equilibrium of this game as a function of p. Two individuals are involved in a synergistic relationship. More effort is better for the relationship, but effort is costly to each individual. Specif- ically, an effort level is a non-negative number, and player 1's payoff function is e1(1+e2 - e1), where ei is player I's effort level and ez is player 2's effort level. For player 2 the cost of effort is either the same as that of player 1, and hence her payoff function is given by 2(1+€1-e2) or effort is very costly for her in which case her payoff function is given by 2 (1+e1-22). Player 2 knows player 1's payoff function and if the cost of effort is high for herself or not. Player 1, however, is uncertain about player 2's cost of effort. He believes that the cost of effort is low with probability p, and high with probability 1-p, where 0 < p < 1. All of this is common knowledge. Find the Bayesian equilibrium of this game as a function of p.

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The image contains a game theory problem statement that discusses a relationship between two individuals characterized as players in a game The players have to decide on their effort levels e1 and e2 ... View the full answer