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Question 20 Consider a two-player contractual setting in which the players produce as a team. In the underlying game, players 1 and 2 each select high (H) or low (L) effort. A player who selects H pays a cost of 6; selecting L costs nothing. The players equally share the revenue that their efforts produce. If they both select H, then revenue is 20. If they both select L, then revenue is 0. If one of them selects H and the other selects L, then revenue is x. Thus, if both players choose H, then they each obtain a payoff of. 20 - 6 = 4; if player 1 selects H and player 2 selects L, then player 1 gets .x - 6 and player 2 gets .x; and so on. Assume that x is between 0 and 20. Suppose a contract specifies the following monetary transfers from player 2 to player 1: a if (L, H) is played, ß if (H, L) is played, and y if (L, L) is played. a) Suppose that there is limited verifiability in the sense that the court can observe only the revenue (20, x, or 0) of the team, rather than the players' individual effort levels. How does this constrain a, ß, and y? b) What must be true about x to guarantee that (H, H) can be achieved with limited verifiability?

Question 20 Consider a two-player contractual setting in which the players produce as a team. In the underlying game, players 1 and 2 each select high (H) or low (L) effort. A player who selects H pays a cost of 6; selecting L costs nothing. The players equally share the revenue that their efforts produce. If they both select H, then revenue is 20. If they both select L, then revenue is 0. If one of them selects H and the other selects L, then revenue is x. Thus, if both players choose H, then they each obtain a payoff of. 20 - 6 = 4; if player 1 selects H and player 2 selects L, then player 1 gets .x - 6 and player 2 gets .x; and so on. Assume that x is between 0 and 20. Suppose a contract specifies the following monetary transfers from player 2 to player 1: a if (L, H) is played, ß if (H, L) is played, and y if (L, L) is played. a) Suppose that there is limited verifiability in the sense that the court can observe only the revenue (20, x, or 0) of the team, rather than the players' individual effort levels. How does this constrain a, ß, and y? b) What must be true about x to guarantee that (H, H) can be achieved with limited verifiability?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section3.7: Piecewise And Step Functions
Problem 30PPS
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Question 20 Consider a two-player contractual setting in which the players produce as a team. In the underlying game, players 1 and 2 each select high (H) or low (L) effort. A player who selects H pays a cost of 6; selecting L costs nothing. The players equally share the revenue that their efforts produce. If they both select H, then revenue is 20. If they both select L, then revenue is 0. If one of them selects H and the other selects L, then revenue is x. Thus, if both players choose H, then they each obtain a payoff of .20 - 6 = 4; if player 1 selects H and player 2 selects L, then player 1 gets .x-6 and player 2 gets . x; and so on. Assume that x is between 0 and 20. Suppose a contract specifies the following monetary transfers from player 2 to player 1: a if (L, H) is played, B if (H, L) is played, and y if (L, L) is played. a) Suppose that there is limited verifiability in the sense that the court can observe only the revenue (20, x, or 0) of the team, rather than the players' individual effort levels. How does this constrain a, B, and y? b) What must be true about x to guarantee that (H, H) can be achieved with limited verifiability?
Transcribed Image Text:Question 20 Consider a two-player contractual setting in which the players produce as a team. In the underlying game, players 1 and 2 each select high (H) or low (L) effort. A player who selects H pays a cost of 6; selecting L costs nothing. The players equally share the revenue that their efforts produce. If they both select H, then revenue is 20. If they both select L, then revenue is 0. If one of them selects H and the other selects L, then revenue is x. Thus, if both players choose H, then they each obtain a payoff of .20 - 6 = 4; if player 1 selects H and player 2 selects L, then player 1 gets .x-6 and player 2 gets . x; and so on. Assume that x is between 0 and 20. Suppose a contract specifies the following monetary transfers from player 2 to player 1: a if (L, H) is played, B if (H, L) is played, and y if (L, L) is played. a) Suppose that there is limited verifiability in the sense that the court can observe only the revenue (20, x, or 0) of the team, rather than the players' individual effort levels. How does this constrain a, B, and y? b) What must be true about x to guarantee that (H, H) can be achieved with limited verifiability?
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