Consider a strategic interaction between the General Manager of the Tennessee Titans (GM) and a Free...

  

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Consider a strategic interaction between the General Manager of the Tennessee Titans (GM) and a Free Agent (FA) that the team wants to sign, Bud Dupree. The sequential interaction is depicted in the following game tree. The GM has the choice of offering the free agent player a high (H) or low (L) salary, and Bud responds by either signing the contract to join the team or not signing it and pursing employment elsewhere. If the GM signs the player to a high salary, the Titans increase their total wins for the upcoming season by 3 thanks to adding Bud, but they have no additional money to sign other free agents. If the GM signs Bud to a low salary, the Titans increase their total wins for the season by 4 thanks to adding Bud AND signing another player with their remaining salary cap room. If they don t sign Bud, they improve their win total only by 2 by signing less desirable free agents. Bud gets a payoff of $4 million from the high-salary contract and $2 million from the low-salary contract. Suppose that this is his only offer in free agency, so if he doesn t sign the offered contract, he earns $0. a. Sign FA Don t GM Sign FA Don t Use rollback analysis to find the SPNE of the game. Write out the equilibrium in complete strategies and list the equilibrium payoffs to both players b. Is there a strategic move (promise, threat, or commitment) that the free agent can make to improve their payoffs? Please explain. c. Suppose the free agent has a history of injuries and the GM thinks that there is a 50% chance that Bud will be too hurt to play in the following season. This is determined by Nature. If Bud is hurt and the Titans gave him a high-salary, the team gains no wins at all from their sole free-agent acquisition, but if Bud hurt and they only signed him to a low-salary, they still gain 1 win from their other new players. Assume the GM is risk- neutral (he makes decisions based on expected payoffs). Find the SPNE and equilibrium expected payoffs. Would the Free Agent s strategic move from part b. still work? chance 1/2 Sign 4 FA 1/2 0 Don t ON GM Sign chance 1/2 1/2 2 FA Don t ON d. Finally, suppose that instead Bud s chance of staying healthy is p (a decimal between 0 and 1), instead of 1/2, and now assume that the GM also has the option of not making an offer (N), which immediately ends the game and gives the Titans an payoff of 2 and the free agent a payoff of $0. For what values of p will the SPNE be (N, Sign, Sign)? chance р FA Sign (1-p) 04 H Don t 20 chance р 42 Sign GM FA L 12 N (1-p) Don t 20 Consider a strategic interaction between the General Manager of the Tennessee Titans (GM) and a Free Agent (FA) that the team wants to sign, Bud Dupree. The sequential interaction is depicted in the following game tree. The GM has the choice of offering the free agent player a high (H) or low (L) salary, and Bud responds by either signing the contract to join the team or not signing it and pursing employment elsewhere. If the GM signs the player to a high salary, the Titans increase their total wins for the upcoming season by 3 thanks to adding Bud, but they have no additional money to sign other free agents. If the GM signs Bud to a low salary, the Titans increase their total wins for the season by 4 thanks to adding Bud AND signing another player with their remaining salary cap room. If they don t sign Bud, they improve their win total only by 2 by signing less desirable free agents. Bud gets a payoff of $4 million from the high-salary contract and $2 million from the low-salary contract. Suppose that this is his only offer in free agency, so if he doesn t sign the offered contract, he earns $0. a. Sign FA Don t GM Sign FA Don t Use rollback analysis to find the SPNE of the game. Write out the equilibrium in complete strategies and list the equilibrium payoffs to both players b. Is there a strategic move (promise, threat, or commitment) that the free agent can make to improve their payoffs? Please explain. c. Suppose the free agent has a history of injuries and the GM thinks that there is a 50% chance that Bud will be too hurt to play in the following season. This is determined by Nature. If Bud is hurt and the Titans gave him a high-salary, the team gains no wins at all from their sole free-agent acquisition, but if Bud hurt and they only signed him to a low-salary, they still gain 1 win from their other new players. Assume the GM is risk- neutral (he makes decisions based on expected payoffs). Find the SPNE and equilibrium expected payoffs. Would the Free Agent s strategic move from part b. still work? chance 1/2 Sign 4 FA 1/2 0 Don t ON GM Sign chance 1/2 1/2 2 FA Don t ON d. Finally, suppose that instead Bud s chance of staying healthy is p (a decimal between 0 and 1), instead of 1/2, and now assume that the GM also has the option of not making an offer (N), which immediately ends the game and gives the Titans an payoff of 2 and the free agent a payoff of $0. For what values of p will the SPNE be (N, Sign, Sign)? chance р FA Sign (1-p) 04 H Don t 20 chance р 42 Sign GM FA L 12 N (1-p) Don t 20

Answer rating: 100% (QA)

a To find the Subgame Perfect Nash Equilibrium SPNE of the game we can use rollback analysis starting from the final decision nodes and working our way back 1 At the final decision node if the Free Ag... View the full answer