Case Study Decision Making with Final Offer Arbitration Introduction When a buyer and seller are negotiating a price, at times the process hits an impasse The seller wants a higher price, but the buyer is adamant about paying a lower one In these cases, the buyer and seller may turn to arbitration Sometimes each side of the dispute selects one person to serve on an arbitration panel, and the two arbitrators select a third to complete the panel At other times, one neutral arbitrator is chosen to hear the case Both sides of the controversy present their arguments and their offers to the arbitrator (whether an individual or a panel), who renders a decision Often the arbitrator splits the difference by selecting a price between the two offers In some arbitrations, the two sides must accept the decision in others, the decision is advisory, and one or even both sides can reject it and resume negotiations In one type of arbitration, however, the arbitrator is not allowed to split the difference, and the buyer or seller must accept the judgment In this arbitration, called final offer arbitration, the arbitrator selects one of the offers and cannot change it Several states require final offer arbitration between management and public sector unions that legally are forbidden to strike, such as police, prison guards, and firefighters Major League Baseball (MLB), a professional baseball organization consisting of 29 teams in the United States and 1 team in Canada, also uses final offer arbitration When an MLB player and the owners of his team cannot agree on a salary, final offer arbitration is a mechanism for resolving salary disputes 1 The player is entitled to put the dispute before a three person arbitration panel The three arbitrators are neutral that is, none of them will favor one side or the other Both sides submit their final offers, along with supporting documents, to the arbitrators The arbitrators take the midpoint between the team's offer and the player's demand If the evidence shows that the player's market value is higher than the midpoint, the panel awards the higher salary demanded by the player If the evidence shows that the player's market value is lower than the midpoint, the panel awards the lower salary offered by the team to the player The decision of the panel is binding on the two parties If the panel chooses the team's offer, the player is obligated to sign a one year contract for that salary If the player wins, the team must offer the player a one year contract with the higher salary These salary disputes might seem far removed from the legal disputes examined in this chapter, but the economic analysis of settlements presents a solid framework for a manager or an agent to use to make decisions in this sort of arbitration Indeed, arbitration panels actually hear very few of the MLB cases that players and teams file because, just as is the case with lawsuits, the vast majority of these disputes are settled 1 Only a subset of players is eligible for final offer arbitration Players with one or two years' experience are not entitled to final offer arbitration, and players with six years' or more experience become free agents unless they are under contract with a team Only players in between, those who have three to five years' experience, are eligible for final offer arbitration because the rules allow them to bargain only with their current team Final Offer Arbitration Example In the 2006 baseball season, the Chicago Cubs paid pitcher Carlos Zambrano $6 6 million He had a good year, with a record of 16 wins and 7 losses, an earned run average (ERA) of 3 41, and 210 strikeouts When he and the Cubs could not agree on a salary for the 2007 season, Mr Zambrano filed for arbitration His final offer was $15 5 million, and the Cubs' final offer was $11 0 million Suppose that you are an executive for the Cubs To help determine your strategy, you need to make three important decisions 1 You must determine how much money is at stake In other words, how much money is in dispute At first glance, you might think the answer is $15 5 million, Mr Zambrano's offer This answer, however, is too easy and it is also incorrect If the arbitrators reject Mr Zambrano's $15 5 million offer, they will accept your club's offer of $11 0 million At stake is only the difference between the two offers $4 5 million because the player is guaranteed to receive at least $11 0 million Call the sum of money in dispute, $4 5 million, S 2 You must decide your subjective probability of Mr Zambrano winning the arbitration You think that his agent assembled a strong case, so you assess his probability of winning at 70 percent In other words, you estimate that the arbitrators will select Mr Zambrano's offer 70 percent of the time His 70 percent chance of prevailing leaves you and the Cubs a 30 percent chance of winning Call the probability that Mr Zambrano wins q, so that the probability that the Cubs win is 1 9 3 You must decide on your estimate of the cost of going to arbitration for the Cubs You have already incurred many of the costs necessary to assemble the supporting documents submitted to the arbitrators These sunk costs do not factor into this calculation, but you do need to consider some other costs In particular, if you win the arbitration, Mr Zambrano could possibly be upset and not play to his potential You might set this cost and all the others of going to arbitration at $1 million Call the club's cost of going to arbitration CC Once you have these three numerical estimates, you can calculate the expected cost to the Cubs of going to arbitration This cost is E C cubs, where C refers to the Cubs' cost of arbitration and the E means you are calculating the expected value The expected cost to the Cubs is equal to the amount in dispute multiplied by the probability of losing plus the cost to the Cubs of going to arbitration In terms of a formula, the expected cost is E C cuss (qxS) (1 q)x$0 CC This formula is the same as the formula for the expected loss from litigation for the defendant In this baseball example, the expected cost to the Cubs of allowing the arbitrators to decide the salary is (0 70x$4 5 million) $1 million $4 15 million As a Cubs executive, you know that you will pay Mr Zambrano at least $11 0 million If the contract goes before the arbitrators, add your expected cost of $4 15 million to the $11 0 million for the total expected cost of hiring Mr Zambrano, $15 15 million You can lower the Cubs' expected cost by agreeing to any contract that specifies a salary of $15 15 million or less and settling (not going before the arbitrators) Now suppose that you are Mr Zambrano's agent You realize that he is guaranteed to receive at least $11 0 million, so once again the amount in dispute, S, is $4 5 million If the contract goes to the arbitrators and they decide in favor of Mr Zambrano's offer, he receives a contract of $15 5 million, collecting the entire $4 5 million in contention You attach a probability, p, of 40 percent to this outcome If the arbitrators decide in favor of the Cubs, Mr Zambrano receives a contract of $11 0 million and collects none of the amount in dispute The probability of this outcome is 1 p, or 60 percent Finally, the cost to the player, CP, of going to arbitration is $0 5 million, perhaps because the dispute gives him a reputation of being hard to deal with, which makes other teams less likely to sign him Call the expected gain to Mr Zambrano E G ZAMBRANO, where G refers to his gain from arbitration The expected gain from arbitration to Mr Zambrano is equal to the amount in dispute multiplied by the probability that he will prevail minus the cost of going to arbitration E G ZAMBRANO (PxS) ((1 p) $0 CP Using this formula, which is precisely the same as the formula for the expected gain from litigation for the plaintiff, Mr Zambrano's expected gain from arbitration is (0 40x$4 5 million) $0 5 million $1 3 million Because he is guaranteed to receive at least $11 0 million, his expected contract is $11 0 million $1 3 million $12 3 million As Mr Zambrano's agent, you can increase the expected contract by agreeing to any contract specifying a salary of more than $12 3 million The Cubs are willing to sign any contract for less than $15 15 million Mr Zambrano is willing to sign any contract for more than $12 3 million Clearly, there is room to settle the contract before the arbitrators issue their ruling So does it surprise you that the final offers Mr Zambrano and the Cubs submitted to the arbitrators are not really final offers The two sides reached an agreement on a one year deal for $12 4 million The fact that the agreement was only marginally above the minimum Mr Zambrano would accept is perhaps a testament to the bargaining prowess of the Cubs' negotiator The data show that approximately 90 percent of the MLB cases of final offer arbitration settle before the arbitrators issue their decision This statistic is interesting and certainly in keeping with the analysis above, but the important general point is that you can analyze final offer arbitration in the exact same way as the litigation settlements you learned about in this chapter The lesson from this observation is clear Economic principles, such as how to analyze the profit or loss from a lawsuit, apply in a wide variety of situations, and they can aid you in numerous managerial decisions Your Decisions In Canada, disputes between commercial shippers and railways that carry the freight can be resolved via final offer arbitration The Canadian Transportation Act allows shippers to appeal the freight rates charged by the Canadian Pacific Railway and Canadian National Railway to the Canadian Transportation Agency (CTA) The CTA appoints an arbitrator who then uses final offer arbitration to determine what the shipper will pay the railroad The shipper and the carrier are allowed to present a variety of information to help support their offers For example, they can present evidence of the following The presence (or absence) of alternative shipping methods and the cost of using the alternative The freight rate charged immediately before the dispute Any special cost incurred by the railroad to transport the shipper's product The market for the shipper's product Suppose that you are an owner of a company that wants to ship its product on a Canadian railroad Last year your company paid $12 million for shipping by rail This year you and the railroad's executives have been negotiating, but the best offer they have made is $16 million If you use a trucking company, shipping will cost you $15 million You know that if you accept the trucking company's offer, you will make zero economic profit, so that you will receive only your competitive return You are deciding whether to go to the CTA and ask for final offer arbitration, during which you expect the railroad will ask for $16 million If you use final offer arbitration, you must abide by the arbitrator's decision that is, if the arbitrator chooses the railroad's offer, you will pay the railroad $16 million for shipping for this year and cannot use the trucking company's lower cost offer of $15 million You are thinking of presenting one of two possible offers to the arbitrator $12 million and $13 million You estimate that if you offer $12 million, you have a 25 percent chance that the arbitrator will select your offer, while if you offer $13 million, you have an 80 percent chance that the arbitrator will select your offer You also think that it will cost you $0 5 million to go to arbitration QUESTIONS 1 If you go to arbitration and offer $12 million, what is the expected cost of the contract 2 If you go to arbitration and offer $13 million, what is the expected cost of the contract 3 If you decide to go to arbitration, which of your two possible offers will you make If you do not worry about risk and care only to minimize your expected cost, explain whether or not you will ask the CTA for arbitration 4 If you go to arbitration, what risk do you face Explain how this affects your decision to ask the CTA for arbitration 5 As the owner of the business, will you ask the CTA for arbitration Explain your decision Case Study Decision Making with Final Offer Arbitration Introduction When a buyer and seller are negotiating a price, at times the process hits an impasse The seller wants a higher price, but the buyer is adamant about paying a lower one In these cases, the buyer and seller may turn to arbitration Sometimes each side of the dispute selects one person to serve on an arbitration panel, and the two arbitrators select a third to complete the panel At other times, one neutral arbitrator is chosen to hear the case Both sides of the controversy present their arguments and their offers to the arbitrator (whether an individual or a panel), who renders a decision Often the arbitrator splits the difference by selecting a price between the two offers In some arbitrations, the two sides must accept the decision in others, the decision is advisory, and one or even both sides can reject it and resume negotiations In one type of arbitration, however, the arbitrator is not allowed to split the difference, and the buyer or seller must accept the judgment In this arbitration, called final offer arbitration, the arbitrator selects one of the offers and cannot change it Several states require final offer arbitration between management and public sector unions that legally are forbidden to strike, such as police, prison guards, and firefighters Major League Baseball (MLB), a professional baseball organization consisting of 29 teams in the United States and 1 team in Canada, also uses final offer arbitration When an MLB player and the owners of his team cannot agree on a salary, final offer arbitration is a mechanism for resolving salary disputes 1 The player is entitled to put the dispute before a three person arbitration panel The three arbitrators are neutral that is, none of them will favor one side or the other Both sides submit their final offers, along with supporting documents, to the arbitrators The arbitrators take the midpoint between the team's offer and the player's demand If the evidence shows that the player's market value is higher than the midpoint, the panel awards the higher salary demanded by the player If the evidence shows that the player's market value is lower than the midpoint, the panel awards the lower salary offered by the team to the player The decision of the panel is binding on the two parties If the panel chooses the team's offer, the player is obligated to sign a one year contract for that salary If the player wins, the team must offer the player a one year contract with the higher salary These salary disputes might seem far removed from the legal disputes examined in this chapter, but the economic analysis of settlements presents a solid framework for a manager or an agent to use to make decisions in this sort of arbitration Indeed, arbitration panels actually hear very few of the MLB cases that players and teams file because, just as is the case with lawsuits, the vast majority of these disputes are settled 1 Only a subset of players is eligible for final offer arbitration Players with one or two years' experience are not entitled to final offer arbitration, and players with six years' or more experience become free agents unless they are under contract with a team Only players in between, those who have three to five years' experience, are eligible for final offer arbitration because the rules allow them to bargain only with their current team Final Offer Arbitration Example In the 2006 baseball season, the Chicago Cubs paid pitcher Carlos Zambrano $6 6 million He had a good year, with a record of 16 wins and 7 losses, an earned run average (ERA) of 3 41, and 210 strikeouts When he and the Cubs could not agree on a salary for the 2007 season, Mr Zambrano filed for arbitration His final offer was $15 5 million, and the Cubs' final offer was $11 0 million Suppose that you are an executive for the Cubs To help determine your strategy, you need to make three important decisions 1 You must determine how much money is at stake In other words, how much money is in dispute At first glance, you might think the answer is $15 5 million, Mr Zambrano's offer This answer, however, is too easy and it is also incorrect If the arbitrators reject Mr Zambrano's $15 5 million offer, they will accept your club's offer of $11 0 million At stake is only the difference between the two offers $4 5 million because the player is guaranteed to receive at least $11 0 million Call the sum of money in dispute, $4 5 million, S 2 You must decide your subjective probability of Mr Zambrano winning the arbitration You think that his agent assembled a strong case, so you assess his probability of winning at 70 percent In other words, you estimate that the arbitrators will select Mr Zambrano's offer 70 percent of the time His 70 percent chance of prevailing leaves you and the Cubs a 30 percent chance of winning Call the probability that Mr Zambrano wins q, so that the probability that the Cubs win is 1 9 3 You must decide on your estimate of the cost of going to arbitration for the Cubs You have already incurred many of the costs necessary to assemble the supporting documents submitted to the arbitrators These sunk costs do not factor into this calculation, but you do need to consider some other costs In particular, if you win the arbitration, Mr Zambrano could possibly be upset and not play to his potential You might set this cost and all the others of going to arbitration at $1 million Call the club's cost of going to arbitration CC Once you have these three numerical estimates, you can calculate the expected cost to the Cubs of going to arbitration This cost is E C cubs, where C refers to the Cubs' cost of arbitration and the E means you are calculating the expected value The expected cost to the Cubs is equal to the amount in dispute multiplied by the probability of losing plus the cost to the Cubs of going to arbitration In terms of a formula, the expected cost is E C cuss (qxS) (1 q)x$0 CC This formula is the same as the formula for the expected loss from litigation for the defendant In this baseball example, the expected cost to the Cubs of allowing the arbitrators to decide the salary is (0 70x$4 5 million) $1 million $4 15 million As a Cubs executive, you know that you will pay Mr Zambrano at least $11 0 million If the contract goes before the arbitrators, add your expected cost of $4 15 million to the $11 0 million for the total expected cost of hiring Mr Zambrano, $15 15 million You can lower the Cubs' expected cost by agreeing to any contract that specifies a salary of $15 15 million or less and settling (not going before the arbitrators) Now suppose that you are Mr Zambrano's agent You realize that he is guaranteed to receive at least $11 0 million, so once again the amount in dispute, S, is $4 5 million If the contract goes to the arbitrators and they decide in favor of Mr Zambrano's offer, he receives a contract of $15 5 million, collecting the entire $4 5 million in contention You attach a probability, p, of 40 percent to this outcome If the arbitrators decide in favor of the Cubs, Mr Zambrano receives a contract of $11 0 million and collects none of the amount in dispute The probability of this outcome is 1 p, or 60 percent Finally, the cost to the player, CP, of going to arbitration is $0 5 million, perhaps because the dispute gives him a reputation of being hard to deal with, which makes other teams less likely to sign him Call the expected gain to Mr Zambrano E G ZAMBRANO, where G refers to his gain from arbitration The expected gain from arbitration to Mr Zambrano is equal to the amount in dispute multiplied by the probability that he will prevail minus the cost of going to arbitration E G ZAMBRANO (PxS) ((1 p) $0 CP Using this formula, which is precisely the same as the formula for the expected gain from litigation for the plaintiff, Mr Zambrano's expected gain from arbitration is (0 40x$4 5 million) $0 5 million $1 3 million Because he is guaranteed to receive at least $11 0 million, his expected contract is $11 0 million $1 3 million $12 3 million As Mr Zambrano's agent, you can increase the expected contract by agreeing to any contract specifying a salary of more than $12 3 million The Cubs are willing to sign any contract for less than $15 15 million Mr Zambrano is willing to sign any contract for more than $12 3 million Clearly, there is room to settle the contract before the arbitrators issue their ruling So does it surprise you that the final offers Mr Zambrano and the Cubs submitted to the arbitrators are not really final offers The two sides reached an agreement on a one year deal for $12 4 million The fact that the agreement was only marginally above the minimum Mr Zambrano would accept is perhaps a testament to the bargaining prowess of the Cubs' negotiator The data show that approximately 90 percent of the MLB cases of final offer arbitration settle before the arbitrators issue their decision This statistic is interesting and certainly in keeping with the analysis above, but the important general point is that you can analyze final offer arbitration in the exact same way as the litigation settlements you learned about in this chapter The lesson from this observation is clear Economic principles, such as how to analyze the profit or loss from a lawsuit, apply in a wide variety of situations, and they can aid you in numerous managerial decisions Your Decisions In Canada, disputes between commercial shippers and railways that carry the freight can be resolved via final offer arbitration The Canadian Transportation Act allows shippers to appeal the freight rates charged by the Canadian Pacific Railway and Canadian National Railway to the Canadian Transportation Agency (CTA) The CTA appoints an arbitrator who then uses final offer arbitration to determine what the shipper will pay the railroad The shipper and the carrier are allowed to present a variety of information to help support their offers For example, they can present evidence of the following The presence (or absence) of alternative shipping methods and the cost of using the alternative The freight rate charged immediately before the dispute Any special cost incurred by the railroad to transport the shipper's product The market for the shipper's product Suppose that you are an owner of a company that wants to ship its product on a Canadian railroad Last year your company paid $12 million for shipping by rail This year you and the railroad's executives have been negotiating, but the best offer they have made is $16 million If you use a trucking company, shipping will cost you $15 million You know that if you accept the trucking company's offer, you will make zero economic profit, so that you will receive only your competitive return You are deciding whether to go to the CTA and ask for final offer arbitration, during which you expect the railroad will ask for $16 million If you use final offer arbitration, you must abide by the arbitrator's decision that is, if the arbitrator chooses the railroad's offer, you will pay the railroad $16 million for shipping for this year and cannot use the trucking company's lower cost offer of $15 million You are thinking of presenting one of two possible offers to the arbitrator $12 million and $13 million You estimate that if you offer $12 million, you have a 25 percent chance that the arbitrator will select your offer, while if you offer $13 million, you have an 80 percent chance that the arbitrator will select your offer You also think that it will cost you $0 5 million to go to arbitration QUESTIONS 1 If you go to arbitration and offer $12 million, what is the expected cost of the contract 2 If you go to arbitration and offer $13 million, what is the expected cost of the contract 3 If you decide to go to arbitration, which of your two possible offers will you make If you do not worry about risk and care only to minimize your expected cost, explain whether or not you will ask the CTA for arbitration 4 If you go to arbitration, what risk do you face Explain how this affects your decision to ask the CTA for arbitration 5 As the owner of the business, will you ask the CTA for arbitration Explain your decision

Question

Case Study  Decision Making with Final Offer Arbitration Introduction When a buyer and seller are negotiating a price, at times the process hits an impasse  The seller wants a higher price, but the buyer is adamant about paying a lower one  In these cases, the buyer and seller may turn to arbitration  Sometimes each side of the dispute selects one person to serve on an arbitration panel, and the two arbitrators select a third to complete the panel  At other times, one neutral arbitrator is chosen to hear the case  Both sides of the controversy present their arguments and their offers to the arbitrator (whether an individual or a panel), who renders a decision  Often the arbitrator  splits the difference  by selecting a price between the two offers  In some arbitrations, the two sides must accept the decision  in others, the decision is advisory, and one or even both sides can reject it and resume negotiations  In one type of arbitration, however, the arbitrator is not allowed to split the difference, and the buyer or seller must accept the judgment  In this arbitration, called final offer arbitration, the arbitrator selects one of the offers and cannot change it  Several states require final offer arbitration between management and public sector unions that legally are forbidden to strike, such as police, prison guards, and firefighters  Major League Baseball (MLB), a professional baseball organization consisting of 29 teams in the United States and 1 team in Canada, also uses final offer arbitration  When an MLB player and the owners of his team cannot agree on a salary, final offer arbitration is a mechanism for resolving salary disputes 1 The player is entitled to put the dispute before a three person arbitration panel  The three arbitrators are neutral  that is, none of them will favor one side or the other  Both sides submit their final  offers, along with supporting documents, to the arbitrators  The arbitrators take the midpoint between the team's offer and the player's demand  If the evidence shows that the player's market value is higher than the midpoint, the panel awards the higher salary demanded by the player  If the evidence shows that the player's market value is lower than the midpoint, the panel awards the lower salary offered by the team to the player  The decision of the panel is binding on the two parties  If the panel chooses the team's offer, the player is obligated to sign a one year contract for that salary  If the player wins, the team must offer the player a one year contract with the higher salary  These salary disputes might seem far removed from the legal disputes examined in this chapter, but the economic analysis of settlements presents a solid framework for a manager or an agent to use to make decisions in this sort of arbitration  Indeed, arbitration panels actually hear very few of the MLB cases that players and teams file because, just as is the case with lawsuits, the vast majority of these disputes are settled  1 Only a subset of players is eligible for final offer arbitration  Players with one or two years' experience are not entitled to final offer arbitration, and players with six years' or more experience become free agents unless they are under contract with a team  Only players in between, those who have three to five years' experience, are eligible for final offer arbitration because the rules allow them to bargain only with their current team  Final Offer Arbitration Example In the 2006 baseball season, the Chicago Cubs paid pitcher Carlos Zambrano $6 6 million  He had a good year, with a record of 16 wins and 7 losses, an earned run average (ERA) of 3 41, and 210 strikeouts  When he and the Cubs could not agree on a salary for the 2007 season, Mr  Zambrano filed for arbitration  His final offer was $15 5 million, and the Cubs' final offer was $11 0 million  Suppose that you are an executive for the Cubs  To help determine your strategy, you need to make three important decisions  1  You must determine how much money is at stake  In other words, how much money is in dispute  At first glance, you might think the answer is $15 5 million, Mr  Zambrano's offer  This answer, however, is too easy and it is also incorrect  If the arbitrators reject Mr  Zambrano's $15 5 million offer, they will accept your club's offer of $11 0 million  At stake is only the difference between the two offers $4 5 million because the player is guaranteed to receive at least $11 0 million  Call the sum of money in dispute, $4 5 million, S  2  You must decide your subjective probability of Mr  Zambrano winning the arbitration  You think that his agent assembled a strong case, so you assess his probability of winning at 70 percent  In other words, you estimate that the arbitrators will select Mr  Zambrano's offer 70 percent of the time  His 70 percent chance of prevailing leaves you and the Cubs a 30 percent chance of winning  Call the probability that Mr  Zambrano wins q, so that the probability that the Cubs win is 1 9  3  You must decide on your estimate of the cost of going to arbitration for the Cubs  You have already incurred many of the costs necessary to assemble the supporting documents submitted to the arbitrators  These sunk costs do not factor into this calculation, but you do need to consider some other costs  In particular, if you win the arbitration, Mr  Zambrano could possibly be upset and not play to his potential  You might set this cost and all the others of going to arbitration at $1 million  Call the club's cost of going to arbitration CC  Once you have these three numerical estimates, you can calculate the expected cost to the Cubs of going to arbitration  This cost is E C cubs, where C refers to the Cubs' cost of arbitration and the E means you are calculating the expected value  The expected cost to the Cubs is equal to the amount in dispute multiplied by the probability of losing plus the cost to the Cubs of going to arbitration  In terms of a formula, the expected cost is E C cuss (qxS)  (1 q)x$0  CC  This formula is the same as the formula for the expected loss from litigation for the defendant  In this baseball example, the expected cost to the Cubs of allowing the arbitrators to decide the salary is (0 70x$4 5 million) $1 million $4 15 million  As a Cubs executive, you know that you will pay Mr  Zambrano at least $11 0 million  If the contract goes before the arbitrators, add your expected cost of $4 15 million to the $11 0 million for the total expected cost of hiring Mr  Zambrano, $15 15 million  You can lower the Cubs' expected cost by agreeing to any contract that specifies a salary of $15 15 million or less and settling (not going before the arbitrators)  Now suppose that you are Mr  Zambrano's agent  You realize that he is guaranteed to receive at least $11 0 million, so once again the amount in dispute, S, is $4 5 million  If the contract goes to the arbitrators and they decide in favor of Mr  Zambrano's offer, he receives a contract of $15 5 million, collecting the entire $4 5 million in contention  You attach a probability, p, of 40 percent to this outcome  If the arbitrators decide in favor of the Cubs, Mr  Zambrano receives a contract of $11 0 million and collects none of the amount in dispute  The probability of this outcome is 1 p, or 60 percent  Finally, the cost to the player, CP, of going to arbitration is $0 5 million, perhaps because the dispute gives him a reputation of being hard to deal with, which makes other teams less likely to sign him  Call the expected gain to Mr  Zambrano E G ZAMBRANO, where G refers to his gain from arbitration  The expected gain from arbitration to Mr  Zambrano is equal to the amount in dispute multiplied by the probability that he will prevail minus the cost of going to arbitration  E G ZAMBRANO (PxS) ((1 p) $0  CP  Using this formula, which is precisely the same as the formula for the expected gain from litigation for the plaintiff, Mr  Zambrano's expected gain from arbitration is (0 40x$4 5 million) $0 5 million $1 3 million  Because he is guaranteed to receive at least $11 0 million, his expected contract is $11 0 million $1 3 million $12 3 million  As Mr  Zambrano's agent, you can increase the expected contract by agreeing to any contract specifying a salary of more than $12 3 million  The Cubs are willing to sign any contract for less than $15 15 million  Mr  Zambrano is willing to sign any contract for more than $12 3 million  Clearly, there is room to settle the contract before the arbitrators issue their ruling  So does it surprise you that the final offers Mr  Zambrano and the Cubs submitted to the arbitrators are not really final offers  The two sides reached an agreement on a one year deal for $12 4 million  The fact that the agreement was only marginally above the minimum Mr  Zambrano would accept is perhaps a testament to the bargaining prowess of the Cubs' negotiator  The data show that approximately 90 percent of the MLB cases of final offer arbitration settle before the arbitrators issue their decision  This statistic is interesting and certainly in keeping with the analysis above, but the important general point is that you can analyze final offer arbitration in the exact same way as the litigation settlements you learned about in this chapter  The lesson from this observation is clear  Economic principles, such as how to analyze the profit or loss from a lawsuit, apply in a wide variety of situations, and they can aid you in numerous managerial decisions  Your Decisions In Canada, disputes between commercial shippers and railways that carry the freight can be resolved via final offer arbitration  The Canadian Transportation Act allows shippers to appeal the freight rates charged by the Canadian Pacific Railway and Canadian National Railway to the Canadian Transportation Agency (CTA)  The CTA appoints an arbitrator who then uses final offer arbitration to determine what the shipper will pay the railroad  The shipper and the carrier are allowed to present a variety of information to help support their offers  For example, they can present evidence of the following  The presence (or absence) of alternative shipping methods and the cost of using the alternative The freight rate charged immediately before the dispute Any special cost incurred by the railroad to transport the shipper's product The market for the shipper's product Suppose that you are an owner of a company that wants to ship its product on a Canadian railroad  Last year your company paid $12 million for shipping by rail  This year you and the railroad's executives have been negotiating, but the best offer they have made is $16 million  If you use a trucking company, shipping will cost you $15 million  You know that if you accept the trucking company's offer, you will make zero economic profit, so that you will receive only your competitive return  You are deciding whether to go to the CTA and ask for final offer arbitration, during which you expect the railroad will ask for $16 million  If you use final offer arbitration, you must abide by the arbitrator's decision  that is, if the arbitrator chooses the railroad's offer, you will pay the railroad $16 million for shipping for this year and cannot use the trucking company's lower cost offer of $15 million  You are thinking of presenting one of two possible offers to the arbitrator  $12 million and $13 million  You estimate that if you offer $12 million, you have a 25 percent chance that the arbitrator will select your offer, while if you offer $13 million, you have an 80 percent chance that the arbitrator will select your offer  You also think that it will cost you $0 5 million to go to arbitration  QUESTIONS 1  If you go to arbitration and offer $12 million, what is the expected cost of the contract  2  If you go to arbitration and offer $13 million, what is the expected cost of the contract  3  If you decide to go to arbitration, which of your two possible offers will you make  If you do not worry about risk and care only to minimize your expected cost, explain whether or not you will ask the CTA for arbitration  4  If you go to arbitration, what risk do you face  Explain how this affects your decision to ask the CTA for arbitration  5  As the owner of the business, will you ask the CTA for arbitration  Explain your decision  Case Study  Decision Making with Final Offer Arbitration Introduction When a buyer and seller are negotiating a price, at times the process hits an impasse  The seller wants a higher price, but the buyer is adamant about paying a lower one  In these cases, the buyer and seller may turn to arbitration  Sometimes each side of the dispute selects one person to serve on an arbitration panel, and the two arbitrators select a third to complete the panel  At other times, one neutral arbitrator is chosen to hear the case  Both sides of the controversy present their arguments and their offers to the arbitrator (whether an individual or a panel), who renders a decision  Often the arbitrator  splits the difference  by selecting a price between the two offers  In some arbitrations, the two sides must accept the decision  in others, the decision is advisory, and one or even both sides can reject it and resume negotiations  In one type of arbitration, however, the arbitrator is not allowed to split the difference, and the buyer or seller must accept the judgment  In this arbitration, called final offer arbitration, the arbitrator selects one of the offers and cannot change it  Several states require final offer arbitration between management and public sector unions that legally are forbidden to strike, such as police, prison guards, and firefighters  Major League Baseball (MLB), a professional baseball organization consisting of 29 teams in the United States and 1 team in Canada, also uses final offer arbitration  When an MLB player and the owners of his team cannot agree on a salary, final offer arbitration is a mechanism for resolving salary disputes 1 The player is entitled to put the dispute before a three person arbitration panel  The three arbitrators are neutral  that is, none of them will favor one side or the other  Both sides submit their final  offers, along with supporting documents, to the arbitrators  The arbitrators take the midpoint between the team's offer and the player's demand  If the evidence shows that the player's market value is higher than the midpoint, the panel awards the higher salary demanded by the player  If the evidence shows that the player's market value is lower than the midpoint, the panel awards the lower salary offered by the team to the player  The decision of the panel is binding on the two parties  If the panel chooses the team's offer, the player is obligated to sign a one year contract for that salary  If the player wins, the team must offer the player a one year contract with the higher salary  These salary disputes might seem far removed from the legal disputes examined in this chapter, but the economic analysis of settlements presents a solid framework for a manager or an agent to use to make decisions in this sort of arbitration  Indeed, arbitration panels actually hear very few of the MLB cases that players and teams file because, just as is the case with lawsuits, the vast majority of these disputes are settled  1 Only a subset of players is eligible for final offer arbitration  Players with one or two years' experience are not entitled to final offer arbitration, and players with six years' or more experience become free agents unless they are under contract with a team  Only players in between, those who have three to five years' experience, are eligible for final offer arbitration because the rules allow them to bargain only with their current team  Final Offer Arbitration Example In the 2006 baseball season, the Chicago Cubs paid pitcher Carlos Zambrano $6 6 million  He had a good year, with a record of 16 wins and 7 losses, an earned run average (ERA) of 3 41, and 210 strikeouts  When he and the Cubs could not agree on a salary for the 2007 season, Mr  Zambrano filed for arbitration  His final offer was $15 5 million, and the Cubs' final offer was $11 0 million  Suppose that you are an executive for the Cubs  To help determine your strategy, you need to make three important decisions  1  You must determine how much money is at stake  In other words, how much money is in dispute  At first glance, you might think the answer is $15 5 million, Mr  Zambrano's offer  This answer, however, is too easy and it is also incorrect  If the arbitrators reject Mr  Zambrano's $15 5 million offer, they will accept your club's offer of $11 0 million  At stake is only the difference between the two offers $4 5 million because the player is guaranteed to receive at least $11 0 million  Call the sum of money in dispute, $4 5 million, S  2  You must decide your subjective probability of Mr  Zambrano winning the arbitration  You think that his agent assembled a strong case, so you assess his probability of winning at 70 percent  In other words, you estimate that the arbitrators will select Mr  Zambrano's offer 70 percent of the time  His 70 percent chance of prevailing leaves you and the Cubs a 30 percent chance of winning  Call the probability that Mr  Zambrano wins q, so that the probability that the Cubs win is 1 9  3  You must decide on your estimate of the cost of going to arbitration for the Cubs  You have already incurred many of the costs necessary to assemble the supporting documents submitted to the arbitrators  These sunk costs do not factor into this calculation, but you do need to consider some other costs  In particular, if you win the arbitration, Mr  Zambrano could possibly be upset and not play to his potential  You might set this cost and all the others of going to arbitration at $1 million  Call the club's cost of going to arbitration CC  Once you have these three numerical estimates, you can calculate the expected cost to the Cubs of going to arbitration  This cost is E C cubs, where C refers to the Cubs' cost of arbitration and the E means you are calculating the expected value  The expected cost to the Cubs is equal to the amount in dispute multiplied by the probability of losing plus the cost to the Cubs of going to arbitration  In terms of a formula, the expected cost is E C cuss (qxS)  (1 q)x$0  CC  This formula is the same as the formula for the expected loss from litigation for the defendant  In this baseball example, the expected cost to the Cubs of allowing the arbitrators to decide the salary is (0 70x$4 5 million) $1 million $4 15 million  As a Cubs executive, you know that you will pay Mr  Zambrano at least $11 0 million  If the contract goes before the arbitrators, add your expected cost of $4 15 million to the $11 0 million for the total expected cost of hiring Mr  Zambrano, $15 15 million  You can lower the Cubs' expected cost by agreeing to any contract that specifies a salary of $15 15 million or less and settling (not going before the arbitrators)  Now suppose that you are Mr  Zambrano's agent  You realize that he is guaranteed to receive at least $11 0 million, so once again the amount in dispute, S, is $4 5 million  If the contract goes to the arbitrators and they decide in favor of Mr  Zambrano's offer, he receives a contract of $15 5 million, collecting the entire $4 5 million in contention  You attach a probability, p, of 40 percent to this outcome  If the arbitrators decide in favor of the Cubs, Mr  Zambrano receives a contract of $11 0 million and collects none of the amount in dispute  The probability of this outcome is 1 p, or 60 percent  Finally, the cost to the player, CP, of going to arbitration is $0 5 million, perhaps because the dispute gives him a reputation of being hard to deal with, which makes other teams less likely to sign him  Call the expected gain to Mr  Zambrano E G ZAMBRANO, where G refers to his gain from arbitration  The expected gain from arbitration to Mr  Zambrano is equal to the amount in dispute multiplied by the probability that he will prevail minus the cost of going to arbitration  E G ZAMBRANO (PxS) ((1 p) $0  CP  Using this formula, which is precisely the same as the formula for the expected gain from litigation for the plaintiff, Mr  Zambrano's expected gain from arbitration is (0 40x$4 5 million) $0 5 million $1 3 million  Because he is guaranteed to receive at least $11 0 million, his expected contract is $11 0 million $1 3 million $12 3 million  As Mr  Zambrano's agent, you can increase the expected contract by agreeing to any contract specifying a salary of more than $12 3 million  The Cubs are willing to sign any contract for less than $15 15 million  Mr  Zambrano is willing to sign any contract for more than $12 3 million  Clearly, there is room to settle the contract before the arbitrators issue their ruling  So does it surprise you that the final offers Mr  Zambrano and the Cubs submitted to the arbitrators are not really final offers  The two sides reached an agreement on a one year deal for $12 4 million  The fact that the agreement was only marginally above the minimum Mr  Zambrano would accept is perhaps a testament to the bargaining prowess of the Cubs' negotiator  The data show that approximately 90 percent of the MLB cases of final offer arbitration settle before the arbitrators issue their decision  This statistic is interesting and certainly in keeping with the analysis above, but the important general point is that you can analyze final offer arbitration in the exact same way as the litigation settlements you learned about in this chapter  The lesson from this observation is clear  Economic principles, such as how to analyze the profit or loss from a lawsuit, apply in a wide variety of situations, and they can aid you in numerous managerial decisions  Your Decisions In Canada, disputes between commercial shippers and railways that carry the freight can be resolved via final offer arbitration  The Canadian Transportation Act allows shippers to appeal the freight rates charged by the Canadian Pacific Railway and Canadian National Railway to the Canadian Transportation Agency (CTA)  The CTA appoints an arbitrator who then uses final offer arbitration to determine what the shipper will pay the railroad  The shipper and the carrier are allowed to present a variety of information to help support their offers  For example, they can present evidence of the following  The presence (or absence) of alternative shipping methods and the cost of using the alternative The freight rate charged immediately before the dispute Any special cost incurred by the railroad to transport the shipper's product The market for the shipper's product Suppose that you are an owner of a company that wants to ship its product on a Canadian railroad  Last year your company paid $12 million for shipping by rail  This year you and the railroad's executives have been negotiating, but the best offer they have made is $16 million  If you use a trucking company, shipping will cost you $15 million  You know that if you accept the trucking company's offer, you will make zero economic profit, so that you will receive only your competitive return  You are deciding whether to go to the CTA and ask for final offer arbitration, during which you expect the railroad will ask for $16 million  If you use final offer arbitration, you must abide by the arbitrator's decision  that is, if the arbitrator chooses the railroad's offer, you will pay the railroad $16 million for shipping for this year and cannot use the trucking company's lower cost offer of $15 million  You are thinking of presenting one of two possible offers to the arbitrator  $12 million and $13 million  You estimate that if you offer $12 million, you have a 25 percent chance that the arbitrator will select your offer, while if you offer $13 million, you have an 80 percent chance that the arbitrator will select your offer  You also think that it will cost you $0 5 million to go to arbitration  QUESTIONS 1  If you go to arbitration and offer $12 million, what is the expected cost of the contract  2  If you go to arbitration and offer $13 million, what is the expected cost of the contract  3  If you decide to go to arbitration, which of your two possible offers will you make  If you do not worry about risk and care only to minimize your expected cost, explain whether or not you will ask the CTA for arbitration  4  If you go to arbitration, what risk do you face  Explain how this affects your decision to ask the CTA for arbitration  5  As the owner of the business, will you ask the CTA for arbitration  Explain your decision

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Case Study: Decision Making with Final Offer Arbitration Introduction When a buyer and seller are negotiating a price, at times the process hits an impasse:

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