Labran Jones has played for the Cleveland professional basketball team for the past eight seasons and has established himself as one of the top players in the league. He has recently become a free agent, meaning he can sign a new contract with Cleveland or sign a contract with any other team in the league. Cleveland has never seriously contended for a championship, and Labran is strongly considering moving to Miami, where he would have a better chance at a championship, or to New York, which is a bigger media market and would give him more financial opportunities and endorsements. All three teams are offering Labran a 6-year contract, but because of a salary cap rule, Miami can only offer Labran $110 million, while New York is offering $120 million and Cleveland $125 million. Odds makers give Miami a 70% chance of winning the championship with Labran, while they give Cleveland a 40% chance and New York only a 10% chance. If Labran wins a championship, he will almost certainly finish his career with the team he wins it with. If that team is New York, he will sign a new contract after 6 years hat with endorsements and financial deals is estimated to be worth around $500 million by the end of his career. However, if New York doesn’t win a championship during his 6 years, he will either stay with New York for a career total of $200 million, or sign a new 4-year contract with a new team. If he signs with a new team, he assumes he will sign with a team good enough to give him a 50–50 chance of winning a championship but, because of his likely diminished abilities, he will have eventual earnings of only around $120 million if he wins a championship with his new team. However, if he doesn’t win a championship, his eventual earnings would only be about $65 million. If he signs with Miami and Miami wins the championship, he will stay with the team and have eventual long-term earnings of $375 million, but if Miami doesn’t win a championship, he will either stay with Miami for earnings of about $90 million or sign with a new team, with the same expected outcomes if he signs with a new team after playing in New York. If he re-signs with Cleveland and Cleveland wins a championship, his eventual earnings are expected to be $300 million by the end of his playing career, but if Cleveland doesn’t win, he can stay with the team and expect eventual possible earnings of around $145 million or sign with a new team with the same expected outcomes if he signs with a new team after playing in New York and Miami. Using decision tree analysis, determine which team Labran should sign a new contract with and the expected value of his decision.
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