He Got Game Theory: A Melodrama

Transcription

1 He Got Game Theory: A drama Free Riders Will Hinckley Jansen Lai Shan Park Ricardo Salem March 30, 2011

2 1 Background Carmelo Anthony, the superstar of the NBA team Denver Nuggets, was in the final year of his contract and needed to come to a decision about his future playing career. The Denver Nuggets were determined to retain their franchise player. The New York Knicks had recently lost out in the highly publicized courting of LeBron James in the summer of They instead settled for a $100 million consolation prize in forward Amar e Stoudemire, a player of slightly less caliber. Eager to boost their attendance and performance, New York began to publicly woo native son Carmelo to sign with its team. This sets the backdrop for a season long game that took place between Carmelo Anthony, the Denver Nuggets and the New York Knicks as to where the superstar would end up playing. Initial Game Setup In accordance with NBA league regulations, the Denver Nuggets, as Carmelo Anthony s current team, was able to offer a maximum contract. The Nuggets did just that and offered a 3 year, $65 million deal. Carmelo went on to reject the offer and it soon became publicly known that he preferred to play for the New York Knicks. Denver was now in a position where it could lose Carmelo Anthony to free agency at the end of the season, getting nothing in return, or they could trade him to another team and hope to recoup a portion of the value of their star player. Players Carmelo Anthony: The superstar at the center of the game. His key source of leverage is his ability to veto any trade, which allows him to exercise control over which team(s) he can be traded to. Since Carmelo is in the final year of his current contract, he can veto a trade by

3 2 refusing to sign a contract extension with his new team. Teams transacting with Denver for Carmelo Anthony will only execute a trade if they know that they can retrain his services for the long-term. If Carmelo does not agree to a contract extension with his new team, it immediately diminishes his trade value and Denver will not be able to receive any type of substantive deal in return. His main motivation to cooperate with Denver is so he can receive the maximum contract before being traded away. He can also threaten to not cooperate with Denver and enter free agency, but this threat may not be credible given the impending expiration of the NBA players collective bargaining agreement ( CBA ). It is widely assumed that under the new CBA, maximum salaries will be curtailed. Thus Carmelo is highly unlikely to carry out his threat to become a free agent, since he would then have to sign for a significantly less amount of money. Denver Nuggets: Carmelo s current team. They are mainly motivated to trade Carmelo Anthony and receive the best deal in return. Their main source of power comes from their ownership rights of Carmelo Anthony and ability to offer a maximum contract. A source of negotiating weakness is the fact that every team in the NBA knows that Carmelo wants out of Denver. Teams are likely to give low-ball offers to Denver since they know Denver would rather receive something in return than to lose Carmelo Anthony for nothing. New York Knicks: The team that Carmelo wishes to play for. They are in the best possible position because Carmelo has publicly expressed his wish to play for no team other than the Knicks. This position would allow them to pick up Carmelo on the cheap by making low offers to Denver. In case the Nuggets don t accept the low offers, New York can always wait to claim

4 3 Carmelo once he is a free agent. Because their BATNA is a free agency acquisition, they are not compelled to make Denver a competitive offer. New Jersey Nets: A team on the outside of the negotiation looking in. They are in position to offer Denver a great trade, but Carmelo unfortunately is not interested in signing an extension with the Nets. The Nets are a secondary player in this game because they don t have a decision to make: they have a very strong offer on the table, which the Nuggets are considering. Outcome Rankings 1. Low offer, trade to Knicks, Low offer, trade to Knicks, Low offer, trade to Nets, Low offer, trade to Nets, High offer, trade to Knicks, High offer, trade to Knicks, High offer, trade to Nets, High offer, trade to Nets, This game can be modeled with a decision tree with three main players. The Knicks act first: they make either a low offer or a high offer to the Nuggets. The Nuggets act second: they can either accept the Knicks offer or go with the best alternative on the table, which is the Nets offer. And finally, Carmelo goes last: he can either accept the trade or reject it.

5 4 There are eight possible outcomes in this game (see Decision Tree). Each of these outcomes is ranked on a scale from 1 to 8 for each of the three primary players, 1 being the least desirable and 8 being the most desirable. New York Knicks: Best outcome is if they obtain Carmelo Anthony with a low offer. The next best outcome is if they acquire Carmelo with a high offer. The worst outcomes are the two in which Carmelo agrees to a trade to the Nets. In all other situations, no deal is reached. t reaching a deal is risky for the Knicks. If they don t trade for Carmelo now, they can potentially sign Carmelo as a free agent and not have to give up assets in a trade. However, this runs the risk of Carmelo giving in and ultimately signing a contract extension with the Nuggets or agreeing to a trade with the Nets. Although Carmelo desperately wants to play for the Knicks, he also wants to sign a maximum contract now before the new CBA is negotiated at the end of the season (which will reduce salaries). So in order to make the most money, Carmelo can t allow himself to become a free agent. Denver Nuggets: Best outcome is if they trade Carmelo to the Knicks for a high offer. The second best outcome is if they trade Carmelo to the Nets. The third best outcome is trading Carmelo to the Knicks for a low offer. The worst outcomes are ones in which Carmelo does not agree to a trade. Carmelo Anthony: Best outcome is if Denver trades him to New York, preferably with New York making a low offer so he can join a resource richer team. Second best outcome is if Denver trades him to New York for a high offer Carmelo gets to play for the team he wants to

6 5 join but the team is not as strong since it had to give up players. The worst outcomes are the ones in which he agrees to a trade to the Nets, since he does not want to play there. Decision Tree Trade to Knicks 8,5,8 3,1,3 Knicks Low offer High offer Nuggets Nuggets Trade to Nets Trade to Knicks Trade to Nets 1,6,1 5,2,4 7,8,7 4,3,5 2,7,2 6,4,6 By plotting the possible outcomes and payoffs on to a decision tree, we are able to look forward, reason back to determine the outcome. Given Carmelo s preferences, it is in Denver s best interest to decide to trade him to the Knicks. Aware of the game s current characteristics, the Knicks are in a position of power because they do not need to make a high offer to trade for Carmelo. Whether their offer is high or low, the Nuggets and Carmelo will take the path of agreeing to a trade to the Knicks. Therefore there is no motivation to offer more than a low amount for Carmelo. Thus from analyzing this tree, we can predict that the Knicks make a low offer, the Nuggets trade Carmelo to the Knicks, and Carmelo accepts the trade. Game Changer: Impact of Threats

7 6 The Nuggets needed a way to change the game in a way that would coerce the Knicks into making them a high offer. With the trade deadline of February 24, 2011 fast approaching, Carmelo and the Denver Nuggets coordinated to shift the outcome. It is leaked to the media that Carmelo, the Nuggets and the Nets had a fantastic meeting and that the two teams were in the midst of serious discussion. From the Knicks perspective, it has become increasingly likely that Carmelo will agree to a deal with the Nets. The shift in Carmelo s preferred outcome drastically changes the landscape. w, the Knicks start to panic because they may lose their chance to acquire Carmelo. Decision Tree: New Payoffs Trade to Knicks 8,5,8 3,1,3 Knicks Low offer High offer Nuggets Nuggets Trade to Nets Trade to Knicks Trade to Nets 1,6,4 5,2,1 7,8,7 4,3,5 2,7,6 6,4,2 New payoffs w that Carmelo is perceivably open to playing with the Nets, look forward, reason back shows a new reality. In this scenario, unless the Knicks make a higher offer, it seems likely that the Nuggets will trade Carmelo to the Nets.

8 7 Final Outcome Two days after the meeting between the Nets and Carmelo, it is reported that the Knicks and Nuggets had come to an agreement. Fearing that Carmelo would go to the Nets, the Knicks approached the Nuggets with a high offer that was much better for the Nuggets than the Knicks initial offer. Carmelo Anthony: Was traded to the team that he wanted to play for, the New York Knicks, and receives a maximum contract. New York Knicks: Obtained the player that they wanted, albeit at a higher cost than they hoped for. Denver Nuggets: Successfully trades Carmelo Anthony and receives a competitive package of players, future draft picks and cash. New Jersey Nets: Did not acquire Carmelo, but assisted in depleting division rival of resources. Key Takeaways Observing how the situation surrounding Carmelo, Denver and New York unfolded, we can appreciate the importance of developing mental models of your counterparts. It is critical to understand the motivation of each player in the game in order to predict outcomes and to exercise influence over the actions of other players. By understanding New York s motivation, Denver and Carmelo were able to alter the game in a way that resulted in better outcomes for them. We also can appreciate the power of coordination in games. Without the cooperation of Carmelo, Denver and New Jersey, the Nets would never have become a credible threat in the

9 8 eyes of the Knicks. Their ability to work together made the game play out in a manner that was preferable to them. Finally, this example shows how credible threats can be important tools for changing outcomes in your favor. It is critical to accurately judge the credibility of threats made by other players in the game and to take steps to ensure that threats you make are perceived as credible by other players. The clear change between the 1 st and 2 nd tree was the size of the Knicks offer, which could have been avoided had they developed better mental models of the other players and really thought if the Nets threat was indeed a real one.