The following two articles explain some of the strategic moves that go on in the last minutes of an NBA game. We all know that depending on the point differential and remaining time, coaches constantly change their strategies to be ahead of the game. Due to the certainty feature of this timed sport, a tie option is 3 times more heavily observed than it normally would have been as can be seen in the second link. Strategies include slowing down the game, fouling, taking breaks, changing players etc. Over the past decades these strategies have matured and came almost to a perfection thanks to the repetition of the game. Coach of a team estimates the potential moves of the other team, and calculates his best move to get the highest payoff. Since the major aim is to be strategically unpredictable to the other team, the dynamic/competitive nature of basketball results in a mixed strategy equilibrium.
http://www.sportshistory.us/uncertainty.html
http://cheeptalk.wordpress.com/2009/06/10/the-overtime-spike-in-nba-basketball
Saturday, December 5, 2009
Friendship as an Assurance Game
Well, another personal example of game theory! Assume two rational players: self (S) and friend (F). Assume also that these people already know each other and they will make a decision whether to invest into the friendship with the other person or not. Similar to other interpersonal meta games like dating, this game could be simplified into a 2x2 matrix assurance game as follows:
Imagine that both players are simultaneously thinking about the other and deciding whether to invest or not, but not sharing this decision with the other person. This meta-game portion is a simultaneous, partial information, repeated (or one-shot), variable sum game with manipulable rules.
There are two Nash equilibria that can be found using Best-response analysis: (Invest, invest) and (Do not invest, do not invest). The first one has a higher individual and total relative payoffs (say, in terms of happiness) for both players. So, if the two players talk and cooperate, they might achieve higher payoffs using (Invest, Invest). If S invests, but F cheats the agreement by not investing in the friendship, then F does not get any payoffs but S is now worse off than not investing because he spent time and resources. In this case he/she may be punished in future games with S and other players.
Obviously, the actual meta-game is a lot more complex and we cannot be friends with everyone. However, when we choose the right opponent player in the "Friendship" game, we should show the game table and let him/her know that cooperation provides better payoffs for both!!
Imagine that both players are simultaneously thinking about the other and deciding whether to invest or not, but not sharing this decision with the other person. This meta-game portion is a simultaneous, partial information, repeated (or one-shot), variable sum game with manipulable rules.There are two Nash equilibria that can be found using Best-response analysis: (Invest, invest) and (Do not invest, do not invest). The first one has a higher individual and total relative payoffs (say, in terms of happiness) for both players. So, if the two players talk and cooperate, they might achieve higher payoffs using (Invest, Invest). If S invests, but F cheats the agreement by not investing in the friendship, then F does not get any payoffs but S is now worse off than not investing because he spent time and resources. In this case he/she may be punished in future games with S and other players.
Obviously, the actual meta-game is a lot more complex and we cannot be friends with everyone. However, when we choose the right opponent player in the "Friendship" game, we should show the game table and let him/her know that cooperation provides better payoffs for both!!
Dividing the Wi-fi
When I moved in to my new house a year ago, among so many different issues was the internet/cable requirement. I am not a big TV fan, so I decided to subscribe only to internet. I do not use internet very often, and when I do so I do not need the whole band. I feel like most average users are the same way. So, it seemed really redundant to pay $50 a month for the internet subscription that I would only use few hours a month. On the other hand, I really needed it because of the school. I had this idea to talk to my neighbors but I hardly knew them so i could not. Result: I subscribed myself and am still paying $50 a month:)
So imagine 3 adjacent houses in a townhome community Say A, B and C. Each needs a low amount of internet usage at different times. Residents at A use internet only at weekends, residents at B use it only during the weekdays because they are working from home and residents at C demonstrate a more scattered but occassional internet usage at random hours. Let's assume that they know each other and they do not have internet service at this point. Cost of internet per month per house is $50. If A, B and C have this information in front of them and have some basic Game Theory perspective they would be able to create an efficient and fair division by understanding their requirements. If A and B cooperate and get the Wi-fi together, they would share the service and the cost, each paying $25 dollars for almost the same service experience. Obviously, division does not have to be exactly like that. For a 2-person coalition, the line between -50 dollars on x and y axis forms the ZOPA and Pareto efficient frontier, similar to Goreton and Bushville discussion in the class. Their BATNA is to install their own equipment and their reservation price is $50 each.
If C also joins the coalition, then the cost per person would reduce to $17 and the service would still be almost the same. Obviously, we need to assume that the Wi-fi router is located near the window at B and provides good service to neighbors. Residents could sign "Terms and Conditions" between the three of them pertaining to rules of service acquisition, usage, payment and termination. Note that the differences in the level and timing of internet usage are key to creating and achieving this efficient frontier. Another key issue here is the access to information among the neighbors...
So imagine 3 adjacent houses in a townhome community Say A, B and C. Each needs a low amount of internet usage at different times. Residents at A use internet only at weekends, residents at B use it only during the weekdays because they are working from home and residents at C demonstrate a more scattered but occassional internet usage at random hours. Let's assume that they know each other and they do not have internet service at this point. Cost of internet per month per house is $50. If A, B and C have this information in front of them and have some basic Game Theory perspective they would be able to create an efficient and fair division by understanding their requirements. If A and B cooperate and get the Wi-fi together, they would share the service and the cost, each paying $25 dollars for almost the same service experience. Obviously, division does not have to be exactly like that. For a 2-person coalition, the line between -50 dollars on x and y axis forms the ZOPA and Pareto efficient frontier, similar to Goreton and Bushville discussion in the class. Their BATNA is to install their own equipment and their reservation price is $50 each.
If C also joins the coalition, then the cost per person would reduce to $17 and the service would still be almost the same. Obviously, we need to assume that the Wi-fi router is located near the window at B and provides good service to neighbors. Residents could sign "Terms and Conditions" between the three of them pertaining to rules of service acquisition, usage, payment and termination. Note that the differences in the level and timing of internet usage are key to creating and achieving this efficient frontier. Another key issue here is the access to information among the neighbors...
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