# The game theory behind the new NBC show called “Take it All”

There’s a new NBC game show called Take it All which recreates a well-studied problem in game theory called the Prisoner’s dilemma.   According to the Prisoner’s dilemma Wikipedia article, a “classic” example of this game is as follows:

“Two men are arrested, but the police do not have enough information for a conviction. The police separate the two men, and offer both the same deal: if one testifies against his partner (defects/betrays), and the other remains silent (cooperates with/assists his partner), the betrayer goes free and the one that remains silent gets a one-year sentence. If both remain silent, both are sentenced to only one month in jail on a minor charge. If each ‘rats out’ the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept secret from his partner until the sentence is announced. What should they do?”

This game is called the Prisoner’s dilemma because the solution to the game involves joint betrayal rather than joint cooperation, even though joint cooperation is the better outcome for both.  To see this, consider the following “payoffs” (in terms of prison time) that Prisoner 1 and Prisoner 2 associate with the strategies “Betray” and “Keep Silent”.

 Prisoner 2 Prisoner 1 Betray Keep Silent Betray A) 3 months in jail, 3 months in jail C) Go free, 1 year in jail Keep Silent B) 1 year in jail, Go free D) 1 month in jail, 1 month in jail

Suppose Prisoner 2 decides to betray Prisoner 1.  Under the “Prisoner 2 Betrays Prisoner 1” scenario, Prisoner 1 will only have to spend 3 months in jail if he betrays Prisoner 2 (corresponding to cell A above), and a full year in jail if he keeps silent (corresponding to cell B above).  Now suppose Prisoner 2 decides to keep silent.  Under the “Prisoner 2 keeps silent” scenario, Prisoner 1 goes free if he betrays Prisoner 2 (corresponding to cell C above), and spends 1 month in jail if he keeps silent (corresponding to cell D above).  So no matter what Prisoner 2 does, Prisoner 1 always spends less time in jail if he betrays Prisoner 2.  By symmetry, no matter what Prisoner 1 does, Prisoner 2 always spends less time in jail if he betrays Prisoner 1.   Thus the dilemma…

Now, let’s consider how Take it All recreates the Prisoner’s dilemma.  The show begins with five contestants playing a first round, four contestants playing a second round, and three contestants playing a third round.  The final two contestants after round three advance to the “Prize Fight” which mimics the Prisoner’s dilemma game shown above.  In the Prize Fight, the strategy pair for each contestant is “Keep Mine” (i.e., keep my winnings from Rounds 1–3) and “Take it All” (i.e., keep my winnings from Rounds 1–3 and also take my opponent’s winnings from Rounds 1–3).  If both contestants choose to “Keep Mine,” they will each keep the prizes they have won in the prior rounds (this is analogous to ending up in cell D in the Prisoner’s dilemma payoff matrix shown above). If one contestant chooses “Keep Mine” and the other chooses to “Take it All,” the contestant that chose “Take it All” will go home with all the prizes — theirs and their opponents (this is analogous to ending up in either cell B or cell C D in the Prisoner’s dilemma payoff matrix).  But if both choose “Take it All,” they both go home with nothing (this is analogous to ending up in cell A in the Prisoner’s dilemma payoff matrix).  If one were to play this game purely on the basis of self-interested action, then the obvious strategy would be to always “Take it All”, in which case NBC doesn’t have to pay out at all.  However, the interesting (and somewhat creepy and provocative twist) here is that the show’s host (Howie Mandel) gives both contestants time to try to convince each other that they won’t betray each other.  Thus, the “suspense” is whether one’s opponent follows through on his or her verbal “promise” to “Keep Mine”.

Now consider what happened earlier this week on a “Take it All” episode:

From a business perspective, I think that it is quite clever to produce a game show based upon a prisoner’s dilemma game.  The production costs for a show like this are nominal, and most of the time the production company won’t have to pay out a jackpot.  It doesn’t take a game theory expert to figure out that the incentive structure of the game is incompatible with a (Keep Mine, Keep Mine) outcome.  The  likely outcome is (Take It All, Take It All), in which case no prize is paid.  Occasionally one can expect a (Keep Mine, Take It All) outcome, as was the case earlier this week.  This also works to the NBC’s benefit; the “drama” of the game creates a buzz and possibly more viewership (thus bringing in more revenue from commercials).  In all likelihood, NBC also manages the risk of a (Keep Mine, Take It All) outcome by purchasing an insurance policy covering the cost of the jackpot from Lloyds of London…

Let me make one final point about Prisoners Dilemmas and television shows.  The next time you watch a Law and Order re-run, keep in mind that virtually every Law and Order episode is organized around some variation of a Prisoners Dilemma game.  The downside of realizing this is that this makes Law and Order much less interesting to watch, since you can often deduce what will likely happen just a few minutes into each episode!

# The game theory behind the new NBC show called "Take it All"

Take it All which recreates a well-studied problem in game theory called the Prisoner’s dilemma.   According to the Prisoner’s dilemma Wikipedia article, a “classic” example of this game is as follows:

“Two men are arrested, but the police do not have enough information for a conviction. The police separate the two men, and offer both the same deal: if one testifies against his partner (defects/betrays), and the other remains silent (cooperates with/assists his partner), the betrayer goes free and the one that remains silent gets a one-year sentence. If both remain silent, both are sentenced to only one month in jail on a minor charge. If each ‘rats out’ the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept secret from his partner until the sentence is announced. What should they do?”
This game is called the Prisoner’s dilemma because the solution to the game involves joint betrayal rather than joint cooperation, even though joint cooperation is the better outcome for both.  To see this, consider the following “payoffs” (in terms of prison time) that Prisoner 1 and Prisoner 2 associate with the strategies “Betray” and “Keep Silent”.
 Prisoner 2 Prisoner 1 Betray Keep Silent Betray A) 3 months in jail, 3 months in jail C) Go free, 1 year in jail Keep Silent B) 1 year in jail, Go free D) 1 month in jail, 1 month in jail

Suppose Prisoner 2 decides to betray Prisoner 1.  Under the “Prisoner 2 Betrays Prisoner 1” scenario, Prisoner 1 will only have to spend 3 months in jail if he betrays Prisoner 2 (corresponding to cell A above), and a full year in jail if he keeps silent (corresponding to cell B above).  Now suppose Prisoner 2 decides to keep silent.  Under the “Prisoner 2 keeps silent” scenario, Prisoner 1 goes free if he betrays Prisoner 2 (corresponding to cell C above), and spends 1 month in jail if he keeps silent (corresponding to cell D above).  So no matter what Prisoner 2 does, Prisoner 1 always spends less time in jail if he betrays Prisoner 2.  By symmetry, no matter what Prisoner 1 does, Prisoner 2 always spends less time in jail if he betrays Prisoner 1.   Thus the dilemma… Now, let’s consider how Take it All recreates the Prisoner’s dilemma.  The show begins with five contestants playing a first round, four contestants playing a second round, and three contestants playing a third round.  The final two contestants after round three advance to the “Prize Fight” which mimics the Prisoner’s dilemma game shown above.  In the Prize Fight, the strategy pair for each contestant is “Keep Mine” (i.e., keep my winnings from Rounds 1–3) and “Take it All” (i.e., keep my winnings from Rounds 1–3 and also take my opponent’s winnings from Rounds 1–3).  If both contestants choose to “Keep Mine,” they will each keep the prizes they have won in the prior rounds (this is analogous to ending up in cell D in the Prisoner’s dilemma payoff matrix shown above). If one contestant chooses “Keep Mine” and the other chooses to “Take it All,” the contestant that chose “Take it All” will go home with all the prizes — theirs and their opponents (this is analogous to ending up in either cell B or cell C D in the Prisoner’s dilemma payoff matrix).  But if both choose “Take it All,” they both go home with nothing (this is analogous to ending up in cell A in the Prisoner’s dilemma payoff matrix).  If one were to play this game purely on the basis of self-interested action, then the obvious strategy would be to always “Take it All”, in which case NBC doesn’t have to pay out at all.  However, the interesting (and somewhat creepy and provocative twist) here is that the show’s host (Howie Mandel) gives both contestants time to try to convince each other that they won’t betray each other.  Thus, the “suspense” is whether one’s opponent follows through on his or her verbal “promise” to “Keep Mine”. Now consider what happened earlier this week on a “Take it All” episode: From a business perspective, I think that it is quite clever to produce a game show based upon a prisoner’s dilemma game.  The production costs for a show like this are nominal, and most of the time the production company won’t have to pay out a jackpot.  It doesn’t take a game theory expert to figure out that the incentive structure of the game is incompatible with a (Keep Mine, Keep Mine) outcome.  The  likely outcome is (Take It All, Take It All), in which case no prize is paid.  Occasionally one can expect a (Keep Mine, Take It All) outcome, as was the case earlier this week.  This also works to the NBC’s benefit; the “drama” of the game creates a buzz and possibly more viewership (thus bringing in more revenue from commercials).  In all likelihood, NBC also manages the risk of a (Keep Mine, Take It All) outcome by purchasing an insurance policy covering the cost of the jackpot from Lloyds of London… Let me make one final point about Prisoners Dilemmas and television shows.  The next time you watch a Law and Order re-run, keep in mind that virtually every Law and Order episode is organized around some variation of a Prisoners Dilemma game.  The downside of realizing this is that this makes Law and Order much less interesting to watch, since you can often deduce what will likely happen just a few minutes into each episode!  ]]>

Yesterday, David Brooks published an interesting essay in the New York Times entitled “Is Our Adults Learning?”  The basic premise behind his essay can be summarized in the following quote, “Government doesn’t profit from experience because of the way it goes about testing its policy problems. It should try learning the way businesses do.”

My purpose in posting this commentary on Brooks’ article is to challenge his presumption that it’s even remotely possible for the government to conduct itself like a business.  Avinash Dixit’s 1997 American Economic Review article entitled “Power of Incentives in Private versus Public Organizations” provides the framework for my critique.  In this (admittedly somewhat dated) academic journal article, professor Dixit takes on an earlier version of Brooks’ ideas as exemplified in Al Gore’s 1995 tome entitled “Common sense government”.  In this book, Gore argues for “reinventing”  government by measuring and  rewarding “results, not red tape.”  However, Dixit shows that the problem with Gore’s and Brooks’ platitudes about getting the government to act more like a business is that these “theories” fundamentally ignore the nature of government bureaucracy.  Dixit argues that “a distinct feature of government bureaucracies is that they must answer to multiple principals”, and he goes on to “… develop a model of a common agency to show how the interaction among many principals results in a loss of the power of incentives.”  To illustrate this, Dixit notes that in the real world, a government agency may be formally answerable only to the executive, but in practice Congress, courts, media, and organized lobbies all have a say.  He notes that one way to resolve this “weak incentive” problem at the federal level is to devolve political power to states or localities, where “…agencies can be so designed that each performs fewer tasks, thus reducing the externalities among the principals affected by its actions.”  So basically Dixit rigorously proves with the game theory the wisdom behind federalism!

In closing, it would seem that the least likely place for “decentralizing policy experimentation as much as possible to encourage maximum variation” to be successful would be at the level of the federal government.   The weak incentive problem identified by Dixit explains why government agencies are typically focused on red tape, and not results; it’s all about process and procedure, and rarely ever about results.

# Dilbert and the Prisoner’s Dilemma game

Unfortunately for Dilbert, he is confused about the prisoner’s dilemma game, which occurs when the players of a game rationally choose not to cooperate with each other even if it is in their best interests to do so!

# Dilbert and the Prisoner's Dilemma game

Unfortunately for Dilbert, he is confused about the prisoner’s dilemma game, which occurs when the players of a game rationally choose not to cooperate with each other even if it is in their best interests to do so!

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Here’s a list of articles that I have been reading lately:

Judy Shelton: The Recovery Starts With Sound Money – WSJ.com
Source: online.wsj.com

Source: online.wsj.com

Daniel Henninger: A New Age of Reform – WSJ.com
Source: online.wsj.com

Source: www.thecrimson.com

Christie for President – WSJ.com
Source: online.wsj.com

Source: mindyourdecisions.com

Source: www.theatlantic.com

David Malpass: The Panic, Round Two: What Would Reagan Do? – WSJ.com
Source: online.wsj.com

Source: www.theatlantic.com
“Fox Business has made something of a splash claiming that Senator Casey has introduced a bill to bail out union pensions that will cost \$165 billion. Media Matters lashes back, arguing that the bill will only cost \$8-10 billion and isn’t a bailout. Who’s right?””

Here’s a list of articles that I have been reading lately:

Hard Sell – WSJ.com

Source: online.wsj.com

“John Fund writes in The Wall Street Journal that ObamaCare appears more unpopular than ever.”

Source: www.project-syndicate.org

“The crisis in Greece and the problems in Spain and Portugal have exposed the euro’s inherent flaws, and no amount of financial guarantees – much less rhetorical reassurance – from the EU can paper them over. While the euro is likely to survive the current crisis, not all of the eurozone’s current members may be there a year from now.”

Progressives, Jim Crow, and Selective Amnesia

Source: www.american.com

“The Rand Paul episode reveals a drastic misreading of history and of the government’s role in ending racial discrimination in this nation.”

America’s New Jobs Bill – WSJ.com

Source: online.wsj.com

“The Wall Street Journal dissects this week’s stimulus bill.”

Source: w4.stern.nyu.edu

“Money market funds are the stepchild of finance. Even though they manage more than \$4 trillion in assets, you won’t find them in the Senate’s financial reform bill from last Thursday. Is this justified?”

Source: www2.macleans.ca

“As lazy, feckless, corrupt and violent as Greece undoubtedly is, it’s not that untypical…”

That’s Rich at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas.

Source: www.thebigquestions.com

“It’s now crystal clear what the Tea Party stands for, says Frank Rich midway through a column that makes it crystal clear what Frank Rich stands for, and it isn’t pretty.”

Source: hbswk.hbs.edu “New research from Harvard Business School suggests that federal spending in states appears to cause local businesses to cut back rather than grow. A conversation with Joshua Coval.”

Source: freakonomics.blogs.nytimes.com “Game theory lessons on YouTube.”

Review & Outlook: The New Lords of Finance – WSJ.com

Source: online.wsj.com “The Wall Street Journal editorial page says that Congress’s financial reform is a marriage of Big Finance and Big Government.”

Source: www.econtalk.org

“Russ Roberts, host of EconTalk, discusses his paper, “Gambling with Other People’s Money: How Perverted Incentives Created the Financial Crisis.” Roberts reflects on the past eighteen months of podcasts on the crisis, and then turns to his own take, a narrative that emphasizes the role of government rescues of creditors and the incentives this created for imprudent lending. He also discusses U.S. housing policy, particularly the Government Sponsored Enterprises (GSEs), Fannie Mae and Freddie Mac and how the government’s implicit guarantee of lenders to the GSE’s interacted with housing policy to increase housing prices. This in turn, Roberts argues, helped create the subprime market, created mainly by private investors. The episode closes with some of Roberts’s doubts about his narrative.”

Source: w4.stern.nyu.edu

“On Thursday the Senate passed its version of the financial reform bill, and the reconciliation process with the previously passed House bill will now begin. What are the implications for consumer protection? The similarities between the two bills in the area of consumer protection and more notable than their differences, but there are some distinctions to keep in mind and some troubling issues common to both bills. Consumer protection is a worthy goal, especially given some of the documented abuses leading up to and during the financial crisis, but bad regulation may be worse than under-regulation.”

Economic View – Greece May Not Be as Rich as It Looks – NYTimes.com

Source: www.nytimes.com

“Europe no longer pretends Greece is wealthy. Now the Continent acts as though Greece will quickly become wealthy enough to pay back ever-growing sums of debt.”

# Game Theoretic aspects of racial segregation and executive compensation

I am a big fan of Presh Talwalkar’s Mind Your Decisions blogsite.  He often posts some very thought provoking entries on the general topic of game theory.  Anyway, in a recent entry entitled Game theory videos by Tim Harford, Presh points out a couple of particularly interesting YouTube videos on game theoretic aspects of racial segregation (see Youtube video: racial segregation, which is based upon the Schelling Segregation model) and executive compensation (see Youtube video: why your boss is overpaid , which is based upon tournament theory).