The Art of Kissing

I recently came across a fantastic piece in the new Washington and Lee student journal, the Stone, entitled The Game of Kissing.  The essay, in equal parts subtle wit and academic tone, uses game theory to model the exciting and harrowing experience of deciding whether or not to try to kiss someone.

The author models the decision to go in for a kiss or not as a Stag Hunt game, where each player wants to kiss the other, but neither player knows if the other will accept or reject their advances.  Both players receive their highest payoff when the kiss happens, but each receives their lowest payoff by attempting the kiss and being rejected.  The article presents the following initial payoff matrix:

“C” Stands for cooperate (kiss), and “D” stands for defect (don’t kiss).  The essay shows that while the top left square is socially optimal, the bottom right square is also a stable equilibrium – neither player can improve their payoff by moving unilaterally.  In other words, not kissing is “safe”, and neither player believes they can improve their payoff unless the other player changes decision too.

The essay progresses to add assumptions that make the prospect of going for the kiss better: romance, familiarity, seclusion – but no matter what the bottom right square always remains the “safe” option, a stable equilibrium.

Reading this essay, I was reminded of a passage I recently read in Milan Kundera’s The Art of the Novel, in which he describes the interaction between a man and woman in novelist Hermann Broch’s Sleepwalkers.

On Levin’s estate, a man and a woman meet-two melancholy, lonely people.  They like one another and secretly hope to join their lives together.  All they need is the chance to be alone for a moment and say so.  Finally one day they find themselves unobserved in a wood where they have come to gather mushrooms.  Ill at ease, they are silent, knowing that the moment is upon them and they must not let it slip by.  The silence has already lasted rather a long while when the woman suddenly, “involuntarily, reflexively,” starts to talk about mushrooms.  Then silence again, and the man casts about for a way to declare himself, but instead of speaking of love, “on some unexpected impulse” he too talks about mushrooms, powerless and desperate, for never, they know it, never will they speak of love.

Back at the house, the man tells himself that he did not declare his love because of the memory of his dead mistress, which he cannot betray.  But we know perfectly well: It is a false excuse he invokes to console himself.  Console himself? Yes. Because we can resign ourselves to losing a love for a reason.  We would never forgive ourselves for losing it for no reason at all. 

The stakes are a bit higher in Kundera’s description (talking about true love, not just a kiss) but the interaction itself is certainly reminiscent of the The Kissing Game.

I’ve dabbled in game theory in my academic career, at work, and in my free time.  I’m fascinated by it’s elegant simplifications of real life situations and its many practical applications.  I’m particularly intrigued by models that show why groups of people may make decisions that aren’t in the collective best interest such as the Stag Hunt and the Prisoner’s Dilemma.

Yet, human’s are not wholly rational beings – though we rely on rationality it doesn’t equip us to fully handle the nature of our being.  Our reason has limits.  Experiments with The Ultimatum Game show that people will often defy the predictions of our models.  We are hosts to numerous cognitive biases.  We are the product of a complex  and ill-understood interplay of thought and emotion.

As an economist and amateur game theorist myself it almost feels like sacrilege to admit this… But maybe our models and theories are just the product of a deep-seeded urge to systematize our own chaotic nature, to try to understand ourselves in terms that are simply incongruous with the reality of our existence.

Maybe it’s easier to accept the imperfect mathematical explanation for our perplexing moments, the tragedies of omission, than it is to admit that we simply spoke of mushrooms.

 

MLS’s Beautiful Game Theory

2014 was a huge year for US Soccer. We managed to escape the World Cup group-of-death at the expense of Portugal, with a squad of both veterans and bright young stars, a former World Cup winner in Jurgen Klinsmann at the helm, and without the talismanic if not a bit egomaniacal Landon Donovan anywhere near the USMNT setup.  The MLS playoffs featured some really high quality play, including, I’ll begrudgingly admit, that which ended the playoff run of my beloved DC United.

Then, on the last day of 2014, we learned the truth about Frank Lampard.

Long story short,the supposed marquee signing of a new MLS team, New York City FC turned out to actually be under contract by English Club Manchester City FC, owned by the same parent company. MLS, a league desperate to be taken seriously on the international stage, was treated as a plaything for a powerful European team.

Lampard was touted as the first signing of New York City Football Club, the new MLS that will begin playing in 2015.  NYCFC is owned by the same corporation as Premier League side Manchester City, and us fans were lead to believe that the 35 year old English veteran Lampard was loaned back to Manchester City by NYCFC for the start of the year. Well, a funny thing happened when Lampard started playing for City.  Beginning with a goal against the club Lampard had spent his entire career at, Chelsea FC, Lampard proved at his ripe old age that he still has plenty of ability and went on a run of scoring goals for fun.  Lampard proved to be an important player to City, so important that the Manchester club decided they would hang onto him for the remainder of the 2014-2015 season. We then learned that Lampard never really had a contract with the New York City expansion team, and was in fact signed to Manchester City on a permanent deal.  After NYCFC used Lampard’s image to promote the team and sell season tickets, it was revealed he was never their player at all.  Worse, since all MLS contracts are negotiated through the league and not the individual teams, MLS would likely have been aware of this situation, and may possibly have been content with an English Club treating their assets as a glorified farm system.

 

MLS commissioner Don Garber spoke on the issue on Sunday night in his typical uninformative fashion, claiming that NYCFC doesn’t operate as a farm team for Manchester City without providing any evidence to the contrary.

After this mess, US Soccer fans could use something to be positive about, and an empirical look at the state of the sport in the not-so-distant past gives us, in my opinion, plenty of reason to be positive.

In The Beautiful Game Theory, social scientist Ignacio Palacio-Huerta uses empirical data collected from soccer matches to discuss and test common social sciences and economic hypotheses.  One of his coolest insights relates to penalty shootouts, where he presents evidence showing that the best professional players in the world appear to use mixed-strategies in line with the “minimax theorem” when they decide where to kick the ball.

I’ll try to break it down in laymen’s terms: penalty shootouts work like what economists call a “zero-sum” game.  For each shot, either the shooter wins (by scoring) or the goalie wins (by stopping them from scoring).  Shooters usually have a strong side, where they can hit the ball with more power and accuracy, and a weaker side (the book discusses the possibility of shooting down the middle, but I’m not going to talk about it here for simplicity sake).

So say I’m a professional soccer player, and I’m right footed which means I can shoot better at the left side of the goal.  If I were to use a “pure strategy”, meaning I shoot at the left every time, the goalie would be able to guess which way I will shoot easily, and would therefore be able to save my shot pretty easily.  Instead, my optimal strategy would be to shoot left most of the time, but also shoot right pretty often, so that I play to my strengths without being predictable.  I also want each shot I take to be an “independent trial”, meaning I want to make the decision about where I shoot anew each time, without worrying about whether I shot to that side last time or not.

As a shooter, I want to pick a strategy where my probability of scoring is equal for both sides. An optimal strategy is one where I cannot improve on it by choosing to increase the frequency with which I shoot to one side. An optimal strategy – meaning the perfect breakdown of choosing left/right – is one where for the given strategy: p(R)=p(L) – the probability of scoring if I shoot left is the same as the probability of scoring if I shoot right. If this were not the case, if for instance, p(R)>p(L), this would not be an optimal mixed strategy, because it would make sense for me to shoot to the right more often.  This is called “equating payoffs.”

At least, that’s how economists would predict that a perfectly rational player would make this decision.  Economic models don’t always line up with the way living, breathing, human beings make these decisions in real life situations, but Palacios-Huerta used data from 9,017 penalty kicks taken from September 1995-June-2012 to test whether players actually act the way the perfectly rational hypothetical player would.  He found that the vast majority of players in the top leagues equated pay-offs, and that they passed the “runs test”, meaning they appeared to choose where to shoot independently each time.  In a rare victory for social scientists, theory matched up with real life behavior, because these top professionals chose optimal strategies when they stepped up to the spot.

More technical stuff

The study looked at whether the data could reject the null hypothesis that players would use a pure strategy. At the 95% confidence level, out of 40 players, they were able to reject the null hypothesis for only 2 players (interestingly, those 2 players were David Villa and Frank Lampard, the first two signings of New York City FC), meaning that the other 38 players chose strategies that were close enough to the theoretical predictions that, using the data, they could not conclude the other 38 players did not use pure strategies. I have some issues with the methodology, as Palacios-Huerta seems to treat the thing he’s trying to prove (that players use strategies in line with the minimax theorem) as his null hypothesis. The study also looked at the amount of “runs” that occurred for each player – where a player would shoot at the same spot multiple times in a row, and found that for almost all players, the amount of runs that occurred were consistent with the statistically likely outcome if players selected where to place their penalties independently.

 

What does this have to do with American soccer?  Well, researchers also did a similar test with 20 MLS players with data from the league.  Looking at the players in the top European Leagues, only 2 out of 40 players were shown not to use optimal mixed strategies when choosing where to shoot their penalty kicks (interestingly, one of these players was Lampard). With MLS, 10 out of 20 players,  half of the players that they looked at, used non-optimal strategies when they took penalties.  But that’s not even the worst of it, a 2009 survey asked MLS players where they like to place their PKs, and 44% of MLS players said that they would shoot the ball in the same spot EVERY TIME.  This is the equivalent of professional rock-paper-scissors players saying that their strategy is to “play scissors.”

The date of these studies isn’t specified, but they definitely date back to a bygone era in the history of MLS. This was before the arrival of former Premier League stars like Thierry Henry, Robbie Keane, Tim Cahill, and Obafemi Martins… before the return of Michael Bradley and Clint Dempsey to MLS… before players that graduated from MLS development programs like Perry Kitchen showed they can dominate experienced internationals like Rafa Marquez in midfield battle… before Deandre Yedlin shined against some of the best teams in the world and earned a dream move to Tottenham…before Jurgen Klinsmann instituted changes to the entire structure of youth soccer coaching in the US at all levels, similar to the reforms he pioneered years ago in Germany that may have been crucial to Die Mannschaft’s  2014 World Cup triumph.

Another study by Palacios-Huerta showed that players from the top leagues will pick optimal strategies even when playing a card game with the same payoffs as a penalty kick shootout (but with no direct resemblance to soccer), while players in lower leagues may not.  In other words, players in better leagues are better able to intuitively apply their understanding of the dynamics of penalty kicks, even in situations that look nothing like a penalty kick.

I would be willing to bet that if the preceding studies were conducted today, you’d find that players in MLS are much more competent at choosing where to place their penalty kicks, because the standard of play in the league, and consequently the “footballing brain” required to make it in MLS, has risen considerably.

The Lampard debacle has made it very difficult to take MLS seriously as a professional soccer league, but that shouldn’t overshadow the progress that the league has made.  The analysis of penalty kicks from the past shows that in some regards, the European elites were right to scoff at us.  In spite of setbacks like the Lampard situation and Garber’s tendency to kowtow to anyone with even a moderate amount of influence, things are getting better and its happening quickly.  The more prestigious leagues may be right to think of MLS as a joke for now, but I have a feeling that in a few years time when the gains of improved development structures have been realized, the European has-beens looking to MLS for a cushy retirement in a non-competitive league won’t find us so funny.

 

Game Night with Mitch and Barack

The day after last week’s election, Vox ran this article titled Mitch McConnell may be the greatest strategist in contemporary politics.  Their argument was straightforward: If Obama was able to get things done while in office, and especially if he was able to do so with Republican support, he would look good, and that was ultimately bad for the republicans.  McConnell’s response was to dig his heels in and resist, he made use of the congressional calendar to grind the gears to a halt, slowing down the legislative process and making the democrats who held the presidency look unproductive.

The article reminded me of a famous example discussed by Game Theorist Frank Zagare that I encountered back in college.  For those unfamiliar, Game Theory is just a way of modeling how people – or “players” – are going to behave in a situation.

Zagare discussed in Game Theory: Concepts and Applications the situation in 1981 back when Ronald Reagan was president, and democrats controlled the house but were the minority in the senate.  Sound familiar? It was the same situation as we had in the past two years – only the roles of the parties were switched.

Screen Shot 2014-11-12 at 9.38.47 PM

Zagare included in his discussion the above diagram printed in a newspaper in 1981 that laid out the possible “pay-offs” for Reagan and the Republicans, and for the Democrats.  The pay-off grid above is easier to read than it may seem. The Republicans have two choices:  support Reagan or compromise, and those are laid out across the top.  The Democrats can attack Reagan or compromise, those are laid out on the side of the grid.  The intersection of those two choices tells you which box you end up in, and that tells what “pay-off” or reward each side gets.  Obviously parties want the biggest reward, so this grid can help you guess what each player will do.

Since the situations were nearly identical (One party held the white house and senate, the other held the house of representatives), I updated the grid to reflect today’s situation:

2014 Election Grid

 

This game is similar to what we call a “Chicken Game.”  The Democrats get their best pay-off when they support Obama completely, and convince the Republicans to cave in (top right box), and the Republicans get their best pay-off when they relentlessly attack Obama, and convince the Democrats to compromise (bottom right).  If no one compromises, they end up in the bottom left, and everyone would be worse off than if they both just compromised (top right).

It’s not a true “chicken game” though, because the Democrats, like Reagan back in 1981, had a “dominant strategy”.  Notice that no matter what the Republicans choose, the Democrats get a higher pay-off if they support Obama Completely.  Knowing this, it would be wise for the Republicans to give in, and support Obama a little bit, to avoid that bottom square and their worst pay-off.

 

Is that how it played out? Well, sort of.  These game diagrams like the one above are useful but they’re obviously oversimplified, politicians don’t just make one choice, they make many.  The 2013 shutdown was definitely an example of both parties ending up in the bottom left box.  A CNN poll shortly after the shutdown found that 75% of Americans believed that the republicans should not be reelected, while 54% believed the Democrats should not be reelected. Those percentages break down very similarly to the pay-offs in the bottom left box: both sides lose, but the Republicans, in theory, lost a bit more.

Someone had to cave in to re-open the government.  By most objective standards, it was the Republicans, after most polls throughout the shut down showed that they were earning more of the blame.  The Democrats made few concessions in the bill, a clean CR that kept Sequestration cuts in place and extended the debt limit deadline. “We fought the good fight,” Boehner said, ” We just didn’t win.”

So, just as the Democrats were forced to cave in to the steadfast Reagan back in 1981, Obama stood strong and the Republicans were forced to give up their demands in 2013.  In the election of 1982 the Democrats deepened their majority in the House, just as Republicans did in 2014, and the result in both cases was widely attributed to dissatisfaction with the President.  Yet, back in 1982,  the President’s party held the Senate.  Zagare praised Reagan for being a brilliant game theorist, moreso than Reagan’s advisors who had urged him to compromise.  Hadn’t Obama made the same play? Post shutdown the jury was out.  The game was about the same, the players acted about the same, so why did we end up at a different result?

 

It’s tough to pinpoint why things played out differently when the world has changed so much since 1982.  The obvious culprit may just be that the game is so oversimplified that it’s meaningless, and that Obama and Reagan are so fundamentally different that the comparison is absurd.  That may be the case, but what fun would it be to give up now? Here are a couple contributing factors that may tell part of the story:

One possibility is that Obama simply had less political capital to begin with.  Unlike Obama, Reagan never had to devote significant time to proving he was born a US citizen and eligible to be President.  In the Cold War era, few were going to hurl words like “fascist” at Reagan the way Obama’s been termed a “socialist.”  The Vox article mentioned that McConnell was successful at both obstructing the productivity of the Senate, and getting Obama and the Democrats to take the blame for perceived inaction.  It’s possible that intangibles about how people see the President caused voters to assign blame differently in 2014 than they did in 1982.

Besides this, things happened between the government shutdown and the 2014 election.  The healthcare.gov roll-out was badly botched, sign-ups didn’t go smoothly, sites crashed, private insurers cancelled grandfathered plans that would have otherwise remained eligible.  Economic recovery has been slow.  Numerous foreign policy crises have arisen, and Obama may been seen as too weak in his handling of Ukraine, Syria, and now Iraq.  Some may have wanted a stronger stance on Iran and Israel.  Also, Ebola is now, for some reason, apparently politically relevant.

The government shutdown was barely a year ago, but in light of all recent things that happened, it seems like a distant memory.  Literally, people have all but forgotten about that time when the US government completely stopped, because it was a bit over a year ago.

Cable News Network launched in October of 1980.  Back then there were no competitors until Financial News Network came about in 1981, and even then the two networks catered to different demographics.  There was no need to jazz up coverage to draw eye-balls away from competing news channels.  The internet did not exist. I was not alive back then, but feel I can safely assume that the role of news media in elections was quite different.

I think we can’t ignore the roll 24-hour news may play in increasing the importance of recency in voters’ minds.  Between cable news and internet news, it is easy to hit a point of saturation.The human capacity to prioritize information is limited, and daily saturation of information can easily push older things along the wayside.  I haven’t combed through the 2014 exit polls closely, but the biggest takeaway I’ve seen is that voters are generally dissatisfied at everything.

Obviously, turnout was a huge factor – it was low as it usually is in midterm elections and that generally favors Republicans.  Still, even amongst those who make it to the polls, I think it’s easily possible that after a year of being constantly told of things to be dissatisfied about, people simply forgot about the Government shutdown, it had to be pushed aside to make room for Ebola and missing airliners and resurgences of Cold War posturing.  In late 2013, people were very dissatisfied about the shutdown and they knew who they felt was to blame.  By late 2014, the effect had just faded.  People were still dissatisfied, but they were upset about different things and the old things didn’t matter.  The shutdown was a billion of tweets ago, and who has time to scroll back that far?