A Game of Theorists (Episode 1)

A Game of Theorists (Episode 1)

ESSA Writers
Game Theorya beautiful mind
February 19, 2012

Psychologists refer to game theory as the theory of social situations. More specifically, it is the study of the strategic decisions, available to rational agents, producing outcomes with respect to the utility of those agents. Through analysis of different courses of action a ‘player’ can take, the outcomes which these actions lead to, and the actions which other ‘players’ might take, an optimal outcome – oftentimes a counter-intuitive one – can reveal itself. In the movie ‘A Beautiful Mind’ (2001), starring Russell Crowe as Robert Nash, game theory is explored in one scene.

‘Adam Smith disliked this video’

While the mathematical side of the subject was developed and systematized by John von Neumann and Oskar Morgenstern in 1944, the logic and insights have been around for a long time. In Plato’s two texts, the Laches and the Symposium, Socrates recounts the Battle of Delium. In this story, a framework for the application of game theory may be seen. Consider a soldier at the front lines, awaiting an imminent battle with only his thoughts to keep him company. He thinks: if a victory is probable, how important will his role be in the battle? It is most likely not significant, if victory is probable (he is no Achilles). The marginal contribution he would make is outweighed by the risk of death or injury which he would face if he were to stay. He continues: if the enemy is going to win the battle, the risk of death or injury is much higher, and there is clearly no reason to stay and fight for a lost cause. He deduces that there is no point in staying. Also, given that every other soldier is in the same position as him, and can reach the same conclusions as he has, there is definitely no reason to stay as the battle has been lost before it has been fought. He should’ve listened to his mother, Edwina, who told him not to join the army. Thus no soldier has an incentive to stay: the greater the fear of loss, the greater the urge to abandon lost hope; the greater the confidence of success, the more insignificant the individual contribution is.

Soldier contemplates

Of course, this example is not perfect. Certain abstract variables, which can be strong psychological stimulants, such as hubris, honour and humiliation, have been ignored. This is not to say that the example is flawed. A modern day analogy can be found during election time, in a country such as the US, where voting is not mandatory. Replace a battle with an election, fighting with voting, fleeing with not voting and the risk of death or injury with the opportunity cost of time, and the risk of queuing and getting sieged by desperate campaign representatives. When a candidate is likely to win by a landslide, individual votes are as significant as a drop of water. When a candidate is likely to lose, there is no point voting. Voter turnout was 57.48% in the 2008 Presidential Elections (http://www.presidency.ucsb.edu/data/turnout.php).

Once the strategic options available to economic agents have been examined, parameters of the ‘game’ can be modified to encourage specific behavior. As a general to an army, the mass desertion of your army would be counter-productive. To discourage this, desertion can be limited. The Spanish conqueror, Cortez, upon landing in Mexico, burned his ships so that his soldiers would have no way to retreat. Thus their best hope of self-preservation is to fight ahead. Interestingly, Cortez burned his ships in view of the local Aztecs. This sent them a signal that these foreign invaders were confident in their ability and eventual victory, forcing the Aztecs’ retreat. A less drastic approach might be to make desertion economically impossible, rather than physically impossible: shoot or imprison deserters. Alternatively, the general might make the soldiers’ training brutally brain-washing enough to ensure loyalty, and squash out their faculties of economic reasoning.

With regards to voter turnout, the media and campaign offices always advertise that the election will be close, to magnify the importance of individual votes. Officials try to make the voting as convenient and enjoyable as possible to minimize the opportunity cost of time and increase comfort. It has also been suggested that election day should be a public holiday.

The scope of scenarios which game theory can apply to is amazing. These scenarios can be as trivial as a game of poker or bridge, or as important as social philosophy. In Hobbe’s (Thomas, the philosopher, not Calvin & Hobbes, the cartoon) Leviathan, regarded as the founding work of modern political philosophy, the logic of strategic interaction is applied to propose that only two general political outcomes are possible: tyranny and anarchy, with the former being more desirable (but not good).  In each of the cases of the soldier, the general and Hobbes, the expectations and possible reactions to their strategies by other rational agents must be considered in order to reach the preferred outcome.

Despite these broad applications, game theory has its critics. Defining, and accounting for all variables which would influence a course of action and an outcome is very hard to do in practice. This was observed in the case of the soldier. The more complex the situation, the harder it is to account for all factors, which makes it harder to come to reliable conclusions regarding the optimal strategy. The assumption of rationality may also be invalid, as human behavior is sometimes as unpredictable as the weather, making the prediction of responses to strategies tricky. A more cynical view of the subject is taken by Michael Mandel:

“Game theory is no doubt wonderful for telling stories. However, it flunks the main test of any scientific theory: The ability to make empirically testable predictions. In most real-life situations, many different outcomes — from full cooperation to near-disastrous conflict — are consistent with the game-theory version of rationality.

To put it a different way: If the world had been blown up during the Cuban Missile Crisis of 1962, game theorists could have explained that as an unfortunate outcome — but one that was just as rational as what actually happened. Similarly, an industry that collapses into run-amok competition, like the airlines, can be explained rationally by game theorists as easily as one where cooperation is the norm.”