Game Theory in the News: The Selfish Will Not Survive

A very cool and interesting article describing the work of Christoph Adami and Arend Hintze (a Michigan State University professor and his protege) highlight how the Prisoner's Dilemma shows that when people are selfish, they will not survive.

The article from Popular Science online, entitled Evolution Punishes Selfish People, Game Theory Study Says explains how this Michigan State duo performed an analysis of what happens in Game Theory's Prisoner's Dilemma - knowing players should cooperate with each other to get the best amount of resources and split them, players will actually act in self-interest, trying to create the best possible payoffs for themselves.

The study published by Nature Communications highlights "zero-determinant" strategies. In this scenario, although in the short-run it may benefit a player to use an "aggressive" strategy, in the long run when all there exists are aggressive opponents, there will be no gains, just an unfair distribution of assets. 

This actually sounds more like the Predator-Prey scenario to me, but it relates to Prisoner's Dilemma since when the prisoners cooperate with each other, they both receive a lighter sentence than if they defect on each other. The problem occurs when the prisoners both act in self-interest - they end up ratting each other out to avoid the max sentence of 5 years and try to get no time in jail.

The Nash Equilibrium

John Nash, expanding upon his Game Theory work in the 1920s, collaborated with other mathematicians an wrote a book that described what was later termed Nash equilibrium. 

In Game Theory, Nash equilibrium represents a state in which it would do a player no good to change their strategy, since they could obtain no more gain from a strategy change. In other words, no matter what a second player does, player one's best bet is to choose a particular strategy (the Nash equilibrium). 

Interestingly enough, the Nash equilibrium can be found with an algorithm when considering 'mixed strategies' of a game. This is when the players' choices deviate from one another. I found a great video that describe this in 9 minutes. It might be a challenge to present this information to our class in half the time.

http://www.youtube.com/watch?v=aa8USttcDoE&list=SPKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo

Game: The Prisoner's Dilemma

The Prisoner's Dilemma

Image Credit: http://www.environmentalgraffiti.com/people/news-are-humans-selfish-concept-homo-economicus

As you can see from the above comic, when two parties make decisions independent from one another, it doesn't always work out well. In this case, we have the community suffering through a stock market crash. One community member decides that he's had enough and will start spending again (with the thought that if he decides to do it, others will follow suit). 

Option 1: If "Guy" spends and the "Community" spends, it will be a the best case scenario since it will bolster the economy.

Option 2: If Guy spends and Community doesn't, Guy will lose much more and the Community won't lose what they still have, even if they do not gain from it.

As you can guess from the 4th panel, option 2 has occurred!

I really like the way the article's author Orco describes the Prisoner's Dilemma:

"Are humans evolutionally constructed to be ultimately self-interested, or might there be more complex systems acting behind this rather simplified idea and if so, why do we continue to talk about the idea of 'homo economicus'?"

Source: How Game Theory Economics Explain Human Altruism

Brief Explanation - Prisoner's Dilemma in Game Theory

Two people commit a crime together and get caught as they are leaving the scene. Unfortunately, there is not enough evidence to convict the perpetrators. As a result, they are separately taken in for questioning with the following deal that police give them:

If both testify against each other, they will receive a sentence of 1 year in prison.

If one rats on the other while the other stays quiet, the "defector" or rat will get off scott free while the other criminal will serve a 5-year sentence.

If both criminals do not rat each other out and stay quiet, then both will go to jail for 3 years.

You can probably see the conundrum here where it would be difficult to decide what the other criminal, or player might do. Will the first criminal act rationally and try for getting only 1 year in jail, expecting the other to do the same? Or will the 1st criminal decide to try for a 0-year sentence by ratting the other out? (And if they do, will they end up ratting each other out and therefore both getting 3 years in prison?)

Orco describes also this as a test of "human altruism."

Relevant and Meaningful Applications of Game Theory: Steven J. Brams Guest Speaker

Steven J. Brams presenting Game Theory and the Humanities: Bridging Two Worlds at Mount Saint Mary College, November 12, 2013. Photo Credit: Clarisa Rosario

 

When Steven Brams, established professor and author, introduced the title of his presentation "Game Theory and the Humanities: Bridging Two Worlds", I was very happy to put my foreign languages interest to use (the title was written in Portuguese).   

He presented interesting ways to look at historical events through the scope of Game Theory. Some of the historical topics he presented mirrored the Game Theory concepts of the “Game of Chicken”, the “Prisoner’s Dilemma”, and I believe “Predator-Prey” as well. Professor Brams was able to show Game Theory in the areas of Shakespeare (literature), Biblical studies, War strategies, and others such as the witch trials.

Due to my studies thus far on Game Theory, I was able to follow his explanations of the payoff matrices without too much trouble, and I was very happy to see some of the ideas I have come across in his presentation. In addition, he talked about some of the Game Theory concepts I have yet to master, which is the Nash equilibrium of each ‘game’, and  a different kind of equilibrium specific to when ‘players’ plot the potential strategies of their competitors (or cooperators). 

In addition, Brams briefly mentioned some more Game Theory topics I have currently been researching but have not yet come to an understanding of, including the dominant strategy, and an active vs passive approach. I am looking forward to doing more research with my classmate on this topic as it is very interesting to me and I'd like to know more. The topic is so broad and rich that it will be a challenge to find out what to focus on when we spend the 15 minutes presenting it to our class!

The Payoff Matrix Discovered

The investigation continues!

After starting to read through some of our resources, we discovered that the functionality of players' gains and losses are shown with what's called a "payoff matrix". There are the "players", the choices they might make, and the possible outcomes when both players make a decision. Let's examine this simple diagram:

As you can see there are 2 possible decisions Firm A and Firm B will make. In each quadrant, the set of numbers describes the "payoff" of making these decisions. For every set of numbers, the first number in the set represents the payoff for Firm A's decision and the second number is the payoff for Firm B's decision. Keep in mind that the decisions made are interdependent, so what one player does will directly affect the other in either a positive or negative way.

Take for instance when Firm A and Firm B both decide to start a new campaign. This is represented by the set 10,5 meaning that if Firm A starts a new campaign, their payoff is "10", and since Firm B is also starting a new campaign, their payoff is "5". Now compare that to if neither firm decides to start a campaign (lower right quadrant). The set is now 10,2 which means that Firm A's payoff will still be 10 and Firm B's gain will only be "2". Knowing this information, Firm B should decide to start a new campaign, for at least they will gain from it.

Does it get more complicated? It certainly does, but we hope to increase our understanding of game theory when we attend the lecture of a guest speaker at our college.

(Book Find: Thinking Strategically by A. Dixit and B. Nalebuff (Norton, 1991) --> An introductory explanation of Game theory is a suggested read which I found from Game Theory: An Introductory Sketch (will open in a new window).

Our Journey's First Steps

2 Undergraduate College Students...
One Path of Discovery

Hello and welcome to the next blog in the "Journey/Exploring" series: Journey Into Game Theory!

This time "the game" has changed as I am working in collaboration with another student in order to research the many aspects of Game Theory - a branch of mathematics that analyzes decision-making in terms of profit/loss, active/passive strategies, and cooperation/competition.


How are we going to accomplish a presentation on Game Theory when we both know nothing about it?

Research - And lots of it!

• We have taken quite a few books out of our college library to help us begin to understand the concepts and origination of Game Theory as well as important definitions.
• We are accessing many websites that are teaching us important Game Theory related topics such as "Understanding the Payoff Matrix", "Systems of Game Theory", and "Game Theory in the News".
• We have discovered the iPhone app, Nash Equilibrium Calculator - to be explained in its own blog post.

Please look forward to our explanations and interesting research articles and websites to take the journey with us!