Game Theory: The Prisoners Dilemma and the concept of Nash Equilibrium.

Hello readers, welcome back to rsira-economics.com.

In my last post I decided to focus upon the recent announcement the cancelling of Kenya’s 2017 election. I discussed what reporters know so far and some of the immediate impacts that have taken place since the announcement. The full explanation for this could take up to 21 days and the re-election will take place within the next 60 days.

In this post I thought I would introduce something you might have heard before, something which has become synonymous to economists and a concept which has led to a number of academics winning Nobel prizes. Game Theory. Having just finished “The art of strategy” by Dixit and Nalebuff, which by the way is a very interesting and engaging book, I was eager to share some of my knowledge about concepts like the Prisoners Dilemma and Nash Equilibrium. These concepts can be a little confusing especially if you are not used to the economic jargon, although I will try to explain them in a simplified way as well as illustrating this post with a number of examples. Feel free to comment below if you have any questions are are still unsure about certain aspects by the end of the post. I will keep this post relatively short so that you don’t have too much of an ‘economics overload’. If you were hoping for more current affairs stuff like Brexit or the future of electric cars in this post, stay tuned as these are some of the topics coming up next.

Before we begin, in game theory and in a number of models in economics, a number of assumptions are often made and it is crucial that we understand and consider these assumptions so that when we come to apply our findings to the real world, we can factor these in.

Game theory is the process of modeling the strategic interaction between two or more players in a situation containing set rules and outcomes.

 

Assumptions in game theory:

  1. Perhaps the most important assumption is that in most games each player is Rational and therefore always makes the best possible choice. The term you might often here is Homo Economicus. Homo economicus attempts to maximize utility as a consumer and economic profit as a producer. Homo economicus, or economic man, is the figurative human being characterized by the infinite ability to make rational decisions. Certain economic models have traditionally relied on the assumption that humans are rational and will attempt to maximize their utility for both monetary and non-monetary gains. However, modern behavioral economists and neuroeconomists, have demonstrated that human beings are in fact, not rational in their decision making, and argue a “more human” subject (that makes somewhat predictable irrational decisions) would provide a more accurate tool for modeling human behaviour.
  2. Each player is aware that all other players are also rational and that they know that he is rational too.

Common Terms used in game theory:

 

  1. Game: Any set of circumstances that has a result dependent on the actions of two of more decision makers (“players”).
  2. Players: A strategic decision maker within the context of the game.
  3. Strategy: A complete plan of action a player will take given the set of circumstances that might arise within the game.
  4. Payoff: The payout a player receives from arriving at a particular outcome. The payout can be in any quantifiable form, from dollars to utility.
  5. Equilibrium: The point in a game where both players have made their decisions and an outcome is reached.

The concept of Nash Equilibrium was named after the economist John Nash, who focused his research into different types of scenarios and games, where he developed some revolutionary theories upon them. Nash Equilibrium occurs when an equilibrium is reached in a game from which neither player has an incentive to deviate to some other strategy and would rather stick to the current. This concept helps economists work out things such as how competing companies set their prices and how governments should design auctions to squeeze the most from bidders.

The most famous example used to explain this concept is the Prisoners Dilemma which I will now try to explain.

There are two criminals who have both committed a murder and they are placed in two separate cells in a police station. If they both confess that they committed the murder then they each face 10 years in jail. If one keeps quiet whilst the other confesses, then the one who confesses gets to go free while the other spends a lifetime in jail and vice versa. If they both keep quiet they will face a minor charge and will both go to jail for one year. If the two criminals could collaborate or discuss this together then the optimal solution would be for them both to keep quiet. However by using the concept of Nash-Equillibirum it makes sense to always confess.

The table below, is from an article in the economist and it helps to visualise this situation. Screen Shot 2017-09-01 at 16.17.59.png

If you think you’ve sussed it out as to why this is the case then congratulations! You have just assimilated and understood a very famous concept in game theory. For those of you who don’t know or to re-enforce your knowledge, let’s take this idea further.

To understand this, lets go back to what Nash Equilibrium means-every person in a group makes the best decision for themselves, based on what they think the others will do. And no-one can do better by changing strategy: every member of the group is doing as well as they possibly can.

Ih the prisoners dilemma you should never keep quiet whatever the other person chooses, since one suspect may have confessed. If the other then confesses it avoids the prospect of a life sentence, and if the other does keep quiet then confessing sets the other free.

The Nash equilibrium helps economists understand how decisions that are good for the individual can be terrible for the group. This “tragedy of the commons” explains why we overfish the seas, and why we emit too much carbon into the atmosphere. Everyone would be better off if only we could agree to show some restraint. But given what everyone else is doing, fishing or polluting with impunity makes individual sense.

So how does knowing about two murders in a jail cell help us:

Game theory helps policymakers come up with solutions to tricky problems. Armed with the Nash equilibrium concept, economists claim to have raised billions for the public purse. In the Art of Strategy the authors describe how in 2000 the British government used economists to help design a special auction that sold off its 3G mobile-telecoms operating licences for £22.5 billion ($35.4 billion). Their trick was to treat the auction as a game, and tweak the rules so that the best strategy for bidders was to make confident and aggressive bids.

Sources Used:

The art of strategy by Dixit and Nalebuff

https://www.economist.com/blogs/economist-explains/2016/09/economist-explains-economics

http://basicsofgametheory.blogspot.co.uk/p/nash-equilibrium.html

http://www.investopedia.com/terms/h/homoeconomicus.asp

http://www.investopedia.com/articles/financial-theory/08/game-theory-basics.asp

 

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