Game Theory / Formal Models

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The use of game theory and formal models is most associated with Economics. However, a significant proportion of political science research also utilizes these methods.  While it is impossible for this website to impart a thorough understanding of how these models work, it can be useful to identify some of the key terms and point out additional resources that might make it easier to understand models encountered while reading research.

The Prisoner’s Dilemma: key concepts and the use of game theory

Game theory is essentially an approach to understanding collective decision-making. A classic “game” is the Prisoner’s Dilemma. The scenario presented in the game resembles a typical Law and Order episode. Two suspects are taken into custody for a crime they allegedly committed together.  The detectives put them in separate interview rooms and try to get the suspects to confess.  They are told that if they confess, they will get a lighter sentence and — if the other suspect doesn’t confess — they will go free.  However, if they don’t confess and the other suspect does, then they will get a heavier sentence. This classic game is presented in the strategic form. There are two players (the suspects). The payoffs in this case are the number of years in prison. The game makes a number of assumptions:

(a) the prisoners cannot communicate with each other;

(b) the prisoners know what their payoffs will be and can make comparisons between the payoffs;

(c) the prisoners are rational and intelligent; they seek to maximize their utility (which is a way of saying they are looking for the best deal for themselves); and

(d) the prisoners are only facing this situation once (the game does not repeat).

Prisoner B
Don’t Confess Confess
Prisoner A Don’t Confess Both prisoners get 2 years Prisoner A gets 10 years; Prisoner B goes free
Confess Prisoner A goes free; Prisoner B gets 10 years Both prisoners get 5 years

Based on our knowledge of this game, we would predict that both prisoners would “confess”. Even though cooperating with each other would lead to a lesser prison sentence, it is clear that given the uncertainty surrounding their partner’s actions, a prisoner is always better off confessing.  If “A” doesn’t confess and “B” doesn’t confess, then “A” has missed an opportunity to go free. If “B” does confess, then “A” is still better off confessing because otherwise they would spend more time in prison.  When both players have dominant strategies such that they have no rational reason to change their decision, then the result is known as a Nash equilibrium.

This simple situation has been used as a metaphor for understanding a range of political phenomena from cooperation on arms control to pollution of the environment.  Also, interesting things can happen when the payoffs of the game are changed; it is not always the case that both players have dominant strategies.

A great place to begin is Branislav Slantchev’s UC San Diego course on “Game Theory”. There are two general forms to the “games” that we often use.  He introduces the strategic form in his lecture: “Strategic Form: Dominance, Nash Equilibrium, Symmetry”. An example of the strategic form is the classic Prisoner’s Dilemma game illustrated above. Professor Slantchev’s lecture on “Elements of Basic Models” is a great introduction to the extensive form. In that form decisions are modeled as taking place on a sequential basis. For instance, imagine how the Prisoner’s Dilemma above would be different if A had to make a decision before B and B could witness A’s decision.

Game Theory: limitations

Game theory has its ardent defenders and detractors within political science. While most understand its great potential as a heuristic device for understanding basic political phenomena, some are concerned about the limitations of game theory. Most concerns focus on the assumptions games make about the world:

  • Are people rational and intelligent?
  • How can we measure “payoffs” in a meaningful way?  1 year in prison might seem different to a young man whose wife has just given birth to a baby than it does to a 40 year-old man who has no family.
  • Does either the strategic form OR the extensive form really represent how decisions are made? How often does collective decision-making evolve without communication or with sequential communication?
  • Most game theory models limit the number of players to 2 or 3. How might decision-making change as the number of players increases?

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