POLSCI 331 Lecture Notes - Lecture 1: Nash Equilibrium, Pareto Efficiency, Non-Cooperative Game Theory
4 May 2018
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Game Theory and Prisoner’s Dilemma
Class Introduction 8.25.15
Classical prisoner’s dilemma
Prisoner B Snitch
Prisoner B Silence
Prisoner A Snitch
5 years/5 years
Free/1 years
Prisoner A Silence
10 years/Free
5 months/5 months
No matter what B does, snitching is A’s best choice. A will either get 5 or years if B snitches, or he will
be free or 5 months if B is silent.
The Nash equilibrium:
In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving
two or more players, in which each player is assumed to know the equilibrium strategies of the other
players, and no player has anything to gain by changing only their own strategy.
In this case, the Nash equilibrium is: A and B both snitch.
Pareto efficiency, or Pareto optimality:
A state of allocation of resources in which it is impossible to make any one individual better off without
making at least one individual worse off
In this case, the Pareto optimal choice is: A and B both stay silent.
A situation is a Prisoner’s Dilemma only when the Nash equilibrium is not the Pareto optimum.
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
No matter what b does, snitching is a"s best choice. A will either get 5 or (cid:883)(cid:882) years if b snitches, or he will. Prisoner a silence be free or 5 months if b is silent. In this case, the nash equilibrium is: a and b both snitch. A state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off. In this case, the pareto optimal choice is: a and b both stay silent.
