The State of nature

1
The State of nature

• Lecture 2

2
outline

• Hobbes Leviathan
• definition of a game
• the Prisoners Dilemma game
• the Nash equilibrium
• what the Prisoners Dilemma game teaches us about
  Hobbes claims.

3
Hobbes Leviathan

• A theory of human intentions
• Passions (CHAP. IV)
• Power (CHAP. X)
• a theory of anarchy (CHAP. XIII)
• a theory of the social contract (CHAP XIVfuture
  lecture)

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Passions (CHAP VI)

• All passions are reducible to Appetite, Desire,
  Love, Aversion, Hate, Joy, and Griefe.
• Weighing the desirable and the undesirable is
  Deliberation.
• The last passion to survive deliberation is Will.
• The rest is Speech.
• CAVEAT What do men desire? Fear?
• CHAP VI hints at diversity of intentions,
• and perhaps at mutual ignorance of one anothers
  intentions.

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Power (CHAP X)

• Power is the universal means of achieving
  intentions.
• Power is measured by the Worth of a man.
• Honoring and Dishonoring
• an honorable action is not necessarily a just
  action.

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The state of nature (CHAP XIII)

• Anarchy is the absence of state power.
• Humans have an equal ability to fight.
• Equality make them enemies.
• Attack is the only sure defense
• a warre of every man against every man.
• Misery no Industry, no Culture of the Earth, no
  Navigation, no commodious Building, etc.
• ...the life of man, solitary, poore, nasty,
  brutish, and short.
• Evidence
• America
• relations between Kings.

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Hobbes state of nature
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Hobbes view in perspective

• For Adam Smith, the pursuit of self-interest is
  to the advantage of all.
• The market

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Hobbes view in perspective (continued)

• In the field of International Relations, Hobbes
  state of nature is seen as an accurate
  description of the anarchic structure of the
  international system by Realists (Morgenthau) and
  Neo-Realists (Waltz, Mearsheimer).
• In game theory, Hobbes state of nature
  corresponds to the dilemma of collective action
  as captured in the Prisoners Dilemma game.

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What is a Game? THE RULES OF THE GAME

• A set of players
• P1,2,,N
• for each player, a set of actions (or strategies)
  
• Aiai1,ai2,,aiK for i1,,N.

• for each player, transitive preferences over the
  set of action profiles with element a(aik,a-ik)
  for k1,,K.
• ui(a)?ui(a)
• for all a and a in

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The origins of the Prisoners Dilemma

• An intellectual riddle that had puzzled many a
  19th-century thinker
• French Victorien Sardous play, which became
  Giacomo Puccinis Tosca.
• First cast in game theoretic terms in January
  1950 by two RAND scientists
• Merrill Flood and Melvin Dresher.
• Current story and name given in May 1950 by
  Albert W. Tucker.

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The Prisoners Dilemma

• Two men, charged with a joint violation of law,
  are held separately by the police.
• Each is told that
• if one confesses and the other does not, the
  former will be released and the latter will be
  jailed for 3 years.
• if both confess, each will be jailed 2 years.
• At the same time, each has a good reason to
  believe that
• if neither confesses, both will be jailed 1 year.

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The Prisoners Dilemmamatrix form
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The Prisoners Dilemmaformal notation

• Two players
• 1,2
• for each player, a set of actions (or strategies)
  
• AiQuiet, Confess

Player 1s action
Player 2s action

• for each player, transitive preferences u1(C,Q)
  ? u1(Q,Q) ? u1(C,C) ? u1(Q,C)
• u2(Q,C) ? u2(Q,Q) ? u2(C,C) ? u2(C,Q)

15
What do you think is the solution to the
Prisoners Dilemma?
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The Nash Equilibrium

• A Nash equilibrium is an action profile that is
  such that
• no player can do better by deviating from this
  profile,
• given that every other player adheres to the
  profile.

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Looking for Nash equilibria in the PD
consider Quiet,Quiet
NOT A NASH
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Looking for Nash equilibria in the PD
consider Confess,Quiet
NOT A NASH
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Looking for Nash equilibria in the PD
consider Quiet,Confess
NOT A NASH
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Looking for Nash equilibria in the PD
consider Confess,Confess
PD has only one Nash equilibrium
NASH
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The Nash equilibriumin formal notation

• Denote as (ai,a-i) the action profile that is a
  Nash equilibrium
• for every player i, (ai,a-i) satisfies
• for every action ai of player i.

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Find the Nash equilibria in Battle of Sexes
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Find the Nash equilibria in Chicken
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Another way of finding the Nash equilibriabest
response functions

• A Nash equilibrium is a set of best replies.

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Back to PD

• Each player gets his next-to-worst outcome.
• The Nash equilibrium in PD is said to be Pareto
  inefficient.
• Other situations with a PD structure
• teamwork
• arms race
• tax evasion
• collective security, hunt for terrorists

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Back to Leviathan

• PD provides us with a sharper understanding of
  Hobbes claims.
• This can be good for Hobbes if it reinforces his
  claims
• the wide application of the PD to social
  interaction is a point in Hobbes favor
• the state of nature is not a mere hypothetical
  construct.
• Aspects of Hobbes theory are now testable.
• Bad if it helps identify limitations
• PD is a one-shot game, unlike Hobbes state of
  nature.