Promoting Norms (an evolutionary approach to norms)

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Promoting Norms(an evolutionary approach to
norms)

• A review of Robert Axelrods essay,
• Eyal Allweil
• Ami Blonder

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What are Norms?A norm exists in a given social
setting to the extent that individuals usually
act in a certain way and are often punished when
seen not to be acting in this way.

• Note the emphasis on actions, as opposed to
  intents.

• Existence of norms is a matter of degree,
  according to the definition.

• Norms Theory - determining how norms arise,
  maintained and displaced.

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• What is the purpose of the Essay?
• To see when cooperation based upon emerging
  norms will develop.
• Learn what conditions favor the development of
  norms so that cooperation can be promoted where
  it might not otherwise exist or be secure.
• The Norms Game is the mechanism with which
  these goals are sought.

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• The Norms Game
• A game-theoretic approach.
• A variation on the N-players Prisoners Dilemma.
• Players play the standard N-players P.D.
  However, if some player defects, others may see
  this and choose to punish the defecting player.
• Such punishment hurts the defecting player
  greatly (Punishment).
• The punishing-player is also hurt (Enforcement
  Cost).
• If no-one sees the defection, the defecting
  player receives positive pay-off (Defection).
  All other player are hurt (Hurt by Others).
• Each of the players score is dependent on other
  players moves.
• Rationality is assumed.

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Summary of the possible moves

• The only way to gain points is through defection
  not a very optimistic approach.

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Strategic Dimensions Boldness, Vengefulness

• Each player has two strategic dimensions
• Boldness which determines how likely is a
  player to defect.
• Vengefulness which determines how likely is a
  player to punish a defecting player.
• Axelrod used 8-levels (3 bits) to represent each
  of these strategies.

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• Introducing The Evolutionary Approach
• The principle what works well for a player is
  likely to be used again.
• Effective strategies are likely to be retained.
• Such approach also allows the introduction of
  random mutations of existing strategies.
• Such approach is inherently probabilistic.
• Computer simulation of this approach can reveal
  the dynamics of the process.

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Simulation the Norms Game

• These are the steps of the simulation
• The strategies for the initial population of 20
  players are chosen at random.
• The score of each player is determined from the
  players own moves and the choices of the other
  players Each individual gets 4 opportunities to
  defect. For each opportunity, the chance of being
  seen, S, is drawn from a uniform distribution
  between 0 and 1.

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Simulation the Norms Game (contd)
An Example Consider player A with Boldness of
2/7 and Vengefulness 4/7.
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Simulation the Norms Game (contd)

• Player A chose to defect only one (of the four
  opportunities), because only once was his
  Boldness level greater than the chance of being
  seen.
• Sadly for A, one other player saw him defecting,
  for which he paid with a (-9) payoff. The player
  that punished A also paid the Enforcement Cost.
  
• In addition, other players were able to defect a
  total of 36 times, causing player A to lose
  (-1)36 points.
• On nine occasions, player A chose to punish
  others who defected, costing him (-2)9 points
  for Enforcement cost.

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Simulation the Norms Game (contd)

• 3. At the end of the game, total scores per
  player are calculated. Those with relatively good
  score are given more offspring than others
• A player that is one standard deviation above the
  average is given two offspring.
• A player that has average score is given one
  offspring.
• A player that is one standard deviation below the
  average is given no offspring.
• The population is adjusted so that it always
  contains 20 individuals.

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Simulation the Norms Game (contd)

• The final step is the introduction of mutation
  into the society, thus allowing new strategies to
  evolve.
• 1 percent change in each bit of every
  individual is allowed.
• This mutation gives a little more than one
  mutation per generation in the entire population.
• 4. Steps 2 and 3 are repeated 100 generations to
  determine how the population evolves.
• 5. Steps 1 to 4 are repeated to give five
  complete runs of the simulation.

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The norms game
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The Norms Game Results
The results are inconclusive 3 completely
different end-game states appear possible
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The Norms Game Results
This result indicates the emergence of a norm
against defection.
While these results indicate the opposite! Huh?
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The Norms Game Results (contd)

• To gain more understanding about these results,
  Axelrod turned to examine the dynamics of the
  game how the generations evolved.
• Axelrod plotted how the average Boldness and
  Vengefulness changed over time.
• These results are indicated by the arrows.
• The picture becomes clearer (?)

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The Norms Game Results (contd)

• now the various outcomes fit into a common
  pattern. All five of the runs begin near the
  middle of the field, with average Boldness and
  Vengefulness().
• The first thing to happen is a dramatic fall in
  the boldness level. The reason for this decline
  is that when there is enough vengefulness in the
  population, it is very costly to be bold.
• Once the Boldness level falls, the main trend is
  the lowering of Vengefulness. The reason for this
  is that to be vengeful and punish an observed
  defection requires paying an enforcement cost
  without any direct return to the individual.

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The Norms Game Results (contd)

• Finally, once the Vengefulness level has fallen
  nearly to zero, the players can be bold without
  impunity.
• This results in an increase in Boldness,
  destroying whatever restraint was established in
  the first stage of the process.
• This is a sad, but stable state in this norms
  game.
• These results raised the questions of just what
  it takes to keep a norm established.
• Next a look at one mechanism that does just
  that a Meta-norm.

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The Meta-Norms Game

• A meta-norm is a norm about norms.
• Within our game, the meta-norm we wish to
  establish is the norm in which defections are
  always punished.
• Consider a simple example with 3 players

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The Meta-Norms Game (contd)

• George, Saddam and Jacques are playing the
  Meta-Norms game.
• On one of his moves, Saddam defects.
• Jacques has seen this, but does not punish him
  (a severe case of low vengefulness).
• George, seeing that Jacques did not punish
  Saddam, chooses to punish Jacques (a severe case
  of high vengefulness).
• By doing that George respects the meta-norm!

Shock awe!
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The Meta-Norms Game (contd)

• A new strategic dimension is introduced
  Meta-Vengefulness. Simply put, it is the
  willingness to punish those who refuse to punish
  defectors.
• Meta-Vengefulness does not have to be linked to
  Vengefulness.
• However, Axelrod chose to equate those two
  measures.
• As before, a set of computer-simulations were
  carried out.
• The results, are unambiguous.

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The Meta-Norms Game Results

• In all 5 runs, a norm against defection was
  established.
• The amount of vengefulness quickly increased to
  very high levels, and this in turn drove down the
  amount of boldness.
• At first, there was a moderate amount of
  vengefulness in the population.
• This meant that a player has a strong incentive
  to be vengeful, namely, to escape punishment for
  not punishing an observed defection.
• When each player is being vengeful out of self
  protection, It does not pay to be bold.
  

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The Meta-Norms Game Results

• The result is a system that is self-policing,
  and the norm becomes well-established.
• This result depends on the populations starting
  with a sufficiently high-enough level of
  vengefulness.
• While the Norms game collapse no matter what the
  initial conditions are, the Meta-Norms game can
  prevent defections if the initial conditions are
  favorable enough.
• The rest of the essay briefly deals with other
  mechanisms that may support the emergence of
  norms. None of these are applicable to the field
  of AI.

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No prisoners were harmed in the making of this
presentation.ltthe endgt