Promoting Norms
(an evolutionary approach to norms)
A review of Robert Axelrod’s essay,
Eyal Allweil
Ami Blonder
Promoting Norms
06/04/03
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.
Promoting Norms
06/04/03
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.
Promoting Norms
06/04/03
The Norms Game:
•A game-theoretic approach.
•A variation on the N-players Prisoner’s 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 player’s score is dependent on other player’s moves.
•Rationality is assumed.
Promoting Norms
06/04/03
Summary of the possible moves:
Event
Defection
Punishment
Hurt by Others
Enforcement
Cost
Payoff per
Event
T=3
P=-9
H=-1
E=-2
•The only way to gain points is through defection – not a very
optimistic approach.
Promoting Norms
06/04/03
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.
Promoting Norms
06/04/03
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.
Promoting Norms
06/04/03
Simulation: the Norms Game
These are the steps of the simulation:
1. The strategies for the initial population of 20
players are chosen at random.
2. The score of each player is determined from the
player’s 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.
Promoting Norms
06/04/03
Simulation: the Norms Game (cont`d)
An Example: Consider player A with Boldness of
2/7 and Vengefulness 4/7.
Event
Defection
Punishment
Hurt by Others
Enforcement
Cost
SCORE
Payoff per
Event
T=3
P=-9
H=-1
E=-2
Number of
Events
1
1
36
9
Payoff
3
-9
-36
-18
-60
Promoting Norms
06/04/03
Simulation: the Norms Game (cont`d)
•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”.
Promoting Norms
06/04/03
Simulation: the Norms Game (cont`d)
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.
Promoting Norms
06/04/03
Simulation: the Norms Game (cont`d)
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.
Promoting Norms
06/04/03
The norms game:
Promoting Norms
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The Norms Game: Results
The results are inconclusive: 3
completely different end-game
states appear possible:
Promoting Norms
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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?
Promoting Norms
06/04/03
The Norms Game: Results (cont’d)
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 (?)
Promoting Norms
06/04/03
The Norms Game: Results (cont’d)
•“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.
Promoting Norms
06/04/03
The Norms Game: Results (cont’d)
•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 Metanorm.
Promoting Norms
06/04/03
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:
Promoting Norms
06/04/03
The Meta-Norms Game (cont’d)
•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).
Shock
& awe!
•By doing that George respects the meta-norm!
Promoting Norms
06/04/03
Promoting Norms
06/04/03
The Meta-Norms Game (cont’d)
• A new strategic dimension is introduced: MetaVengefulness. 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”.
Promoting Norms
06/04/03
Promoting Norms
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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.
Promoting Norms
06/04/03
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 population’s 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.
Promoting Norms
06/04/03
No prisoners were harmed in the
making of this presentation.
<the end>
Promoting Norms
06/04/03