Promoting Norms an evolutionary approach to norms A

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: • 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. 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 06/04/03

The Norms Game: Results The results are inconclusive: 3 completely different end-game states appear possible: Promoting Norms 06/04/03

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: 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”. Promoting Norms 06/04/03

Promoting Norms 06/04/03

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