1. IJCAI’07 Emergence of Norms through Social Learning Partha Mukherjee, Sandip Sen and Stéphane Airiau Mathematical and Computer Sciences Department University of Tulsa, Oklahoma, USA

2. ALAg-07 Introduction Norm: “a convention as an equilibrium that everyone expects in interactions that have more than one equilibrium” [Young, 1996] Use a population of learning agents to simulate a population that faces a problem modeled by a game and study the emergence of norms

3. ALAg-07 Example of a norm: picking the side of the road Agents need to decide on one of several equally desirable alternatives. This game can be extended to m actions 4 4 L R RL

4. ALAg-07 Previous Work Previous work on learning norms assume observation of other interactions between agents.  How norms will emerge if all interactions were private? Social Learning (IJCAI-07): agents play a bimatrix game, at each interaction, an agent plays against another agent, taken at random, in the population  Empirical study: Study effect of population size, number of actions available, effect of learning algorithms, presence of non-learning agents, multiple relatively isolated populations

5. ALAg-07 Social Learning Population of N learning agents A 2-player, k-action game M M is common knowledge Each agent has a learning algorithm (fixed, intrinsic) to play M as a row or a column player Repeatedly, agents play the game M against an unknown, random opponent.

6. ALAg-07 Protocol of play For each iteration, for each agent Pick randomly one agent in its neighborhood For each pair, one agent is randomly considered row, the other column player Each agent pick an action, and can observe only the action of the other agent constituting the pair Each agent gets the reward accordingly, and updates its learning mechanism

7. ALAg-07 Interactions are limited to neighboring agents

8. ALAg-07 Effect of neighboring size

9. ALAg-07 Learning Dynamics D=1 D=15 It 145It 355It 480  Driving on the left  Driving on the right

10. ALAg-07 Influence of non-learners Non-learners use identical strategies D=5

11. ALAg-07 Influence of non-learners Using different strategies  Driving on the left  Driving on the right D=1 D=15 It 45It 535 It 905

12. ALAg-07 Conclusion Bottom up process for the emergence of social norms Depends only on private expertise Agents can learn and sustain useful social norms Agent population with smaller neighborhoods converge faster to a norm