1 / 28

Segregation and Neighborhood Interaction Work in progress

Segregation and Neighborhood Interaction Work in progress. Jason Barr, Rutgers Newark Troy Tassier, Fordham October 31, 2006. Motivation. Schelling tipping model quite “pessimistic.” But says nothing about neighborhood interaction.

lerato
Download Presentation

Segregation and Neighborhood Interaction Work in progress

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Segregation and Neighborhood InteractionWork in progress Jason Barr, Rutgers Newark Troy Tassier, Fordham October 31, 2006

  2. Motivation • Schelling tipping model quite “pessimistic.” • But says nothing about neighborhood interaction. • Only says: given preferences, you move if # different than you hits a certain threshold. • What role does neighborhood interaction play in “counteracting” the tipping phenomena?

  3. Schelling Model w. Utility • NxN lattice (we fix at 12x12). • 130 agents; 10 % free slots; randomly placed at t=0. • Moore neighborhood – 8 surrounding neighbors (except on edges). • Calculate % of neighbors who are alike. • Calculate utility. • Choose randomly open location and calculate new utility. • If new utility>old utility move, otherwise stay. • Asynchronous movement: begin with agent 1 and go through each agent. • Run the system 10,000 periods (each agent has option to move about 79 times). • Segregation Measure: Avg. of % of agents with like neighbors.

  4. Utility Functions β γ=0 γ=.5 α γ=1 0 1 % Same is our measure of preference for integration Utility Functions .5

  5. Some Examples t=0 Seg.=.5 t=10,000 Seg.=.88

  6. t=0 Seg.=.5 t=10,000 Seg.=. 7

  7. Experiment 1: Segregation and Utility

  8. Prisoner’s Dilemma where C>A>D>B Fix A and B: C=A+ε, D=B+μ

  9. The Prisoner’s Dilemma on the Lattice • Agents play the PD against all their neighbors (in the Moore neighborhood). • Payoff to agent is average payoff from the play with neighbors. • Each agent has a probability of playing Coop. (pi), and Defect (1-pi).

  10. PD cont. • Notice every agent is also a neighbor to one or more other agents. • Strategy Approach I: • When agent plays with neighbors, randomly choose action (according to pi) for each neighbor interaction. • Neighbors also choose action according to pj’s. • Strategy Approach II: • Each round, every agent chooses an action (according to their probability). • Plays same action for entire round (both as agent and rival).

  11. Probability Updating Rule Agent’s probability is based on how well the neighbors do. Notice that only the neighbors’ performance matters.

  12. Performance and Probability Denote: xj=1 if rival Cooperates, 0 otherwise. y=1 if agent Cooperates, 0 otherwise.

  13. Example

  14. Equilibria Assuming A/B ≠ ε/μthen all play cooperate or all play defect are the only Nash Equilibria.

  15. Experiment 2 PD on the Lattice: No Movement --Run the system for 100,000 iterations or hit absorbing state, which ever comes first. --Take averages of 250 runs.

  16. Experiment 2 Results

  17. Experiment 3:“Conscious Movement” • Play game with neighbors. • Receive average payoff. • Pick random open location. • “Play” game with neighbors there. • If agent's payoff is higher, move to new neighborhood. • Update probabilities based on chosen location (i.e., new or old).

  18. Experiment 3:“Conscious Movement”

  19. Movement Increases Probability of Cooperation • Agent’s probability adjustment is determined by neighbors’ actions. • If new location gives higher payoff it means that there is more cooperation by the new neighbors. • This, therefore, will increase agent’s probability of cooperating in the future rounds.

  20. Movement vs. No Movement C payoffs that gives 50% prob. of all cooperate

  21. Combined Schelling Plus Game • What does the interaction of the PD and Schelling games do to cooperation and segregation? • Two experiments: • Move if , stay otherwise • Find randomly chosen open spot, compare utilities and move if new utility > old utility

  22. Utility Functions: Move if Utility<0“Low” Cheat payoff

  23. Utility Functions: Move if Utility<0“High” Cheat payoff

  24. Move if Utility<0 • Interaction between nd. composition and game outcome. • If neighbors all defect, you move, regardless of types. • If neighbors all cooperate, agent stays regardless of types. • Movement depends on intermediate game results & % like you. • Increasing cheating payoff: • increases likelihood that an agent will stay, since agent “earns” more against rivals who cooperate. • But as “city” moves toward everybody defect then movement will increase.

  25. Experiment Results: Move if Utility<0Coop. vs. Cheat payoff

  26. Cooperation in RPD vs. Combined Game Random Action

  27. Compare Utilities and Move if New Payoff is Larger

  28. Remaining Issues • Random vs. Fixed action • Initial Conditions and probabilities dynamics. • Conditions where increase coop. decreases segregation?

More Related