Agent based modeling of risk sensitivity and decision making on coalitions

• US 20060059113A1
• Filed: 08/12/2005
• Published: 03/16/2006
• Est. Priority Date: 08/12/2004
• Status: Active Grant

• Current Assignee: Purdue Research Foundation (Purdue University)
• Original Assignee: Purdue Research Foundation (Purdue University)
• Inventors: Sedlmeyer, Robert Louis, Kuznar, Lawrence Anthony, Frederick, William George
• Granted Patent: US 8,057,235 B2
• Time in Patent Office: Days
• US Class Current: 706/45
• CPC Class Codes: G06N 3/004 Artificial life, i.e. computing arrangements simulating life
• CPC Class Codes: G06Q 40/04 Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange

Abstract

An agent based model system provides simulation of the influence of environmental variables and tendencies in individual and social decision making relating to the formation of coalitions and ethnic groups. The system is based on improved understandings of human decision making under risk, and incorporates recent theoretical developments and computational tools. The system gives analysts the ability to predict the development of coalitions and ethnic groups, as well as the ability to manage the behavior of individuals in such groups. The model results provide confidence intervals for various possible scenarios in a mix of agents'"'"' decision rules and distribution of environmental resources. Applications include management of ethnic groups and violent conditions in unstable nations, the tracking of terrorist organizations, development of coalitions and oligopolies in business, and the modeling and interdiction of criminal organizations.

Claims

1. A method in a computer system for simulating individual and social behavior, comprising:

providing for creating a neighborhood of cells;

providing for allocating resources to the cells;

providing for assigning an agent to each cell;

providing for selecting one of a plurality of decision rules for interactions between agents;

providing for iteratively conducting discrete interactions between the agents using the selected decision rule and allocated resources; and

providing for recording interaction outcome.

2. The method of claim 1, wherein one of the plurality of decision rules includes a coordination game.

3. The method of claim 2, wherein the coordination game includes a mixed strategy matrix of:

Join Defect Join R, R S, T Defect T, S P, P

wherein payoffs include R>

P=T>

S.

4. The method of claim 3, wherein R=5, P=3, T=3, and S=0.

5. The method of claim 2, wherein R, P, T, and S are modified with small increases and decreases for payoff sensitivity analysis.

6. The method of claim 2, wherein P=3, T=3, S=0, and R is a random variable ≧

3.

7. The method of claim 2, wherein one of the plurality of decision rules includes a conformist strategy.

8. The method of claim 2, wherein one of the plurality of decision rules includes a prestige-bias strategy.

9. The method of claim 2, wherein one of the plurality of decision rules includes a modified risk posture based on at least one of a sigmoid and an expo-sigmoid function for distribution of resources among agents.

10. The method of claim 2, wherein allocating resources includes uniformly allocating resources to the cells.

11. The method of claim 2, wherein allocating resources includes allocating resources according to a function of a data set, the function including at least one of a sigmoid and an expo-sigmoidal function derived from Fourier signature analysis fit of residuals from at least one of a linear regression to the data and a logarithm of the data.

12. The method of claim 2, wherein the one of the plurality of decision rules includes a join probability according to a function of a data set, the function including at least one of a sigmoid and an expo-sigmoidal function derived from Fourier signature analysis fit of residuals from at least one of a linear regression to the data and a logarithm of the data.

13. The method of claim 2, wherein at least one of the resources and the one of a plurality of decision rules includes a function of a data set, the data set including a measure of at least one of well-being, social status, and social worth.

14. The method of claim 2, wherein the at least one of well-being, social status and social worth include at least one of demographic data, income, net worth, wealth, personal property ownership, real estate ownership, social prestige, mortality, morbidity, marital status, family status, sex, age, education, health, literacy, human development index, geography, environmental factors, movement, communication, informational constraints, mass media, infrastructure, social services, materials, conflict, peacekeeping forces, provocateurs, influential agents, risk sensitivity, cultural norms, ethnic affiliation, ideological affiliation and kinship.

15. The method of claim 14, further comprising providing for analyzing recorded interaction outcome.

16. The method of claim 15, wherein the analyzing outcome includes determining the effect on risk sensitivity of the at least one of well-being, social status and social worth.

17. The method of claim 15, wherein analyzing outcome includes determining an individual'"'"'s likelihood of taking a risk, the distribution of well-being, the distribution of social status, the distribution of social worth, the potential for social unrest due to wealth inequalities, the impact of nepotism on social unrest, influence of class origin of insurgency members, and influence of class origin and terrorist recruitment.

18. The method of claim 2, wherein creating a neighborhood includes mapping the grid onto a sphere, thereby providing eight neighboring cells for each cell.

19. The method of claim 2, wherein iteratively conducting discrete interactions includes one agent interacting with multiple agents in a single iteration.

20. The method of claim 2, wherein iteratively conducting discrete interactions includes an agent interacting with a non-neighboring agent.

21. The method of claim 2, wherein recording interaction outcome includes recording coalition dynamics, including at least one of coalitions, coalition size, join count, total resources, and coalition locations.

22. The method of claim 2, further comprising providing for collecting a predetermined measure of resources from each agent for each iteration.

23. The method of claim 2, further comprising providing for displaying Fourier transform of at least one of coalition size and join count.

24. The method of claim 2, further comprising providing for analyzing risk sensitivity using the analytical function r(x)=−

U″

(x)/U′

(x), where U(x)=α

x−

sin(β

x), α

>

β

>

0, and x>

2π

/β

.

25. The method of claim 2, further comprising providing for analyzing risk sensitivity using the analytical function W(x)=e^{(d+ax+c sin(bx))}, where a>

bc.

26. A computer-readable medium having machine-executable code for simulating the interactions of agents, comprising:

code for creating a neighborhood of cells;

code for allocating resources to the cells;

code for assigning an agent to each cell;

code for selecting one of a plurality of decision rules for interactions between agents;

code for iteratively conducting discrete interactions between the agents using the selected decision rule and allocated resources; and

code for recording interaction outcome.

27. The computer-readable medium of claim 26, wherein one of the plurality of decision rules includes a coordination game.

28. The computer-readable medium of claim 27, wherein the coordination game includes a mixed strategy matrix of:

Join Defect Join R, R S, T Defect T, S P, P

wherein payoffs include R>

P=T>

S.

29. The computer-readable medium of claim 27, wherein one of the plurality of decision rules includes a conformist strategy.

30. The computer-readable medium of claim 27, wherein one of the plurality of decision rules includes a prestige-bias strategy.

31. The computer-readable medium of claim 27, wherein one of the plurality of decision rules includes a modified risk posture based on at least one of a sigmoid and an expo-sigmoid function for distribution of resources among agents.

32. The computer-readable medium of claim 27, wherein allocating resources includes allocating resources according to a function of a data set, the function including at least one of a sigmoid and an expo-sigmoidal function derived from Fourier signature analysis fit of residuals from at least one of a linear regression to the data and a logarithm of the data.

33. The computer-readable medium of claim 27, wherein the one of the plurality of decision rules includes a join probability according to a function of a data set, the function including at least one of a sigmoid and an expo-sigmoidal function derived from Fourier signature analysis fit of residuals from at least one of a linear regression to the data and a logarithm of the data.

34. The computer-readable medium of claim 27, wherein at least one of the resources and the one of a plurality of decision rules includes a function of a data set, the data set including a measure of at least one of well-being, social status, and social worth.

35. The computer-readable medium of claim 27, further comprising code for analyzing recorded interaction outcome.

36. The computer-readable medium of claim 35, wherein the analyzing outcome includes determining the effect on risk sensitivity of the at least one of well-being, social status and social worth.

37. The computer-readable medium of claim 35, wherein analyzing outcome includes determining an individual'"'"'s likelihood of taking a risk, the distribution of well-being, the distribution of social status, the distribution of social worth, the potential for social unrest due to wealth inequalities, the impact of nepotism on social unrest, influence of class origin of insurgency members, and influence of class origin and terrorist recruitment.

38. The computer-readable medium of claim 27, wherein creating a neighborhood includes mapping the grid onto a sphere, thereby providing eight neighboring cells for each cell.

39. The computer-readable medium of claim 27, wherein iteratively conducting discrete interactions includes one agent interacting with multiple agents in a single iteration.

40. The computer-readable medium of claim 27, wherein iteratively conducting discrete interactions includes an agent interacting with a non-neighboring agent.

41. The computer-readable medium of claim 27, wherein recording interaction outcome includes recording coalition dynamics, including at least one of coalitions, coalition size, join count, total resources, and coalition locations.

42. The computer-readable medium of claim 27, further comprising code for collecting a predetermined measure of resources from each agent for each iteration.

43. The computer-readable medium of claim 27, further comprising code for analyzing risk sensitivity using the analytical function r(x)=−

U″

(x)/U′

(x), where U(x)=α

x−

sin(β

X), α

>

β

>

0, and x>

2π

/β

.

44. The computer-readable medium of claim 27, further comprising code for analyzing risk sensitivity using the analytical function W(x)=e^{(d+ax+c sin(bx)}), where a>

bc.

45. A system for agent based modeling, comprising:

a computer; and

software enabling the computer to use a coordination game model to simulate and analyze the interactions of individual agents.

46. The system of claim 45, wherein the computer includes processors configured for parallel processing of the software.

47. The system of claim 45, wherein the coordination game includes a mixed strategy matrix of:

Join Defect Join R, R S, T Defect T, S P, P

wherein payoffs include R>

P=T>

S.

48. The system of claim 45, wherein the coordination game model includes a conformist strategy.

49. The system of claim 45, wherein the coordination game model includes a prestige-bias strategy.

50. The system of claim 45, wherein the coordination game model includes a modified risk posture based on at least one of a sigmoid and an expo-sigmoid function for distribution of resources among agents.

51. The system of claim 45, wherein the coordination game model includes initial allocation of resources according to a function of a data set, the function including at least one of a sigmoid and an expo-sigmoidal function derived from Fourier signature analysis fit of residuals from at least one of a linear regression to the data and a logarithm of the data.

52. The system of claim 45, wherein the coordination game model includes a join probability according to a function of a data set, the function including at least one of a sigmoid and an expo-sigmoidal function derived from Fourier signature analysis fit of residuals from at least one of a linear regression to the data and a logarithm of the data.

53. The system of claim 45, wherein at least one of resources associated with agents and the coordination game model includes a function of a data set, the data set including a measure of at least one of well-being, social status, and social worth.

54. The system of claim 45, wherein the software further enables the computer to analyze recorded interaction outcome.

55. The system of claim 54, wherein analyzing outcome includes determining the effect on risk sensitivity of the at least one of well-being, social status and social worth.

56. The system of claim 54, wherein analyzing outcome includes determining an individual'"'"'s likelihood of taking a risk, the distribution of well-being, the distribution of social status, the distribution of social worth, the potential for social unrest due to wealth inequalities, the impact of nepotism on social unrest, influence of class origin of insurgency members, and influence of class origin and terrorist recruitment.

57. The system of claim 45, wherein the software further enables the computer to map a grid of cells onto a sphere and assign an agent and resources to each cell, thereby providing eight neighboring cells for each cell.

58. The system of claim 45, wherein the software further enables the computer to iteratively conduct discrete interactions between agents.

59. The system of claim 58, wherein iteratively conducting discrete interactions includes one agent interacting with multiple agents in a single iteration.

60. The system of claim 58, wherein iteratively conducting discrete interactions includes an agent interacting with a non-neighboring agent.

61. The system of claim 58, wherein the software further enables the computer to collect a predetermined measure of resources from each agent for each iteration.

62. The system of claim 45, wherein the software further enables the computer to record interaction outcome including recording coalition dynamics, including at least one of coalitions, coalition size, join count, total resources, and coalition locations.

63. The system of claim 45, wherein the software further enables the computer to analyze risk sensitivity using the analytical function r(x)=−

U″

(x)/U′

(x), where U(x)=α

x−

sin(β

X), α

>

β

>

0, and x>

2π

/β

.

64. The system of claim 45, wherein the software further enables the computer to analyze risk sensitivity using the analytical function W(x)=e^{(d+ax+c sin(bx))}, where a>

bc.

65. The system of claim 45, wherein the software further enables the computer to analyze the coalitions of individuals'"'"' adoption of ethnic norms.

66. The system of claim 45, wherein the software further enables the computer to analyze the influence of ethnic affiliation on coalition members'"'"' behaviors.

67. The system of claim 45, wherein the software further enables the computer to analyze the utility of a plurality of different decision rules in predicting and evaluating social behavior relating to coalitions.

68. A method of estimating the distribution of wealth in a population comprising applying the equation W(x)=e^{(d+ax+c sin(bx))}, where a>

bc.

69. The method of claim 68, wherein the variable a is constant across all populations.

70. The method of claim 68, wherein a is equal to 0.4.

71. The method of claim 68, further comprising scaling the equation to a simple periodicity.

72. The method of claim 71, wherein scaling the equation comprises setting the value of the variable b to an integer.

73. The method of claim 72, wherein the value of the variable b is 1.

74. The method of claim 68, further comprising identifying risk prone individuals by applying risk sensitivity measures to the wealth distribution.

75. A method of estimating parameters of an expo-sigmoid model of wealth distribution comprising:

creating a data set by taking the natural log of wealth data of a population;

deriving a linear equation in the form of d+ax by performing an ordinary least squares regression of the data set;

performing a fast-fourier transform on the residuals of the ordinary least squares regression;

picking terms from the fast-fourier transform which are statistically significant to form a trigonometric polynomial in the form of f(x)=Σ

cos(x)+sin(x); and

constructing an equation estimating the wealth distribution of a population by calculating the exponential value of the sum of the linear terms and the trigonometric terms in the form of W(x)=e<sup>(d+ax+π

cos(x)+sin(x))</sup>.