The Freedom of Constraint : A Multilevel Simulation Model of Politics , Fertility and Economic Development
individual benefit and mutual benefit . In this model , variable talkspan defines spatial proximity interactions , ranging from 1 to 20 , defining the grid size radius for the local neighborhood . To model communications and technology diffusion for frequency and social tie formation ( McPherson , Smith-Lovin , & Cook , 2001 ), we have agent i evaluated the likelihood of conducting a simple socio-economic transaction with agent j based on the similarity of the income level | y i
– y j
|, stability of the environment , and physical distance talkspan . This also reflects recent work on the importance of both dynamic strategies and updating rules based on agent attributes affecting co-evolution ( Abdollahian et al ., 2014 , 2015 ; Kauffman , 1993 ; Moyano & Sanchez , 2013 ). After each source agent calculates its probability of playing a game with all possible target agents , it chooses the target with the highest probability to be its partner . The target agent also repeats the same process symmetrically , and then chooses the A ij , pairing the highest probability derived from its preference-proximity function as its partner .
Once agents decide to play , they choose strategies based on | h i
-h j
|. Siero and Doosje ( 1993 ) among others show that messages close to a receiver ’ s position have little effect , while those far from a receiver ’ s position are likely to be rejected . So when the difference of human capital is small , there is a high probability of playing cooperate , while a long distance results in a high probability of playing defect . The relative payoff for each agent is calculated based on simple prisoner ’ s dilemma , noncooperative game theory ( Dixit & Skeath , 2015 ; Nowak & Sigmund , 1993 ; Sigmund , 1993 ) where T > R > P > S , with T = 2 , R = 1 , P = 0 and S = – 1 . When both agents cooperate , they both gain TT ; when one plays cooperate but the other plays defect , the cooperating one loses , while the defecting one gains ST ; when both play defect , they don ’ t gain anything from the transaction PP . The updated goes back to agent i endogenous POFED processing for t + n calculations .
In the next step , we set up noncooperative A ij games whose outcomes condition agent y i values for the next iteration . Following Abdollahian et al . ( 2013 , 2014 , 2015 ), we specifically model socio-economic transaction games as producing either positive or negative values as we want to capture behavioral outcomes from games with both upside gains or downside losses .
Subsequently , A ij games ’ V ij outcomes condition agent values , modeling realized costs or benefits from any particular interaction . The updated = + A ij game payoff for each agent then gets added to the individual ’ s variables for the next iteration . We then repeat individual endogenous processing , aggregated up to society as a whole and repeat the game processes for t + n iterations , where n is the last iterate . In this module , A i strategies are adaptive , which affect A ij pairs locally within an approximate radius as first-order effects . Other agents , within the society but outside the talkspan radius , are impacted through cascading higher orders . Following Abdollahian et al . ( 2013 ), we explicitly model interactions ( Kauffman , 1993 ) to capture co-evolutionary behavior in a simple , yet elegant manner . Memory and history matters , as the sum of all prior individual system
11