====== Games on Cellular Spaces: How Mobility affects Equilibrium ======

|P. R. Andrade, A. M. V. Monteiro, G. Camara, S. Sandri|
  
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//Pawns have their maximum mobility at the start of the game.// W. Jordan Melbourne

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{{  http://www.leg.ufpr.br/~pedro/figures/mobility-figure8.jpg?600  }}

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  * [[http://jasss.soc.surrey.ac.uk/12/1/5.html| Paper]]

=====Revisões=====

  * [[geopro:pedro:mobility:revisao-geoinfo|Revisão do Geoinfo]]
  * [[geopro:pedro:mobility:revisao-jasss|Revisão JASSS]]

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=====Referências=====

====Artigos====

  * [[geopro:pedro:games| Evolutionary Games]]
  * [[geopro:pedro:gamesongrids| Games on Grids]]

====Livros====

  * Dieckmann U //et al// [[http://wiki.dpi.inpe.br/doku.php?id=geopro:pedro:books#the_geometry_of_ecological_interactionssimplifying_spatial_complexity|The Geometry of Ecological Interactions: Simplifying Spatial Complexity]]
  * Axelrod R. [[http://wiki.dpi.inpe.br/doku.php?id=geopro:pedro:books#the_complexity_of_cooperation| The Complexity of Cooperation]]

==== Payoff====

Payoff of my strategy (X) given my opponent strategy (Y), in the chicken game (-10,-1,0,+1):


^ ^0.0^  0.1  ^  0.2  ^  0.3  ^  0.4  ^ 0.5  ^  0.6  ^  0.7  ^  0.8  ^  0.9  ^  1.0  ^
^0.0|  **0.0**|  0.1|  0.2|  0.3|  0.4|  0.5|  0.6|  0.7|  0.8|  0.9|  1.0|  
^0.1|**-0.1**|  **-0.1**| ** -0.1**|  **-0.1**|  **-0.1**|  **-0.1**|  **-0.1**|  **-0.1**|  **-0.1**|  **-0.1**|  **-0.1**| 
^0.2|-0.2|  -0.3|  **-0.4**|  -0.5|  -0.6|  -0.7|  -0.8|  -0.9|  -1.0|  -1.1|  -1.2|  
^0.3|-0.3|  -0.5|  -0.7|  **-0.9**|  -1.1|  -1.3|  -1.5|  -1.7|  -1.9|  -2.1|  -2.3|  
^0.4|-0.4|  -0.7|  -1.0  |  -1.3|  **-1.6**|  -1.9|  -2.2|  -2.5|  -2.8|  -3.1|  -3.4|  
^0.5|-0.5|  -0.9|  -1.3|  -1.7|  -2.1|  **-2.5**|  -2.9|  -3.3|  -3.7|  -4.1|  -4.5|  
^0.6|-0.6|  -1.1|  -1.6|  -2.1|  -2.6|  -3.1|  **-3.6**|  -4.1|  -4.6|  -5.1|  -5.6|  
^0.7|-0.7|  -1.3|  -1.9|  -2.5|  -3.1|  -3.7|  -4.3|  **-4.9**|  -5.5|  -6.1|  -6.7|  
^0.8|-0.8|  -1.5|  -2.2|  -2.9|  -3.6|  -4.3|  -5.0  |  -5.7|  **-6.4**|  -7.1|  -7.8|  
^0.9|-0.9|  -1.7|  -2.5|  -3.3|  -4.1|  -4.9|  -5.7|  -6.5|  -7.3|  **-8.1**|  -8.9|  
^1.0|  -1.0|  -1.9|  -2.8|  -3.7|  -4.6|  -5.5|  -6.4|  -7.3|  -8.2|  -9.1|  **-10.0**|  

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  payoff = function(strat, ostrat)
    return (-10 * strat     * ostrat
            +1  * strat     * (1-ostrat)
            -1  * (1-strat) * ostrat)
  
  resultt = list()
  for(i in 0:10)
  {
    resultt = payoff(c((0:10)/10),i/10)
    cat(paste("^", i/10, "|"))
    for(j in 1:11)
    {
      cat(resultt[j])
      cat("|  ")
    }
    cat("\n")
  }
  

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