Geodesic
A Two Population Growing Model: Exogamic or Endogamic
Contributions to game theory and management, Tome 1 (2007), pp. 7-14

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We show an analytic model for a situation in which two populations are confronted in an exogamic or endogamic way. Our approach is based on Evolutionary Game Theory for Non-Symmetric Games but considering a new rule of imitation: evolutive regret when the probability of selecting the best strategy is included. The rule states to choose the actions with the best results, with a probability proportional to the expected gains. In particular, we show the relation between Dynamic Strategy and Nash equilibrium in an asymmetric game of imitation strategies.
Keywords: Imitation, replicator dynamic, stable population, stability and Nash equilibrium. 
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     author = {Elvio Accinelli and Juan Gabriel Brida and Edgar J. S. Carrera},
     title = {A {Two} {Population} {Growing} {Model:} {Exogamic} or {Endogamic}},
     journal = {Contributions to game theory and management},
     pages = {7--14},
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     volume = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2007_1_a1/}
}
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Elvio Accinelli; Juan Gabriel Brida; Edgar J. S. Carrera. A Two Population Growing Model: Exogamic or Endogamic. Contributions to game theory and management, Tome 1 (2007), pp. 7-14. http://geodesic.mathdoc.fr/item/CGTM_2007_1_a1/