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SUMMARY:Fixation probabilities of mixed-strategies for bimatrix games in f
inite populations
DTSTART;VALUE=DATE-TIME:20180709T094500Z
DTEND;VALUE=DATE-TIME:20180709T100000Z
DTSTAMP;VALUE=DATE-TIME:20220811T014236Z
UID:indico-contribution-272@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Takuya Sekiguchi (RIKEN Center for Advanced Intellig
ence Project)\nStochastic evolutionary game dynamics in finite populations
has recently been examined not only for symmetric games [1] but also for
bimatrix games [2]. While in these studies the fixation probabilities of p
ure strategies are investigated\, this study examines the evolutionary dyn
amics of two-player 2 by 2 bimatrix games with mixed-strategies in finite
populations under weak selection. The game has two populations for row and
column players. In the population consisting of row (column) players\, tw
o types of players\, i.e.\, mutant and wild-type players\, have different
mixed-strategies which assign different weight to the two row (column) str
ategies. Each playerâ€™s fecundity is determined by the average payoff obt
ained by interactions with all players in the opposite population. The pro
cess of death and birth of players is modelled by the frequency-dependent
Moran process.\n\nFor this game\, I derived the fixation probabilities tha
t a pair of mixed-strategies by mutants in the row and column populations
takes over the entire populations from a given initial state. Moreover\, b
ased on the probabilities\, I discuss the stochastic stability of the pair
of mixed-strategies played by wild-type players.\n\nIn addition\, the fix
ation probabilities of mixed-strategies of mutant players when the selecti
on is weak because of mixed-strategies played by mutant and wild-type play
ers being very close in terms of a probability distribution over the set o
f possible strategies\, which are the counterparts of Wild and Traulsen [3
] in bimatrix games\, are also discussed.\n\n[1] Nowak\, M. A.\, Sasaki\,
A.\, Taylor\, C.\, & Fudenberg\, D. (2004). Emergence of cooperation and e
volutionary stability in finite populations. *Nature*\, 428(6983)\, 646.\n
[2] Sekiguchi\, T.\, & Ohtsuki\, H. (2017). Fixation probabilities of stra
tegies for bimatrix games in finite populations. *Dynamic Games and Applic
ations*\, 7(1)\, 93-111.\n[3] Wild\, G.\, & Traulsen\, A. (2007). The diff
erent limits of weak selection and the evolutionary dynamics of finite pop
ulations. *Journal of Theoretical Biology*\, 247(2)\, 382-390.\n\nhttps://
conferences.maths.unsw.edu.au/event/2/contributions/272/
LOCATION:University of Sydney Holme Building/--The Refectory
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/272/
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