Year: 2008
Type: article
Abstract: We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At its turn, each of the two players picks a move among two alternatives in order to maximize its final score, and minimize the opponent's return. For a game of length n , we find that the probability distribution of the final score S_{n} develops a traveling wave form, Prob(S_{n}=m)=f(m-vn) , with the wave profile f(z) decaying unusually as a double exponential for large positive and negative z . In addition, as the only parameter in the game is varied, we find a transition where one player is able to get its maximum theoretical score. By extending this model, we suggest that the front velocity v is selected by the nonlinear marginal stability mechanism arising in some traveling wave problems for which the profile decays exponentially, and for which standard traveling wave theory applies.
Source: Physical Review E
Author: Clément Sire
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2007524924