Minimax Theory and its Applications 08 (2023), No. 1, 235--255
Copyright Heldermann Verlag 2023
Selection Problems in Large Deviations in Games under the Logit Choice Protocol
Hung V. Tran
Department of Mathematics, University of Wisconsin at Madison, U.S.A.
hung@math.wisc.edu
We study large deviations in coordination games under the logit choice protocol. A major open question that W. H. Sandholm and M. Staudigl [ Large deviations and stochastic stability in the small noise double limit, Theoretical Economics 11 (2016) 279--355; Sample path large deviations for stochastic evolutionary game dynamics, Math. Oper. Res. 43/4 (2018) 1348--1377] posed is whether large deviations properties under the small noise double limit and the large population double limit are identical or not. We rephrase this open question in the PDE language as some selection problems, and we provide some definitive answers to these problems.
Keywords: Selection problems, large deviations in games, logit choice protocol, small noise double limit, large population double limit, first-order Hamilton-Jacobi equations, state-constraint boundary conditions, maximal subsolutions, cell problem, viscosity solut
MSC: 35B40, 35F21, 49L25.
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