TY - UNPB
T1 - An Interior-Point Path-Following Method to Compute Stationary Equilibria in Stochastic Games
AU - Dang, Chuangyin
AU - Herings, P. Jean-Jacques
AU - Li, Peixuan
PY - 2020/2/17
Y1 - 2020/2/17
N2 - Subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept used in applications of stochastic games, which makes it imperative to develop efficient numerical methods to compute an SSPE. For this purpose, this paper develops an interior-point path-following method (IPM), which remedies a number of issues with the existing method called stochastic linear tracing procedure (SLTP). The homotopy system of IPM is derived from the optimality conditions of an artificial barrier game, whose objective function is a combination of the original payoff function and a logarithmic term. Unlike SLTP, the starting stationary strategy profile can be arbitrarily chosen and IPM does not need switching between different systems of equations. The use of a perturbation term makes IPM applicable to all stochastic games, whereas SLTP only works for a generic stochastic game. A transformation of variables reduces the number of equations and variables of by roughly one half. Numerical results show that our method is more than three times as efficient as SLTP.
AB - Subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept used in applications of stochastic games, which makes it imperative to develop efficient numerical methods to compute an SSPE. For this purpose, this paper develops an interior-point path-following method (IPM), which remedies a number of issues with the existing method called stochastic linear tracing procedure (SLTP). The homotopy system of IPM is derived from the optimality conditions of an artificial barrier game, whose objective function is a combination of the original payoff function and a logarithmic term. Unlike SLTP, the starting stationary strategy profile can be arbitrarily chosen and IPM does not need switching between different systems of equations. The use of a perturbation term makes IPM applicable to all stochastic games, whereas SLTP only works for a generic stochastic game. A transformation of variables reduces the number of equations and variables of by roughly one half. Numerical results show that our method is more than three times as efficient as SLTP.
KW - Stochastic games
KW - subgame perfect equilibria
KW - stationary strategies
KW - interior-point method
KW - path-following Algorithm
U2 - 10.26481/umagsb.20001
DO - 10.26481/umagsb.20001
M3 - Working paper
T3 - GSBE Research Memoranda
BT - An Interior-Point Path-Following Method to Compute Stationary Equilibria in Stochastic Games
PB - Maastricht University, Graduate School of Business and Economics
ER -