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.
|Publisher||Maastricht University, Graduate School of Business and Economics|
|Number of pages||27|
|Publication status||Published - 17 Feb 2020|
|Series||GSBE Research Memoranda|
- c62 - Existence and Stability Conditions of Equilibrium
- c72 - Noncooperative Games
- c73 - "Stochastic and Dynamic Games; Evolutionary Games; Repeated Games"
- Stochastic games
- subgame perfect equilibria
- stationary strategies
- interior-point method
- path-following Algorithm
Dang, C., Herings, P. J-J., & Li, P. (2020). An Interior-Point Path-Following Method to Compute Stationary Equilibria in Stochastic Games. Maastricht University, Graduate School of Business and Economics. GSBE Research Memoranda, No. 001 https://doi.org/10.26481/umagsb.20001