Game theoretic simulation metamodeling using stochastic kriging

Abstract

This paper presents a new approach to the construction of game theoretic metamodels from data obtained through stochastic simulation. In this approach, stochastic kriging is used to estimate payoff functions of players involved in a game represented by a simulation model. Based on the estimated payoff functions, the players' best responses to the values of the decision variables chosen by the other players are calculated. In the approach, the concept of best response sets in the context of game theoretic simulation metamodeling is applied. These sets contain the values of the players' decision variables which cannot be excluded from being a best response and allow the identification of the potential Nash equilibria. The utilization of the approach is demonstrated with simulation examples where payoff functions are known a priori. Additionally, it is applied to data acquired by using a discrete event air combat simulation model.

Comparison of Gaussian process modeling software

“…Stochastic kriging has been used for modeling simulation data from many fields, such as in game theory simulations (Pousi et al, 2010) and finance for measuring portfolio risk (Liu and Staum, 2010). Stochastic kriging models are often run in two stages.…”

Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems

“…Defined as an extension of Kriging, SK accounts for heteroscedastic noise in the response by estimating the sample variance at each point of the ED using multiple runs of the simulator for each specific input. The effectiveness of SK has been demonstrated on a broad range of applications, including risk and reliability analysis [18,19], industrial welding processes [20], and game theoretic simulations [21], to mention a few.…”

Multiple input and multiple output simulation metamodeling using Bayesian networks

“…The most commonly used metamodels are input-output mappings that project the values of simulation inputs to the expected values of outputs. They include, e.g., regression models (Kleijnen 2008), spline models (Barton 1998), neural networks (Fonseca, Navaresse, and Moynihan 2003), Kriging models (Ankenman, Nelson, and Staum 2010), response surfaces (Kleijnen and Sargent 2000), and game theoretic models Virtanen 2010a, Pousi, Poropudas, andVirtanen 2010). There also exists other metamodeling approaches such as dynamic Bayesian networks describing the time evolution of DES models Virtanen 2007, Poropudas andVirtanen 2011) and influence diagrams used for studying the consequences of decision alternatives in simulation based decision making and optimization (Poropudas and Virtanen 2009).…”