Abstract
The game-theoretic approach to multi-agent systems has been incorporated into the model-checking agenda by using temporal and dynamic logic to characterize notions such as Nash equilibria. Recent efforts concentrate on pure-strategy games, where intelligent agents act deterministically guided by utility functions. We build upon this tradition by incorporating stochastic actions. First, we present an extension of the Probabilistic Computation-Tree Logic (PCTL) to quantify and compare expected costs. Next, we give a discrete-time Markov chain codification for mixed-strategy games. Finally, we characterize mixed-strategy Nash equilibria.
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Góngora, P.A., Rosenblueth, D.A. (2010). A Characterization of Mixed-Strategy Nash Equilibria in PCTL Augmented with a Cost Quantifier. In: Dix, J., Fisher, M., Novák, P. (eds) Computational Logic in Multi-Agent Systems. CLIMA 2009. Lecture Notes in Computer Science(), vol 6214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16867-3_9
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DOI: https://doi.org/10.1007/978-3-642-16867-3_9
Publisher Name: Springer, Berlin, Heidelberg
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