Nash equilibrium in weighted concurrent timed games with reachability objectives

Authors:
Shankara Narayanan Krishna;G. Lakshmi Manasa;Ashish Chiplunkar
Affiliations:
Department of Computer Science and Engineering, IIT Bombay, Mumbai, India;Department of Computer Science and Engineering, IIT Bombay, Mumbai, India;Department of Computer Science and Engineering, IIT Bombay, Mumbai, India
Venue:
ICDCIT'12 Proceedings of the 8th international conference on Distributed Computing and Internet Technology
Year:
2012

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Abstract

Timed automata [1] are a well accepted formalism in modelling real time systems. In this paper, we study concurrent games with two players on timed automata with costs attached to the locations and edges and try to answer the question of the existence of Nash Equilibrium (NE). Considering memoryless strategies, we show that with one clock it is decidable whether there exists a NE where player 1 has a cost bounded by a constant B, while with 3 clocks, it is not. The case of 2 clocks is an interesting open question.