The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Bidding optimally in concurrent second-price auctions of perfectly substitutable goods
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
The complexity of game dynamics: BGP oscillations, sink equilibria, and beyond
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
Computing an approximate jam/fold equilibrium for 3-player no-limit Texas Hold'em tournaments
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Searching for approximate equilibria in empirical games
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Generalised fictitious play for a continuum of anonymous players
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Gradient-based algorithms for finding Nash equilibria in extensive form games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Smoothing Techniques for Computing Nash Equilibria of Sequential Games
Mathematics of Operations Research
Planning against fictitious players in repeated normal form games
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
An Equilibrium Analysis of Competing Double Auction Marketplaces Using Fictitious Play
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
On the rate of convergence of fictitious play
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
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Bayes-Nash Equilibrium (BNE) is at the root of many significant applications of modern game theory to multiagent systems, ranging from airport security scheduling, to network analysis, to mechanism design in e-commerce. However, the computational complexity of calculating BNEs makes the process prohibitively costly, and the process does not scale well. On the other hand, finding BNEs by simulating the repeated interaction of adaptive players has been demonstrated to succeed even in very complex domains. Unfortunately, adaptive algorithms that iteratively shift strategy towards an equilibrium (e.g., the Fictitious Play algorithm) do not provide stable performance across all classes of games. Therefore, active research into these stability issues, and the design of new algorithms for interactive BNE calculation, remain highly important. In this paper we present a variation to the Ishikawa Iteration to calculate a Bayes-Nash Equilibrium. We demonstrate that the Ishikawa algorithm can take an interactive form, which we term Ishikawa Play (I-Play), and apply it in repeated games. Our experimental data shows that variations of the I-Play algorithm are effective in self-play (converge to a BNE), and outperform the Fictitious Play algorithm, while maintaining low computational costs per game cycle.