Ishikawa play
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.