Are there games that are studied both in Game-Theory and in Combinatorial-Game-Theory?

Question

I am looking for examples of games that are subject of research in both fields of game theory and Combinatorial game theory. Does a game that was the subject of a research in both fields exists?

From what I have read, CGT limits the focus to two-player games of perfect information, alternating moves, and no chance. I think that GT have no limitations on games features.

In a different question it is said that there is little to no connection between the fields. If I would to research a game from both fields, what would be the difference in the research questions?

Answer 1

There really aren't such games. GT from the start concentrates on uncertainty and iterated play and equilibria and its motivating examples are sociological/economical (already in Von Neumann and Morgenstern's seminal work "Theory of Games and Economic Behavior"), very much in a mathematical economics framework (utitily and pay-off functions etc.). CGT came more from mathematics (Zermelo being an early example, and of course Conway et al) and wants to solve games where all is known in advance, leading to "nimbers" and surreal numbers etc.

Their "flavour" is very different. GT studies different kinds of equilibria, and what happens if players deviate from them etc. You cannot really do both at the same time, and not many people have even tried, that I have seen. GT focuses on the player, CGT on the game.

Answer 2

If I would to research a game from both fields, what would be the difference in the research questions?

Whatever your goals/interests, I think that this is the wrong question.

The vast majority of games examined in GT simply are not ones you could research with existing CGT tools. As in, no theorems from CGT apply since the game doesn't have perfect/near-perfect information, and the win/loss condition is nothing like what is usually studied in CGT, etc. And conversely, if you start with a game suited to analysis with CGT methods, GT would not typically have anything to say except a reframing of the result of the CGT work (e.g. "technically, when you found a perfect strategy, that was minimax"?)

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I think the way to bridge the gap is not to take a game from one field and try to apply pre-existing methods from another field. Rather, it would be to build a new branch (and perhaps new games out of necessity) that draws upon both fields. I don't think much work has been done in this direction, but there are a few papers I'd like to highlight in this vein:

• "Simultaneous Combinatorial Game Theory" by Huggan, Nowakowski, and Ottaway removes the "alternating moves" tenet of CGT and begins to explore results. In some cases, approaches from GT are relevant/arise naturally.
• A branch off of the above paper is "A Deterministic Model for Simultaneous Play Games: The Cheating Robot and Insider Information" by Huggan and Nowakowski.
• "Cumulative Games: Who is the current player?" by Larsson, Meir, and Zick approaches things a bit differently, making more of an effort to talk about a selected class of games with language/ideas from both CGT and GT (which they call "Economic Game Theory" or EGT).
• "Stable Winning Coalitions" by Loeb doesn't do too much to bridge the gap, but tackles difficulties with analyzing CGT games with more than two players in a way that focuses on probability and coalitions, which is reminiscent of GT.