Timeline for A universal framework for Game Theory?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 18, 2016 at 14:17 | comment | added | arsmath | Anyway, the monoid example is a good one. In an ordinary language sense "game" means whenever you see strategic behavior. For any given formalism, we can invent a more general formalism that might prove to be interesting. Math is full of group-like objects -- quantum groups, quasigroups, pseudogroups, etc. -- and it's not a scandal that we don't have a maximal definition of "grouplike" that covers every future application. | |
| Sep 18, 2016 at 14:11 | comment | added | arsmath | Aren't logical games all two-person zero-sum games of perfect information? | |
| Sep 18, 2016 at 1:18 | comment | added | Mirco A. Mannucci | forget about optimal strategies. or what unsportsmanlike behavior is or is supposed to be. That would be like asking how many types of finite groups there are when there is not even consensus on the right definition of group. What I am saying is that there is some basic intuition about what a general game is, and yet no formal definition that brings football, nintendo, or a Baire topological game under the same rubric | |
| Sep 18, 2016 at 0:40 | comment | added | Douglas Zare | In what sense do you know what football is? I don't. I can point to a rule book, and I've played, but that tells me very little about what the abstract game is, and how you might state an optimal strategy. Is highly unsportsmanlike behavior youtube.com/watch?v=iHsg6Bb02L4 accepted as part of the game? Is part of the game deciding which players should be on the team, and which skills to train? | |
| Sep 17, 2016 at 20:53 | comment | added | Mirco A. Mannucci | actually znt you know what a group is because someone took the pain to add its definition. People knew for thousands of years what symmetry is, but only in the last couple of hundred years we came up with the notion of group. Similarly, I know what football is, what a political game is, and many many other examples, simply do not know how to cast them into a single definition... | |
| Sep 17, 2016 at 20:38 | comment | added | znt | If your game doesn't fit into that framework then that's fine, just make a new framework where it does fit. Conway has an extremely general definition in his book "on numbers and games", which incorporates pretty much all of the games I'm interested in, although it would not include baseball. | |
| Sep 17, 2016 at 20:36 | comment | added | znt | I think I would argue that either the group theory analogue is not good, or there is a good answer to the question. The point is that we know exactly what a group is, and if someone comes along and says "but I don't want to assume every element has an inverse" then we tell them go and invent monoids. If you can really properly define what you mean by a game then one can axiomatise this definition. For example a 2-player game just seems to me to be nothing more than a set, where player 1 chooses an element, and then player 2 chooses an element of the set P1 chose etc. That will do for mostgames | |
| Sep 17, 2016 at 20:15 | comment | added | Michael Greinecker | A very basic obstruction is that there is no obvious mathematical connection between cooperative and noncooperative game theory. For non-cooperative game theory, one can at least ask what is the most encompassing way to represent a strategic situation. Nothing like that is available for cooperative game theory. For the book in question, the obstruction is that it is less clear how one imposes the kind of measurability structures needed to get a satisfactory way of modeling randomization. | |
| Sep 17, 2016 at 20:06 | comment | added | Mirco A. Mannucci | Thanks Michael. But then, what is the obstruction? I find this state of affairs a bit disconcerting. It is as if we worked on many types of group theory, but we do not know what a group is... | |
| Sep 17, 2016 at 20:04 | comment | added | Michael Greinecker | No, there is not. There is an attempt to give a framework for all imaginable extensive form games in the recent book The Theory of Extensive Form Games by Alós-Ferrer and Ritzberger (and the papers it is based on), but even there, gaps still exist. | |
| Sep 17, 2016 at 19:57 | history | asked | Mirco A. Mannucci | CC BY-SA 3.0 |