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Game Theory

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Torrent
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Joined: 08/03/2008

At some points in my schooling, I have taken classes that study game theory. The Prisoner's Delimma is the one most people know. Two people are in jail and have to choice to rat out the other for a lighter sentance. If both stay silent, they both get one 1 year, however if both rat out they each get 2 years, and if one rats out with the other silent the traitor gets out free while the silent one get lots of time. Basically you get a situation where it is really in both people's best interest to stay silent, but the general tendancy is to rat-out to avoid the maximum sentance.

This is a simple example. But there are lots of games like this where various changes in the rules cause the 'best' strategy for players to change. I was just wondering if anyone else has studied this sort of game theory, and applied it to their designs.

There is a piece of Game Theory called Nash Equilibriums (Nash of Beautiful Mind fame I believe). It says that certain games there is a best strategy for each player and if they always persue that strategy there will allways be the same result. Sometimes I read some posts with people having issues in their game about extreme strategies 'locking' the game. Basically , "If we all do this, nothign changes and it isn't fun". It just sounds so like a Nash Equilibrium point.

Maybe this is all high and geeky, but it seems like if you knew enough about game theory you could see the Nash Points and avoid designing into them.

Andy

Anonymous
Game Theory

Yes, that is a very good point. I have studied the game theory at a rudimentary level and see what you are referring to. I was trying to design an abstract game, but I quickly discovered that there was really only one mathematically sound move each player could make. If it was assumed that each player was rational, the first player would always win. Sometimes the payoff table in a game is skewed towards one side, so there is never real choice for players to make. However, if you even out the payoffs too much, you can create a deadlock where no move is more "correct" than another. This causes the players to feel as if they have no control over their situation. I have yet to understand a way to design around this problem - except for randomness (which can make the payoffs more interesting, but also contributes to the no-control situation).
If you do a simple google search for game theory and "solved games" you can get a nice list of games that have a predictable pattern that one can follow to guarantee at least a tie. Maybe studying those games would help one see what to avoid in their own designs.

I'm sure that there are many wiser than I who can answer your question better,

- Silverdragon0

Anonymous
Want to know more about game theory

Where might I find an online or book source for leaning about game theory?

Anonymous
Game Theory

Here's a link to help you:
http://en2.wikipedia.org/wiki/Game_theory

This appears to be a great introduction to the topic

- Silverdragon0

Torrent
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Joined: 08/03/2008
Game Theory

That is a great overview website, thanks SilverDragon.

There is one line in the page about it being really difficult to build a 'game' (payoff matrix in this sense) from things like Snakes and Ladders with high random inputs. This analysis is more for static strategic choices, which seem to be closer to the types of games that this group persues.

Andy

jwarrend
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Joined: 08/03/2008
Game Theory

I'm certainly not versed in game theory per se, but I think a few key principles can break up the problems of "best strategies". The first is to incorporate gentle randomizers. By "gentle" randomizers, I mean things that will make each game different but don't influence the overall strategy in a sweeping way. A good example is the plantation draws in Puerto Rico, a game that couldn't be said to have a "best" strategy yet is still strategic. Slightly less gentle randomizers are the card draws in Web of Power or the tile draws in Carcassonne, yet again, these are still strategic games, and the better players still will typically win. You obviously can't incorporate this into a game like Chess, and so it's more likely that a fixed-setup game will give rise to a "best" strategy.

Incorporating diplomacy and negotiation can help. For example, games like Diplomacy or A Game of Thrones feature a fixed-setup, yet they allow players to negotiate deals, and this can make a big difference. Some of the starting positions seem, on the surface, to be "stronger" than others, but this is all dependent on who allies with whom.

Also, I think that truly multiple paths to victory doesn't lead to an analysis breakdown as the previous poster suggests. It need not be the case that a player must always be able to identify the "best" move. I think the point is more that a player should always have a "good" move available, and should, in general, be selecting between a couple of possible "good" moves. Having multiple ways of getting VPs can secure this, creating different strategic possibilities.

As Darke said somewhere else, the key ingredient is the other players. In physics, the largest motion problem that can be tractably solved is with two bodies. Adding a third makes the calculation intractable. It's sort of the same in gaming. When you have a multiplayer game with different strategic options and some gentle randomizers, there's no way that you can identify a "best" strategy because the problem space is far too big. Since you don't know exactly what the other players will do, there is enough uncertainty there to make things interesting. The converse is when a player can clearly identify what the best move for all the other players will be. Yet even then, a player may not make his "best" move all the time.

So, I think I've played relatively few "German" style games that had this problem, but perhaps it's just that I haven't played any of them enough to see the problem beneath the surface...

-Jeff

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