Wikipedia:WikiProject Game theory/Matrix

Options

As I see it, these are the available options. Most of them are taken from some of the game theory articles around wikipedia. Many of the options can go together. So for instance, you might want to do the image, but with ordered pairs.

Standard ordered pair

	Opera	Football
Opera	2, 1	0, 0
Football	0, 0	1, 2

Used in: Battle of the sexes (no parens), Evolutionary stable strategy (no parens), Matching pennies (parens), Mixed strategy (although with ugly spacing), Normal form game (no parens), Payoff dominant equilibrium, Payoff matrix (along with row only), Pure strategy (parens), Solution concept (no parens), Stag hunt (no parens)

Color coded ordered pair

Canonical PD payoff matrix

	Cooperate	Defect
Cooperate	3, 3	0, 5
Defect	5, 0	1, 1

Used in: Prisoner's dilemma

Row only

	Player 2 adopts strategy 1	Player 2 adopts strategy 2
Player 1 adopts strategy 1	A	B
Player 1 adopts strategy 2	C	D

Used in: Coordination game, Nash equilibrium, Payoff matrix (along with ordered pair)

Two row table

	A	B
A	1 1	0 0
B	0 0	1 1

Not used

Plain text

Table A

                                Player 2 
                    Action A    Action B    Action C
          Action 1    30         -10          20 
Player 1
          Action 2    10          20         -20

Used in: Game theory

Image

Not used

Template: Payoff matrix

	Hunt	Fish
Hunt	0, 0	3, 2
Fish	2, 3	0, 0
A simple crowding game

Used in: Battle of the sexes (game theory)

Discussion

Standard ordered pair

• The primary advantage of this one is that it conforms to standard academic practice, so it familarizes readers with this type of representation. --best, kevin ···Kzollman | Talk··· 06:33, August 1, 2005 (UTC)

Color coded

• It makes it easier to see who gets what payoff, although personally I think it is not terribly nice to look at. --best, kevin ···Kzollman | Talk··· 06:33, August 1, 2005 (UTC)

Row only

• No problem seeing the different payoffs, but makes it harder to see the strategic situation. --best, kevin ···Kzollman | Talk··· 06:33, August 1, 2005 (UTC)

Two row

• Easier to understand, but harder to write and edit. --best, kevin ···Kzollman | Talk··· 06:33, August 1, 2005 (UTC)
• Ugly, non-standard notation, and hard to edit. Nothing going for it. Isomorphic 03:41, 31 August 2005 (UTC)

Plain text

• Easiest to edit, but to me its unappealing to look at. --best, kevin ···Kzollman | Talk··· 06:33, August 1, 2005 (UTC)

Image

• Aesthetically very nice, but cannot be edited without substantial effort and its slower to load. --best, kevin ···Kzollman | Talk··· 06:33, August 1, 2005 (UTC)

Template

• I just started this and am still adjusting formatting issues. Always interested in comments, but going with templates seems to be the best way to achieve standardization. ~ trialsanderrors 19:19, 29 June 2006 (UTC)

Votes

• Overall agree with your comments, however Colour coded one may be easier for the layman to understand than the Standard ordered pair, the others all look terrible or can't be editted, my vote would be for colour, if not then Standard ordered pair. Bluemoose 08:05, 1 August 2005 (UTC)
• I agree with Kevin, but I think that colour-coded isn't bad to look at. The trouble is that the red and blue look, at first glance, like Wikipedia links. Furthermore, I don't really see the need to use it more than once. I think the colour-coded matrix would be useful pedagogically to illustrate which payoffs are whose when the matrix is being explained (i.e. in an article about payoff matrices), but in all other cases (when a payoff matrix is being used not for its own sake), I'd prefer to see the standard ordered pair. Treborbassett 08:55, 1 August 2005 (UTC)
• I prefer the two row table. Is it possible to bottom align the row lables and right justify the column headings? That way the row labels would be at the same height as the payoff is in the cell, same for the column headings. Know what I mean? Pete.Hurd 16:47, 1 August 2005 (UTC)
• Something like this? Ilmari Karonen 14:21:11, 2005-08-29 (UTC)

	Defect	Co-operate
Defect	-9 -9	-10 0
Co-operate	0 -10	-1 -1

• I like Ilmari's version, the code looks nice and it makes reading the matrix by nonspecialists much easier. I have also started putting matrices off to the right and having the text wrap it. Here is an example. What do you all think? --best, kevin ···Kzollman | Talk··· 23:35, August 29, 2005 (UTC)
• I agree with Treborbassett. I prefer the ordered pair, mainly because it's the most standard notation but also because it's easier to edit than the two-row table. Color-coding is nice when first introducing the idea of a payoff matrix, to clarify whose payoff is whose (I always had trouble remembering that, even after I'd been studying the subject for a while.) Isomorphic 03:46, 31 August 2005 (UTC)