interactive-gt

An interactive game theory application for analyzing 2-player games using nashpy and axelrod in a tkinter GUI.

Highlighted equilibria for a Battle of the Sexes, and an axelrod match between a Tit for Tat player and an Alternator:

An SQLite database of matches with a match for every pair of strategies with 1 turn entered in:

The Update Record window:

The Search Records window:

Explanation of the First Image

Suppose that there's a wife and her husband who are in two separate places and can't talk to each other. The wife prefers to go to a ballet ($B$), and the husband prefers to go to a fight ($F$). They must both choose an event and go there. Suppose also that the husband receives $2 if he meets his wife at the fight (because he prefers it) and the wife receives $1 if she meets her husband at the fight. On the other hand, the husband receives $1 if he meets his wife at the ballet, and the wife receives $2 if she meets her husband at the ballet (because she prefers it). If they choose to go to different places, they're sad and both receive $0.

This game is a game of coordination because they have to try to choose the same place, and we call it a Battle of the Sexes. We can call it $G$ and represent it with the following payoff matrix:

$G$		Wife
		F	B
Husband	F	2, 1	0, 0
	B	0, 0	1, 2

We call each pair $(F, F), (F, B), (B, F)$, and $(B, B)$ outcomes. We call the numbers associated with each player in each outcome payoffs. We call the options $F$ and $B$ strategies.

Best Responses

Now, suppose that the wife chooses $F$; ignore the scenario where she chooses $B$.

		Wife
		F
Husband	F	2, 1
	B	0, 0

Here, we see that the husband is choosing between 2 and 0. Obviously, he'll choose 2 because $2 > 0$, so we mark it:

$G$		Wife
		F	B
Husband	F	(2), 1	0, 0
	B	0, 0	1, 2

We call this a best response, and we see that the husband also has a best response when the wife chooses $B$. That is, $1 > 0$:

		Wife
			B
Husband	F		0, 0
	B		1, 2

Therefore, we have all the best responses of the husband:

$G$		Wife
		F	B
Husband	F	(2), 1	0, 0
	B	0, 0	(1), 2

We do exactly the same thing for the best responses of the wife. Again, $1 > 0$:

		Wife
		F	B
Husband	F	2, 1	0, 0

and $2 > 0$:

		Wife
		F	B
Husband	F
	B	0, 0	1, 2

We then have all the best responses

$G$		Wife
		F	B
Husband	F	(2), (1)	0, 0
	B	0, 0	(1), (2)

Pure Equilibria

Note that in the game $G$, every payoff in outcomes $(F, F)$ and $(B, B)$ is marked as a best response. Also, note that this game now looks like the matrix in the first photo (image1.png) above:

When every payoff in an outcome is a best response like this, we call that outcome a pure equilibrium. The main thing to remember about equilibria is that when players (the husband and wife, for example) are playing an equilibrium, no player has an incentive to deviate to a different strategy. In outcome $(F, F)$ the husband wouldn't want to switch from getting 2 to getting 0 because $2 > 0$, and the wife wouldn't want to switch from getting 1 to getting 0 because $1 > 0$, for example, so they have no incentive to deviate from $(F, F)$, nor from $(B, B)$.

Installation

Currently, this application may only be installed by downloading interactivegt.py and running it.