Sum Payoff Function, a.k.a. "Cournot"

Overview

With this payoff function, payoff calculations take into account the sum of players' strategies when finding individual payoffs. Here is a screenshot of a portion of an example config setup:

payoffFunction	type	name	A	sMin	sMax
sum	public_goods	pg1	1.2	0	25
sum	public_goods	pg1	1.1	0	25
sum	public_goods	pg1	0.9	0	25
sum	public_goods	pg1	0.8	0	25
sum	public_goods	pg1	1.2	0	50

The variables "A", (and in later releases of ConG, columns "B", "C", and "D") alter the payoff formula. Currently one calculation is available for use with this payoff function; this is selected in the config with the enum "type". (at least two more sum payoff function types will be released in time)

payoffFunction	type	name	A	sMin	sMax
sum	public_goods	pg1	1.2	0	25

Public Goods

• Payoff Function enum: "sum"
• Type enum: "public_goods"
• 

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Compatible Strategy Selectors

The strategy selectors successfully tested with the sum payoff function include bubbles, pure, and heatmap2d. Highlighted cells in the config examples note changes between discrete and continuous config setups for each strategy selector, if both methods are compatible.

Bubbles

This is perhaps the most intuitive strategy selector for a Sum game. With it, subjects choose by mouse or arrow-key their strategy range along the x-axis (note the rectangle selector). The payoff received is a function (described above) of one's own strategy choice and the choices of all the other participants in the group. The current payout is noted by the vertical height of one's dot (the images below are from the perspective of player GREEN, note the GREEN dot is relatively large).

• The Boolean variable potential helps visualize the function.

(For more information on bubbles, visit the Bubbles selector page.)

Figure - Below are screenshots from a Cournot game using the Bubbles sector. The left image is in discrete time (note the light blue progress bar -- this subperiod is about halfway through), the right image is in continuous time.

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Heatmap2D

(For more information on heatmap2d, visit the wiki page?.)

The strategy selector "heatmap2d" requires an additional column in the config to be functional, as shown in the example configs below. The column is named matrixDisplay, and the value put into each cell in this column is an enum having three possible values:

• HeatmapSingle - Here, subjects
• HeatmapBoth
• Corners

Below are example configs for the continuous time public goods game, each with three screenshots of example demos, one for each matrixDisplay setting in the order listed above.

period	paid	length	subperiods	percentChangePerSecond	groupSize	payoffFunction	name	min	max	Aa	Ab	Ba	Bb	mixed	selector	matrixDisplay	showHeatmapLegend
1	TRUE	60	1	NaN	1	matrix2x2	first	0	17	10	0	18	4	TRUE	heatmap2d	HeatmapSingle	TRUE
2	TRUE	60	1	NaN	1	matrix2x2	first	0	17	10	0	18	4	TRUE	heatmap2d	HeatmapBoth	TRUE
3	TRUE	60	0	NaN	1	matrix2x2	first	0	17	10	0	18	4	TRUE	heatmap2d	corners	TRUE

Pure

With the "Pure" strategy selector, users choose only from two extreme strategy options, sMin & sMax. Subjects see a familiar two-by-two matrix with payoffs for strategy combinations (note this game is from an as-yet unreleased Cournot game.)

Although this selector works for Sum games, it is perhaps not the best option, since mixed strategies are not available.

(For more information on pure, visit the Pure wiki page.)

Figures - the screenshots below are from discrete (left) and continuous time (right) experiments.

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Simplex

(For more information on simplex, visit the wiki page?.)

Currently, it would seem that the strategy selector "simplex" does not work with cournot. However, while the player's interface does not have any working controls, the experimenter interface? seems to be calculating and collecting earnings for all players. The error log only has a few ArrayIndexOutOfBounds exceptions, so it could be that simplex would work with cournot given a small amount of bug-fixing. More info to come.