Continuous Time in ConG

Typical discrete time experiments divide time into discrete increments (subperiods). Subjects make one decisions per subperiod. At the end of the subperiod, decisions are broadcast to all subjects. In one sense ConG simulates continuous time by the minute discretization of time, with each second divided into more than twenty subperiods.

However, at an architectural level ConG software treats continuous time different than discrete. Interactions between server and client computers are event-driven; triggered whenever a user changes their strategy choice by interacting with the user interface. In this sense, the discretization of time is ConG’s reaction lag, the delay between when a user clicks to make a change and when the computer reveals the effect of that change to the user graphically. With minimum hardware requirements met, that reaction lag is far below any human’s ability to perceive it. Thus from the perspective of a human user, decision making is continuous in a ConG experiment.

Configuration

The "subperiods" field of the config csv is used to configure continuous or discrete time. If subperiods is set to 0, the game will be played in continuous time. If subperiods is greater than 0, the period will be divided into even-length subperiods. For example, if the period length is 120 seconds, with 10 subperiods, each subperiod will be 12 seconds long. During the subperiod, the subject receives no feedback on the strategy played by their opponents. When the subperiod ends, the strategies will be revealed for that subperiod, and play moves immediately into the next subperiod.

Continuous vs. Discrete Time

The below screenshots illustrate the differences between continuous and discrete time. Note that all of these screenshots use a pure strategy.

Continuous Time

As you can see above, the player is able to change his or her strategy at any moment. The thin spikes are the result of rapid changing.

In this period there are ten subintervals of equal length. The strategy of a player does not get set until the subperiod ends, so changing in-between periods has no effect.

And lastly, this screenshot shows a period of the same length as the others, but with twice as many periods as the previous one. These subperiods are, of course, half as long as the previous period.

The csv file which produced these periods is attached, an easily readable table of this csv is below.

period	paid	length	subperiods	percentChangePerSecond	groupSize	payoffFunction	name	min	max	Aa	Ab	Ba	Bb	selector
1	TRUE	60	0	NaN	1	matrix2x2	first	0	17	10	0	18	4	pure
2	TRUE	60	10	NaN	1	matrix2x2	first	0	17	10	0	18	4	pure
3	TRUE	60	20	NaN	1	matrix2x2	first	0	17	10	0	18	4	pure