CongVsDiscrete

Morgan Grant edited this page Sep 18, 2017 · 1 revision

Continuous Time in ConG

Typical discrete time experiments divide time into discrete increments (subperiods). Subjects make one decision per subperiod. At the end of each 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 & discrete time differently. Interactions between server and client computers are event-driven, triggered whenever a user changes their actions 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 screenshots below illustrate the differences between continuous and discrete time as perceived by subjects in a prisoner's dilemma, bi-matrix game with a pure strategy selector.

CSV Config File - The csv file which produced these periods is attached -- The csv file contains the table 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

Continuous Time Period One of the attached csv config file.

Figure - In continuous time, players are able to change their action at any moment during the period. The effect of this move will be immediately reflected on the player's screen and in all other players in the affected group. Action changes can be seen in the screenshot below changes in payoffs in the payoff chart.

- The "Seconds left" field in the top center of the screenshot ticks down how many seconds are left in the period.


Discrete Time Treatment One - Ten 6-second subperiods - Period Two of the attached csv config file.

Figure - In this period there are ten subintervals of equal length. During the game, players may move their selector freely. However, only the action chosen at the moment the subperiod ends is logged by ConG, and reflected in the payoff chart. Payoffs associated with this action profile are then applied to subjects' payoffs for the duration of the subperiod.

- Changing actions in-between subperiod ends will not be seen by other players. Only the action chosen at the end of a subperiod is revealed to others. - Note the additional light-blue "progress bar" bar above the payoff matrix - this reveals how much time is left in the subperiod by filling up blue. The subperiod in the screen capture is nearly over.


Discrete Time Treatment Two - Twenty 3-second subperiods - Period Three of the attached csv config file.

Figure - 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.BR

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