heatmap2d

Morgan Grant edited this page Sep 19, 2017 · 1 revision

Table of Contents

Strategy selector: Heatmap2d

Overview

The heatmap2d selector displays a heatmap in the client windows which the players can use to choose their strategies. The players use the mouse to select their strategies on the Y-axis of the heatmap, and the maximum payoffs are displayed on the axis of the heatmap. The payoff of the player is always displayed on the point that the player has selected. The advantage of the heatmap is that it displays "heat" on the selector itself which makes it easy for players to see what is the greatest possible payoff. The redder the region on the heatmap the higher the heat, and therefore the higher the payoff in that region.

Below are some of the example treatments from our prisoner's dilemma game demo experiment. These display the three main options for the heatmap2d selector which are HeatmapSingle, HeatmapBoth, and corners.

Interface

Heatmap Selector

  • The heatmap selector is in the bottom lefthand corner.
  • Y-axis - Players use left-click on their mouse to choose strategies in the Y-axis of the heatmap.
  • X-axis - This is the strategy of the group that the player is playing against.
  • Heatmap Color - The color of the heatmap corresponds to the payoff of that particular point where redder areas have higher payoffs and bluer areas have lower payoffs.

Flow payoffs chart

  • This is the graph to the right of the selector, displaying unfolding flow payoffs over time.
  • Y-axis - Shows the payoffs of the player.
  • X-axis - Time

Actions over time chart

  • Located to the right of the heatmap and above the flow payoffs chart is actions over time chart.
  • Y-axis - Unfolding action choices of the player is charted over the Y-axis and is relative to the range of actions available to the player at that time. In the context of the prisoner's dilemma game, the top of the graph means that the player has chosen to defect, and the bottom means they've chosen to cooperate fully at that time.
  • X-axis - Time

Other information

  • "Subperiods left" - self explanatory.
  • "Previous earnings" - displays earnings over all periods.
  • "Current earnings" - displays earnings of the current period.
  • ShowHeatmapLegend - This is the legend to the left of the payoffs over time field which shows what colors correspond to what payoffs.
  • Note that there is a fourth field above the heatmap selector when HeatmapBoth is chosen.

HeatmapSingle

  • Below is a table abstraction of the configuration file we used in the prisoner's dilemma game demo. To follow along or edit a configuration file simply open the .csv config file in Excel or any spreadsheet program.
period ... mixed selector matrixDisplay showHeatmapLegend
1 ... TRUE heatmap2d HeatmapSingle TRUE
  • This is the default heatmap selector display where the main difference is that the players can use the heatmap to select their strategies.
  • Experimenters should be careful consider whether or not colorblind subject are permitted to play. Some types of colorblindedness may prevent making good use of the heatmap.
  • mixed is set to TRUE. The players can see the heatmap, but you'd only be able to choose A or B (cooperate or defect). This will be useful in the hawk-dove game, with one and two-population games.
  • selector This option enable the player to use the heatmap to change their strategy as opposed to the default option, pure.
  • matrixDisplay We have set this to "HeatmapSingle" which is the default display for heatmaps. We will discuss this option more in the HeatmapBoth treatment.
  • showHeatmapLegend We have set this to TRUE so it displays the heatmap legend.

HeatmapBoth

  • Below is a table abstraction of the configuration file.
period ... mixed selector matrixDisplay showHeatmapLegend
2 ... TRUE heatmap2d HeatmapBoth TRUE
  • Double Rainbow - The screenshot below displays two heatmaps one of which shows how your actions affect the payoffs of the other player's. In discrete time, it gets tricky. For each player's perspective, they are always a 'row' player, meaning players only move up and down, along the y-axis.
  • Important - This option is essentially only useful for bi-matrix, symmetric games where the player is only playing against one other player. If the player is playing against more than one player then the heatmap that is supposed to represent the heatmap of the other players is not accurate. Basically the heatmap that is displayed in the inaccurate scenario does not correspond to any of the player's heatmaps at all and corresponds to something else.
  • selector - as per usual this is set to "heatmap2d"
  • matrixDisplay - this field is set to "HeatmapBoth"
Figure
  • Three of the four fields below are the same as in HeatmapSingle except one more has been added above the heatmap selector in the upper lefthand corner.
  • The field above the heatmap selector is a smaller heatmap that displays the heatmap that is visible to the other player. (Note - again noting that this is the Prisoner's Dilemma Game below where there are only two players. When players are playing against more than one other player the "other player's heatmap" field does not display accurate information about the other players' heatmaps.)

Corners

  • Below is a table abstraction of the configuration file.
period ... mixed selector matrixDisplay showHeatmapLegend
3 ... TRUE heatmap2d corners TRUE
  • With this option there is no heat map. The selector only tells you payoff information in the corners. Players can choose mixed strategies (up for cooperate, down for defect again, but can only see their payoffs in the payoffs over time field.
  • selector - this field is set to "heatmap2d" as per usual (though the heatmap is not visible the selector functions the same way).
  • matrixDisplay - is set to "corners"
Figure
  • The heatmap selector has been replaced with the corners selector which functions the same way as before except all of the "heat" information has been removed.

Compatible payoff functions

The payoff function most strongly related to the heatmap2d strategy selector is [wiki:matrix2x2], which is used in Prisoner's Dilemma and Hawk Dove. Although the heatmap2d selector does technically work with the Sum function this combination is untested.

For more information about selector/payoff function compatibility go here

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