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Aa

Bach or Stravinsky

Game Description

The classic game of (mis)coordination: while both players prefer coordination over miscoordination, each prefers coordinating on a different pure-strategy Nash equilibrium.

Each round, each of two players simultaneously chooses between Concert and Play. Each earns zero if they miscoordinate. Row prefers coordinating on Concert (earning 3) over coordinating on Play (earning 2), while Column prefers coordinating on Play (earning 3) over coordinating on Concert (earning 2).

Learning Objective 1: Miscoordination in a One Shot Game

When played once (or with different partners), miscoordination is common when players disagree on preferred pure-strategy (efficient) Nash equilibrium.

Learning Objective 2: Repetition and Resolution of Miscoordination

Interesting fair and efficient patterns of behavior often emerge when the game is repeated between the same pair, such as turn taking (alternation between the two pure-strategy Nash equilibria, also known as a tit-for-tat strategy).

Brief Instructions

The student’s game screen is shown in Figure 1. For the one-shot game, in addition to the two pure-strategy equilibria where players coordinate, there is a mixed-strategy equilibrium: Row chooses concert with probability 3/5, Column with probability 2/5, resulting in each having an expected payoff of 6/5. By default, each pair plays 5 rounds.

Figure 1: Game Screen

Key Treatment Variations

Repeat play will result in markedly different outcomes than one-shot interactions.

To have each pair interact repeatedly, change Minimum Rounds. For indefinite repetition, once Minimum Rounds has been reached, Ending Probability establishes the likelihood of proceeding to another round conditional on reaching the current round.

For one shot play, keep Minimum Rounds at 1 and Ending Probability at 100. To have students play multiple rounds with re-pairing between rounds, click Replay after a one-round game. Choose Random to randomly assign both roles and partners in the next game.

Results

The results screen presents a graph, a table, and raw data, each focusing on the likelihood of the actions.

Figure 2: View Menu

Use the View menu (Figure 2) to select a different game if you have run multiple games in your playlist. If not, this option is not available. If you used one of the Replay options, you can contrast the results between these linked games using the Compare button. To obtain a screen shot of the results, you can use the Download button beneath the compare button.

At the top of the graphs results page, we depict the payoff matrix (Figure 3). This may be helpful in establishing the multiple equilibria in pure strategies.

Figure 3: Payoff Matrix

Below the payoff matrix, we display the frequency of each action for each round (Figure 4, revealed by clicking the triangle next to Action Frequencies).It shows for each round the average choices and the incidence of the three outcomes: both coordinate on Concert; both coordinate on Play; and the miscoordination that occurs when one chose Concert while the other chose Play.

You can reveal or hide the results for an action by clicking entry in the legend. For the first (or only) interaction between particular pairs, it is common to see aggregate play match mixed-strategy proportions.

Figure 4: Action Frequencies

Within the tables tab, to show the increase of equilibrium play (i.e., reduction of miscoordination) with repeat play, we display the frequency of each of the four outcomes for each round (Figure 5, revealed by clicking the triangle next to Outcome Frequencies). You should expect to see a marked decrease in miscoordination (bottom left, top right) from first to last round.

Figure 5: Outcome Frequencies

Below the outcome frequencies in the table tab, we present a coordination summary (Figure 6) that displays the round number and the number of groups who coordinated and the number who miscoordinated.

Figure 6: Coordination Summary

We present the coordination summary in graphical form under the graphs tab, below the action frequencies (Figure 7). The graph presents the table summary data in a different and visual manner.

Figure 7: Coordination Summary (Graphical)

Finally, the Raw Data tab (Figure 8) presents a player table with each player's choice, their group, and the round number in a table format. This table presents the data from the game that has not been processed in any particular way.

Figure 8: Raw Data
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