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Battle of the Sexes

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 Theater. Each earns zero if they miscoordinate. Row prefers coordinating on Concert (earning 3) over coordinating on Theater (earning 2), while Column prefers coordinating on Theater (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

At the top of the results page, we depict the payoff matrix (Figure 2). This may be helpful in establishing the multiple equilibria in pure strategies.

Figure 2: Payoff Matrix

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 3, 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 3: Outcome Frequency

Next, we display the frequency of each action for each round (Figure 4, revealed by clicking the triangle next to Action Frequencies). 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 Frequency
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