Computer games

Public goods game (PGG)

Following Rand et al. (2009), I employed a standard PGG design (designated the project game), in which groups of four participants interacted repeatedly. In every game round, each participant received 20 monetary points and was asked to decide

how many points (between 0 and 20) they were willing to contribute to the public good (i.e., the group project), on the proviso that they would keep any points they did not contribute for themselves. Participants were given 20 seconds to make their contribution, and were informed that failure to decide in this timeframe would result in a random number of points between 0 and 20 being contributed. Contributions to the public good were then doubled before being split evenly back among the four group members.

Thus, the maximum payoff for the group occurred when all participants contributed 20 points, and each participant received back 40 points (i.e., for each point contributed, all participants received back 0.5 points), but individual participants could increase their own game-round earnings relative to other group members by contributing less while still benefiting from the group pool (the maximum individual payoff was 50 points for an individual who contributed zero when all other group members contributed 20 points).

Learning game

The learning game (designated the monster league game) was adapted from, and closely resembled, a custom-made learning game designed by Wisdom et al. (2013). The aim of the game for each participant was to maximise the number of points earned by a subset of six monster icons (“monster team”) chosen from a larger subset of 48 monster icons (“the monster league”). The game screen included the league of 48 monster icons, an area for the participant’s current team selection, and another area displaying the participant’s best-scoring team alongside their team from the previous round (see Figure 5.1 for a screen shot of the learning game). The scores of the participant’s best-scoring and previous round teams were also visible, and a timer

located in the top right corner of the screen reminded participants of how many seconds remained in the round. In each round of the game, participants were given 20 seconds to choose six icons for their current monster team, after which random monster icons were selected from the available icons in the league to fill any remaining spaces. Participants could click on a button to “clear” their current team entirely, or alternatively could clear individual monster icons they wished to change by clicking on the icon. Monster icons could be selected from any part of the screen by clicking on the icon, except those icons that already appeared in the participant’s current team which were highlighted with a green border. In addition, the current team could be replaced entirely by a previous team through clicking on the “copy” button that appeared beneath it.

Other&Teams&&

Figure 5.1. Screen shot of the learning game during the practice rounds. During interactive gameplay participants could also view the monster teams of other participants who had agreed to share with them (see Figure 5.3)

In each new experimental session, the league and monster icon positions were generated randomly from a larger set of 149 monster icons, but then remained fixed for the duration of the session. Following Wisdom et al. (2013), each monster icon was associated with a specified positive points score, and some ‘interaction’ pairs of monster icons were associated with additional points bonuses or penalties when they appeared in the same team together. Thus, the score for each monster team represented the sum of points associated with each monster icon plus or minus the value of any interaction pairs that were present. There was no overlap between interaction pairs, and their distribution, which concentrated bonuses among low- scoring pairs and penalties among high-scoring pairs, was previously found to be challenging for experimental participants (Wisdom et al. 2013; see Figure 5.2a for an outline of the points distribution).

1" 1" 1" 1" 1" 1" 1" 1" 1" 1" 2" 2" 2" 2" 2" 2" 2" 2" 2" 3" 3" 3" 3" 3" 3" 3" 3" 4" 4" 4" 4" 4" 4" 4" 5" 5" 5" 5" 5" 6" 6" 6" 6" 7" 7" 7" 8" 8" +20$ +15$ +5$ +10$ '10$ '15$ '20$ '5$ Individual$icon$score$$ Interac6on$bonus/penalty$$

Figure 5.2a. The score distribution applied to individual monster icons and the interaction bonuses and penalties applied to pairs of icons, for a league size of 48 monster icons (adapted from Wisdom et al., 2013).

Participants were provided with information about the maximum possible team score achievable (i.e., 60 points), to motivate continued striving for high scores throughout repeated rounds of the game, and were informed that some pairs of

monster icons conferred bonuses or penalties, but were not given any information about the score distribution (see Figure 5.2b for the probability distribution of scores among all possible teams).

Score Pr o b ab ili ty -10 0 10 20 30 40 50 60 0.00 0.02 0.04 0.06 0.08 Last%round% All%rounds% First%round% Mean%score:%

Figure 5.2b. The probability distribution of monster team scores [-6,60] for a league of size 48 and the score distribution displayed in Figure 2a. The mean score in the first round (green line), last round (blue line), and overall (red line) for all participants is also shown.

Participants played the learning game in the same group of four participants with whom they played the public goods game. In each round, participants could choose which of the other three participants they wished to share their previous round monster team and score with, and were permitted to copy all, some or none of the solutions that the other participants had chosen to share with them, which were displayed in a separate area of the game screen (see below, section 5.2.3. Design, for

further details of participant interactions in the learning game across experimental conditions).

5.2.3. Design

In a between-groups design, I randomly allocated groups of four participants to one of two experimental conditions. Participants were informed they would interact with the same three people throughout the experiment. In the first condition (the linked identity condition, N=40), each participant was assigned a single identity at the beginning of the experiment (e.g., ‘Player 1’), which they kept in both the PGG and learning game for the duration of the experiment. In contrast, participants allocated to the second condition (the unlinked identity condition, N=40) were allocated separate identities for each game (e.g., ‘Player 1’ in the PGG and ‘Player Blue’ in the learning game), which also remained fixed for the duration of the experiment, but were not linkable between games. Participants interacted anonymously via their computer stations (it was not possible to link the player identities in the games to the other people in the room).

At the beginning of each session, participants then undertook an extensive computer-based tutorial in the rules and mechanics of the learning game (known to players as the monster league game) followed by the PGG (known to players as the project game), before beginning iterative rounds of interactive gameplay with group members (see section 5.2.2. for a description of the games). During the game tutorials, participants were also instructed that individual bonus payments of up to £15 would be calculated at the end of the experimental session, and would consist of their cumulative points earned in both games following a conversion of: 145 points = £1.

The learning game tutorial included five practice rounds of the game, which participants played individually. Participants were instructed that the scores they

obtained in the practice rounds would not contribute to their final payment, but that they would carryover their score and game information (i.e., monster team) from the final practice round into the first round of the interactive game. Following Rand et al. (2009), the public goods game tutorial included detailed instructions about the game rules, including a series of worked hypothetical examples, but did not involve a practice period. Participants were permitted to complete the game tutorials in their own time, with those who completed early held in a game ‘waiting room’ until all other group members had completed.

Participants in the linked identity condition were informed that in each game round, one play of the public goods game would always be followed by one play of the learning game. Participants were also aware that they would learn of each other’s public goods contributions before each play of the learning game, and would have to decide with whom they wished to share information from their last attempt at the learning game (i.e., their monster team and score from the previous round) in the next play of the game (see Figure 5.3a). Participants in the unlinked identity condition received the same instructions, with one important exception. After participants in the unlinked identity condition had learned of each other’s contributions to the PGG, they were reassigned their separate learning game identities, and had their screen positions randomly shuffled, before deciding whom they wished to share their last round’s monster team with (i.e., individual identities and reputations gained in the public goods game could not be linked to identities and directed-sharing decisions in the learning game, and vice versa; see Figure 5.3b).

5

Figure 5.3a. Screenshot example of decision-making screen as seen by participants in the linked identity condition in each round prior to playing the learning game

5" (i)"

(ii)"

Figure 5.3b.Screenshot examples of public goods game results screen (i), which was immediately followed by identity reassignment and the learning game decision- making screen (ii), as seen by participants in the unlinked identity condition in each round prior to playing the learning game

Participants were given 20 seconds to decide which of the other players they would share information with, before playing one round of the learning game. While playing the learning game, participants had visual access to the scores and monster teams submitted in the previous round by group members who had agreed to share with them, but the scores and monster teams of group members who had not agreed to share remained hidden (see Figure 5.4 for a screenshot example from the linked identity condition). Players could copy some or all of their own monster team from the information provided by other group members, but were also free to ignore this information.

Figure 5.4. Screenshot example of the interactive learning game in the linked identity condition (Screen as seen by Player 2: Player 1 and 3 agreed to share their previous team with Player 2, but Player 4 withheld information in this round.)

At the end of every round, participants saw a summary of the round, reminding them of the contributions made by each player to the public good, and of which players had shared information with them. The summary also detailed the participant’s current round points and cumulative points separately for the public goods game and learning game. Participants then began the next round of game play until 20 rounds had elapsed, after which the session ended (20 rounds was chosen as Wisdom et al. (2013) previously reported a performance plateau in in the learning game after 24 rounds). Participants were informed that they would play an unspecified number of rounds, and that their behaviour during the game would not affect the total number of rounds played, so were unaware of when the game would end (see Figure 5.5 for a schematic of the game structure).

One$play$of$ public$goods$ game$ START$ !  View$PGG$ contribu=ons$ !  Choose$share$ One$play$of$ learning$game$ Linked'iden(ty' Condi(on' Unlinked'iden(ty' Condi(on' !  View$PGG$ contribu=ons$ !  Reassign$Player$ID$ !  Choose$share$ See$round$$ and$score$ summary$$ round<20' FINISH$ General$$ Intro$to$games$ and$gameEround$ structure$$ Tutorial$&$ prac=ce:$ Learning$game$ (LG)$$$ Tutorial:$Public$ goods$game$ (PGG)$ Reminder$about$ game$structure$ &$bonus$ payment$ Tutorial:$ informa=on$ sharing$in$LG$$ Round=20'

Figure 5.5. Schematic of the game stages and progression of participants through iterative rounds of the public goods game (PGG) and learning game (LG), in the linked identity and unlinked identity conditions

5.2.4. Procedure

Participants were recruited for a study on ‘Interactive decision-making,’ and those who were known to each other were prevented from participating in the same experimental session. On arrival, participants were given a verbal and written briefing by the experimenter, and provided with an opportunity to ask questions. The experimenter then started the experiment on participants’ computers remotely from a server computer located in an adjoining room. The experimenter remained in the adjoining room with the connecting door open for the duration of the experiment, to ensure that no participants communicated. There were no instances of between- participant communication observed. The experiment lasted approximately 45 minutes, and after it had ended the experimenter returned to debrief participants and answer any remaining questions. Participants were then free to collect their payment and leave.