Can loss framing improve coordination in the minimum effort game?

Abstract

I study how framing payoffs as losses affects group coordination using the minimum effort game. The previous literature shows groups as small as four have a difficult time coordinating on an efficient outcome, even in the presence of higher payoffs for more efficient outcomes. Though penalties for inefficient coordination behavior have been studied in a variety of contexts, the role of losses on coordination behavior has not. Loss framing has been shown to induce more efficient actions in a variety of other areas, since individuals tend to be more sensitive to losses than gains. I examine the framing effect of losses, specifically if framing payoffs as losses can lead to payoff-dominant coordination, using three treatments. These treatments help tease out the effects and dynamics of coordination behavior when payoffs are framed as losses. I find that framing payoffs as losses leads to improvements in coordination, demonstrating the robustness of loss framing in the setting of the minimum effort game.

Appendices

6 Appendix A: Additional results

1.1 6.1 Heterogeneity

To assess the degree of heterogeneity in each treatment, it is instructive to look at group-level behavior in each treatment. Figures 3, 4, 5, and 6 show the mean choices by group and treatment. The baseline condition results in the most stable behavior of the treatments. In the first 10 rounds, all groups either achieve or are strongly trending toward coordination failure. In period 11, all groups increase their actions, but then 5 of the 6 groups revert back to exerting a low level of effort. Most groups end up with actions between 1 and 2 by period 20. Figure 3 shows that group 6 is able to increase coordination to a level of 6 by the end of the experiment. This group is the main reason why it appears that coordination levels increase above two in Figs. 1 and 2. To assess whether this is really an outlier, the median action is informative. Looking at the treatment-level median across periods 11-20, the highest median achieved is 3 in period 11; otherwise, the median action is at most 2 (in period 12 and 16) and is more commonly 1 or 1.5. This confirms that group 6 is an outlier, so it is fair to say the baseline condition successfully achieves coordination failure. The minor improvement in part 2 in the baseline condition is due to the behavior of a single group, which, when aggregated with the rest of the groups, gives the appearance of better coordination.

Figure 4 shows the heterogeneous responses by group in the Gain–Loss treatment. Here, the dynamics of the treatment can be assessed group by group. In the first part, two trends emerge. Groups 4 and 5 coordinate between 6 and 7 for the majority of part 1. These two groups maintain their high level of coordination through part two. With their history of high level of effort in the part 1, it is not surprising that these participants are able to maintain their high level of coordination through period 20, even in the face of the loss condition. Having a static group throughout the experiment can help facilitate this behavior. I will explore this further in relation to risk preferences in the next section. The remaining four groups do not achieve coordination failure per se, but are trending toward failure. By trending toward failure, I mean that the trend of participant choices is decreasing in a manner similar to what we see in Fig. 1 with the baseline treatment. Average choices in these four groups are decreasing and it would be plausible that they would achieve failure given further rounds of play without interruption. For these four groups, the effect of moving into the loss condition is also heterogeneous. Group 2 is the only group who responds to the introduction of the loss table exactly as hypothesized. This group achieves and maintains a coordination level of 7 beginning in period 13 and continues at this level through the final period. Group 6 has a temporary improvement in period 11, but then gradually decrease their effort to an average between 2 and 3 in the last 5 periods. Groups 1 and 3 have very inconsistent choices throughout the last 10 periods. It is clear any previous action does not result in a precedent for these groups.

Overall, it does not appear that the loss frame has any conclusive positive effect on coordination for groups 1, 3, and 6 in the Gain–Loss treatment. This is contrary to the expectation in hypothesis 1, which suggests that sensitivity to losses will lead to better coordination in part 1. Many of the groups in this treatment are able to maintain relatively high coordination throughout the experiment, regardless of the presentation of the payoffs. In part 1, outside of group 4, participants either achieve, or are trending toward coordination failure in the Loss–Gain treatment. This is contrary to hypothesis 2 which suggests that framing payoffs as losses will lead to more efficient, specifically payoff-dominant, equilibrium. The likely reason for this is a lack of experience of play and the strategic uncertainty that comes with encountering the loss frame in period 1.

Most papers, when including a treatment intervention, do not address the actual dynamics of the intervention by including it in the initial rounds of play. It is far more common for participants to play 10 rounds of the game first (to assess coordination failure replication), and then apply the intervention for the successive 10 periods as I did in the Gain–Loss treatment. By doing this, we are deprived of any information about how the intervention may affect initial choices. Previous works have shown that initial conditions matter in these experiments. Regardless of the results, this design would reflect that conclusion. However, since assessing dynamics of framing payoffs as losses is the main goal of this experiment, this structure is necessary. The interaction of the behavior with risk preferences in part one will be discussed extensively in the next section, but here, the secure action of 1 is chosen at the highest rate (42.5%). It is likely that this treatment added to strategic uncertainty about group actions or dynamics of participants. Results in coordination games are sensitive to initial conditions and add exogenous risk to an already uncertain decision (Van Huyck et al. 1990, 1991; Devetag and Ortmann 2007). This can lead to deterioration of coordination equilibria toward the secure equilibrium of 1.

The greater issue with heterogeneity in the Loss–Gain treatment is in response to the shift from the loss to the gain frame. In part two, Fig. 5 shows two separate patterns of behavior after the shift to the gain frame. Groups 1, 2, and 4 all increase their choices in the gain frame. Groups 1 and 4 are actually able to achieve payoff-dominant coordination by period 15, and maintain it through period 20. Group 2 increases their actions close to 7 initially, but after period 12, the choices decrease until it settles close to 4. The remaining three groups continue their path toward coordination failure from the first two periods and achieve it by period 20. Why do we see this dichotomous response in the transition to the gain treatment? The rationale behind continuing with the secure actions makes sense because it reduces uncertainty, and with a history of play, participants know that they will be able to coordinate on at least this action (due to precedent). For the three groups who are able to achieve a high level of coordination, I need to explore the role of risk preferences and their relation to riskier actions. It is possible that the psychological effect of failed coordination during the first 10 periods induces participants to seek compensatory gains during the gain frame. If this is the case, risk may be an effective lens through which to gauge this shift.

Fig. 3

Baseline mean choice by group

Fig. 4

Gain–Loss mean choice by group

Fig. 5

Loss–Gain mean choice by group

Fig. 6

Gain–Mix mean choice by group

1.2 6.2 Risk preferences

To control for differences in risk preferences that may affect actions during the experiment, I used the Dave et al. (2010) version of the Eckel and Grossman (2002) measure. Participants are asked to choose one of the 6 gambles listed in Table 7. Each of the possible options of the gamble has a 50% chance of happening. Since selecting the payoff-dominant action is inherently riskier than the secure action, this may help explain the results. For the following figure, a risk preference marked as 1 indicates the lowest value of a constant relative risk aversion parameter. A chosen gamble of 6 has the lowest risk aversion parameter, since it is the most risky gamble. Table 7 reports the frequency of choices of risk gamble by treatment. There are no differences in the distribution of risk preferences between the baseline and any of the treatments. The majority of participants (53/72 or 74%) select a gamble of 3 or lower. If risk is a significant parameter in guiding choices in the minimum effort game, this may be an important explanation for why we see the lack of coordination on the payoff-dominant equilibrium. Ultimately, what I am interested in is how these risk preferences affect actions over the course of the experiment. Figures 7, 8, 9, and 10 present the mean choices by risk preference in each treatment.

Table 7 Risk preferences

Fig. 7

Baseline mean choice by risk preference

Fig. 8

Gain–Loss mean choice by risk preference

Fig. 9

Loss–Gain mean choice by risk preference

Fig. 10

Gain–Mix mean choice by risk preference

Figure 7 shows that, in part 1 of the baseline, participants are mostly sticking with the secure action regardless of risk preference. There is some exploration throughout the period, but all 6 risk groups, on average, choose an action below 2 by period 10. In part 2, four of the risk groups continue coordinating on the secure action. However, two of the risk groups, those who chose gambles 3 and 4, see some increase in risky actions in part 2. It should be noted that only one participant chose gamble 4 in the baseline, so it would be irresponsible to put too much weight on this observation. The 6 participants who chose gamble 3 are choosing an action near 4 beginning in period 11. Here, 7 of the 24 participants are willing to risk not coordinating on any of the equilibria in exchange for the hope of a better payoff.

The Gain–Loss choices based on risk preference is shown in Fig. 8. For gambles 4 and 5, there is only one observation. The participant who chooses gamble 4 seems to have no consistent pattern of choices throughout the experiment. There are sustained high choices of 6 or 7 for the participant who chooses a gamble of 5. The 22 participants who choose the remaining 4 gambles have a fairly similar decreasing trend in part 1. They begin at an action of 5 or 6, and then, coordination deteriorates to an action between 3 and 5. These groups stabilize their choices in part 2 by choosing an action between 4 and 6 with less variability than in part 1. This increase in risky actions in the Gain–Loss treatment, regardless of risk preference, is one explanation for why we see coordination at a higher effort level than in the baseline in part 1. Participants in this treatment overall exhibit a higher preference for risk than in the baseline, as we see in Table 7. This emerges as an explanation of the surprising part 1 result when both sets of participants are playing under the same condition and achieve different levels of coordination. However, I am not able to say for certain this was the only reason behind this behavior.

The treatment with the most risk averse participants is the Loss–Gain treatment. Overall, 20/24 subjects choose a gamble of 3 or less. The choices for all of the 4 gambles chosen reflect much of what we see in Table 3. Overall, there is a strong trend toward coordination failure in part 1, as shown in Fig. 9. Those with the highest risk preference (who choose gamble 6) are choosing the most risky actions in part 1, but they are only slightly better than their less risk tolerant counterparts. In part 2, the binary response to the Gain table shift shown in Fig. 5 emerges here. Participants with the highest preference for risk are the ones who increase their choices toward the payoff-dominant equilibrium and those with the lowest tolerance for risk resume their quest toward coordination failure. However, these risk parameters, in conjunction with the choices made by participants, suggest that participants are not willing to choose a riskier action, even when payoffs are framed as losses. The higher risk preference in the Gain–Loss treatment emerges as an explanation for why this different result in part 1 emerges when compared to the baseline. However, it seems like participants are more willing to coordinate at a high effort level, regardless of risk preference of payoff framing.

Table 8 Summary statistics of participants

Table 9 Treatment effect on group minima (ordered probit)

1.3 6.3 Variance

Table 8 shows summary statistics of participants. A helpful way to further assess choice heterogeneity in the treatment conditions is to look at variances at the treatment level. Figure 11 shows the variance in participant choices by treatment across all periods. For the baseline condition, the variance looks relatively stable, but numerically it is fairly large, especially in periods 11–20. This is largely due to the influence of a single group, though since these variances are calculated at the treatment level, they will be much larger than if they were calculated at a smaller level of aggregation. It is easy to see the influence of this group, Group 6, in Fig. 3. When the mean choices of every other group are around 1, this group is coordinating close to an effort level of 6. A more accurate representation of the behavior in the baseline condition is in Fig. 2. Both of the treatment conditions trend toward a higher amount of variance as the period gets closer to 20. The variance in the Gain–Loss treatment is fairly consistent across all periods. The variance of 6 is still high, but easy to explain. Figure 4, as noted earlier, presents a pattern of divergence where 3 of the groups in this treatment choose an average of 6 or 7, and the other three are roughly between 1 and 4. The Loss–Gain variance seems to reflect the general pattern in Fig. 5. In the first 10 rounds, the actions gradually decrease. For the second 10 rounds the results are more heterogeneous, resulting in the high variance in Fig. 11. Two groups coordinate on 7, one group coordinates on 4, and the other three are between 1 and 2 by period 20, creating this large variance. Table 9 shows the treatment effects based on group minima.

Fig. 11

Variance of choices by treatment

7 Appendix B: Experimental instructions

What follows are the instructions my experiment. I am only including directions for the Gain–Loss treatment. To replicate this experiment, the full instructions can easily be reconstructed in the following manner: For the baseline condition, use the gain instructions twice, and for the Loss–Gain treatment, use the loss instructions and then the gain instructions. Below there is an introductory section that was included at the beginning of each session. These instructions are modified from Brandts and Cooper (2006).

1.1 7.1 Gain–Loss treatment instructions

Welcome.

Today you will be asked to participate in an experiment. The purpose is to study how people make decisions in different situations. From now until the end of the experiment, any communication with other participants is prohibited. Please silence and put away your cell phones, and do not talk. If you have any questions please raise your hand at any time and one of the experimenters will assist you. If you are unsure about any of the directions I encourage you to ask a question.

You will receive $5 dollars as a show-up fee for this experiment. In addition, you will earn money during the experiment. Upon completion, the amount that you earn will be paid to you in cash. Payments are confidential and will be administered privately.

The experiment has two parts. You will receive instruction for Part II after we complete Part I.

Please click okay to go to the instructions for part 1

PART 1: Gains Condition

In Part 1 there will be 10 Rounds. In each round you will be in a group with three other participants. The participants you are grouped with are the same throughout the experiment.

For each Round you are to choose a number between 1 and 7. Your payoff depends on your choice, and the SMALLEST number chosen by the four members of the group, as in the table that follows.

(At this point I put the Gain payoff table (Table 2) on the screen at the front of the room, and handed out a paper copy to each of the participants. Participants do not know these are called gains or loss tables, it just says Payoff Table on the screen and handout.)

Your payment for the round will be the amount determined from the table. For each round the computer will display a screen showing the above payoff table. Each participant will choose their number between 1 and 7 using the text box on the screen and clicking the OK button. When you make your decision you will not know who is in your group, or the actions they take. All actions are confidential.

After each Round you will be informed of the action you chose in that round, the smallest number chosen by your group in that round, your payoff for this round, and your accumulated payoff through the current round. You will be shown the history of your decisions and the history of decisions of your entire group in each round.

Payoff Quiz (for the Gain Table)

Before we begin the experiment, please answer the following questions. We will go through the answers to a sample problem first, and then you will finish the quiz on your own. Each question deals with calculating your payoff in a single round.

Sample Question: Suppose you choose the action 3. The other members of your group choose 2, 5, and 7 respectively.

What is the minimum action chosen by your group? (2)

What is your payoff? (0.55)

1. Suppose you choose the action 7. The other members of your group choose 4, 5, and 6.

What is the minimum action chosen by your group? (4)

What is your payoff? (0.55)

2. Suppose you choose the action 1. The other members of your group choose 7, 6, and 2.

What is the minimum action chosen by your group? (1) What is your payoff? (0.55)

Remember that you are grouped with the same individuals throughout the 20 Rounds of this experiment. All actions and payoffs are confidential.

PART 2: Losses Condition

In Part 2 there will be 10 Rounds. In each round you will be in a group with three other participants. The participants you are grouped with are the same throughout the experiment.

For each Round you are to choose a number between 1 and 7. Your payoff depends on your choice, and the SMALLEST number chosen by the four members of the group, as in the table that follows.

(At this point I put the Loss payoff table (Table 3) on the screen at the front of the room, and handed out a paper copy to each of the participants. Participants do not know these are called gains or loss tables, it just says Payoff Table on the screen and handout.)

Your payment for the round will be the amount determined from the table plus $1.35.

For each round the computer will display a screen showing the above payoff table. Each participant will choose their number between 1 and 7 using the text box on the screen and clicking the OK button. When you make your decision you will not know who is in your group, or the actions they take. All actions are confidential.

After each Round you will be informed of the action you chose in that round, the smallest number chosen by your group in that round, your payoff for this round, and your accumulated payoff through the current round. You will be shown the history of your decisions and the history of decisions of your entire group in each round.

Payoff Quiz (for the Loss Table)

Before we begin, please answer the following questions. We will go through the answers to a sample problem first, and then you will finish the quiz on your own. Each question only deals with calculating your payoff in a single round.

Sample Question: Suppose you choose the action 3. The other members of your group choose 2, 5, and 7 respectively.

What is the minimum action chosen by your group? (2)

What is your payoff? (-0.80)

1. Suppose you choose the action 7. The other members of your group choose 4, 5, and 6.

What is the minimum action chosen by your group? (4)

What is your payoff? (-0.80)

2. Suppose you choose the action 1. The other members of your group choose 7, 6, and 2.

What is the minimum action chosen by your group? (1)

What is your payoff? (-0.80)

Remember that you are grouped with the same individuals throughout the 20 Rounds of this experiment. All actions and payoffs are confidential.