Simultaneous decision-making in competitive and cooperative environments.

Savikhin, Anya C. ; Sheremeta, Roman M.

I. INTRODUCTION

Individuals, firms, and policy makers simultaneously interact in many different environments in practice. In the workplace, workers may engage in sub-optimal behavior such as exerting effort to undermine co-workers to get a promotion, while they may also put forth effort on cooperative team projects assigned by the manager. Farm owners may compete daily with each other in the market for their products and at the same time they may cooperate to build facilities that would be mutually beneficial to reduce waste management costs.

The contribution of the current study is that we experimentally investigate individual behavior when competitive and cooperative environments are present simultaneously. To induce a cooperative environment, we employ a voluntary contribution mechanism (a public good game) and for a competitive environment we employ a lottery contest. In the voluntary contribution mechanism (VCM), individuals make contributions in order to provide a public good. In the contest, individuals make bids in order to win a prize. The type of contest we consider here is one in which higher bids lead to more socially wasteful outcomes. The main difference between these two games is that bids in the contest exert a negative externality on others, while contributions in the VCM exert a positive externality. The findings from the literature when these games are played in isolation are clear. In contests, individuals overbid relative to Nash equilibrium (Millner and Pratt 1989, 1991; Morgan, Orzen, and Sefton 2012; Sheremeta 2011). (1) In VCMs, individuals contribute halfway between the equilibrium free riding and the Pareto optimal level, with contributions declining over time (Fischbacher, Gachter, and Fehr 2001; Ledyard 1995). (2) The contest is similar to a wide variety of situations in practice, such as patent races, political contests, competitions for promotions in the workplace, or advertising campaigns. The VCM is similar to another broad class of situations, including the decision to volunteer for various groups or associations and monetary contributions to public goods or charities. The design of the experiment permits us to analyze the correlation between each individual's bid in the contest and contribution in the VCM.

The standard assumption in game theory is game independence, suggesting that the institutional context in which a decision is made does not matter. However, a number of experiments find that context may matter greatly. Learning and knowledge transfer is found to occur in games played in sequence (Ahn et al. 2001; Brandts and Cooper 2007; Cooper and Kagel 2008; Devetag 2005; Kagel 1995; Knez and Camerer 2000; Schotter 1998; Van Huyck, Battalio, and Beil 1991). A "behavioral spillover" is said to have occurred whenever observed behavior differs when a game is played together with other games, compared to behavior observed when the game is played in isolation (Cason, Savikhin, and Sheremeta 2012). Recent experiments directly measure behavioral spillovers, and find that spillovers occur when games are played simultaneously, causing behaviors exhibited in one game to be carried over to the other game in a predictable way (Bednar et al. 2012; Cason, Savikhin, and Sheremeta 2012; Falk, Fischbacher, and Gachter 2012; Huck, Jehiel, and Rutter 2011). Bednar et al. (2012) report a laboratory experiment with different two-player games and find that simultaneous game-play differs from isolated controls. Huck, Jehiel, and Rutter (2011) study two dissimilar two-player games played simultaneously and find that learning spillovers occur when feedback is not readily available for each game. Cason, Savikhin, and Sheremeta (2012) report a laboratory experiment where the same group of five players participate in two different coordination games and find that cooperative behavior spills over from one game to the other when games are played sequentially. Finally, Falk, Fischbacher, and Gachter (2012) investigate groups of different individuals playing two identical coordination games or two identical public goods games, and find that behavior does not differ from a baseline where only one game is played at a time. (3) The main difference of our study is that we investigate behavior in both competitive and cooperative environments, while previous studies consider coordination and public good games (Cason, Savikhin, and Sheremeta 2012; Falk, Fischbacher, and Gachter 2012) or bimatrix games such as the prisoner's dilemma (Bednar et al. 2012).

We find that overbidding in the contest is significantly reduced when individuals simultaneously participate in the VCM. This is a favorable outcome because higher bids in this type of contest lead to sub-optimal results (i.e., lower payoffs). However, we do not find significant differences in VCM contributions between the simultaneous-play and baseline treatments. The direction of behavioral spillover can be explained by differences in strategic uncertainty and path-dependence across the two games. The design of our experiment also allows us to comment on the correlation in competitiveness and cooperativeness of individuals. In early periods of the experiment, we find a negative correlation between decisions made in the lottery contest and in the VCM, suggesting that individuals who are more competitive tend to be less cooperative and vice versa. As discussed in the conclusion, this research has implications for political and management institutional design, and for related research that attempts to solve problems of overbidding in contests and under-contribution in public goods.

II. EXPERIMENTAL ENVIRONMENT, DESIGN, AND PROCEDURES

A. The Contest and the VCM

The experimental design employs two laboratory games, a lottery contest and a VCM. The lottery contest is based on the theoretical model of Tullock (1980). In this contest, n identical risk-neutral players with initial endowment levels e compete for a prize v by submitting bids. The probability that a player i wins the prize is equal to player i's own bid [b.sub.i] divided by the sum of all players' bids. Given this, the expected payoff from the contest for player i can be written as:

(1) [[pi].sup.C.sub.i] = e - [b.sub.i] + [upsilon][b.sub.i] / [summation over (j)][b.sub.j].

Differentiating Equation (1) with respect to [b.sub.i] and accounting for the symmetric Nash equilibrium leads to the classic solution of [b.sup.*] = [upsilon](n - 1)/[n.sup.2], while the Pareto optimal level of bids is [b.sup.PO] = 0.

The VCM is based on a linear public goods game where n identical risk-neutral players choose a portion of their endowments e to contribute to a public good (Groves and Ledyard 1977). Player i's contribution [c.sub.i] to the public good is multiplied by m and given to each of n players in the group, where 0 < m < 1 and m x n > 1. Thus, the payoff from the VCM for player i can be written as:

(2) [[pi].sup.VCM.sub.i] = e - [c.sub.i] + m [summation over (j)] [c.sub.j].

The Nash equilibrium in the VCM is to free ride by contributing nothing, that is [c.sup.*] = 0, while the Pareto optimal solution is to contribute one's full endowment to the public good, that is [c.sup.PO] = e.

In the VCM (2), over-contribution relative to the Nash equilibrium leads to outcomes that are closer to the Pareto optimal result. On the other hand, in the contest (1), bidding is socially wasteful and the most socially desirable outcome is for all participants to bid 0. While playing the games in ensemble does not change the standard Nash equilibrium prediction in either game, Section III provides conjectures about the direction of probable spillover when games are played in ensemble.

B. Experimental Procedures

The experiment was conducted at the Vernon Smith Experimental Economics Laboratory. Subjects were recruited from a pool of undergraduate students at Purdue University. A total of 120 subjects participated in six sessions, with 20 subjects participating in each session. All subjects participated in only one session of this study. Some students had participated in other economics experiments that were unrelated to this research.

The computerized experimental sessions used z-Tree (Fischbacher 2007) to record subject decisions and also (in the Simultaneous treatment) to record the order of decisions. We conducted three treatments as summarized in Table 1: a Baseline Contest treatment, a Baseline VCM treatment, and a Simultaneous treatment in which these two games were played simultaneously. (4) Subjects were given the instructions (available in Supporting Information) at the beginning of the session and the experimenter read the instructions aloud. In each session, 20 subjects were randomly assigned to groups of n = 4 players and stayed in the same group throughout the entire experiment, playing each game for a total of 20 periods.

At the beginning of each period, each subject received an endowment of 80 francs in the contest (or VCM) and was asked to enter his or her bid (or contribution in the VCM). In the lottery contest, subjects competed with each other for the prize value of [upsilon] = 80 francs. In the VCM, each subject chose a portion of the 80-franc endowment to contribute to the public good, and kept the other portion for him/herself. Each player's contribution to the public good was multiplied by m = 0.4 and the total of all contributions given to each of the four players in the group. We selected parameters that result in theoretically expected payoffs that are close in both games (85 and 80). Subjects did not know others' decisions before making their own decisions. After all subjects made their decisions, the sum of all bids (or contributions in the VCM) in each group was displayed on the output screen together with the outcome, and earnings were determined.

During the Simultaneous treatment, the contest and VCM games were displayed side by side on the same screen. (5) Each subject received a separate endowment of 80 francs in the contest and a separate endowment of 80 francs in the VCM at the beginning of each period. These endowments could not be transferred between games. Subjects were required to input their choices for each of the two games before moving on to the next period. To account for any order effect within each period, in one of the two Simultaneous sessions, the contest game was displayed on the left (the VCM game was on the right), and in the other Simultaneous session, the contest game was displayed on the right (the VCM game was on the left). (6)

At the end of the experiment, two periods from the game were selected for payment using a random draw from a bingo cage. In the Simultaneous treatment, two periods from each game (contest and VCM) were selected using the same method. Experimental francs were used throughout the experiment, with a conversion rate of 25 francs = $1. Subjects earned S18 on average, and sessions (including instruction time) lasted on average 75 minutes.

III. HYPOTHESIS DEVELOPMENT

A. Behavioral Spillover

Although standard theoretical models do not predict that behavior during simultaneous interaction in two games should differ from behavior when each game is played in isolation, related work has found that behavioral spillovers do occur (Bednar et al. 2012; Cason, Savikhin, and Sheremeta 2012; Huck, Jehiel, and Rutter 2011). (7) Our study is intended to contribute additional evidence to inform the discussion of what behavioral effects may impact individual decisions when two disparate environments are experienced simultaneously. We provide two conjectures that predict the direction of behavioral spillovers in this context based on strategic uncertainty and path-dependence.

B. Strategic Uncertainty

Related work suggests that we can predict which game will, and which game will not, be affected by simultaneous play in another game by observing the characteristics of the games and behavior when each game is played in isolation (Bednar et al. 2012; Cason, Savikhin, and Sheremeta 2012). One dimension on which two games may be compared is strategic uncertainty. Games with higher strategic uncertainty are more demanding on subjects' belief formation and therefore may produce greater cognitive load relative to games with lower strategic uncertainty. When playing ensembles of games, subjects may apply common analogies to disparate situations if the cognitive cost of developing a separate strategy for each game is too high (Samuelson 2001). Related work has conjectured that games with lower strategic uncertainty have a stronger behavioral spillover effect onto games with higher strategic uncertainty (Bednar et al. 2012; Cason, Savikhin, and Sheremeta 2012). One reason cited for this effect is that learning a strategy requires less effort or cognitive load in a game with lower strategic uncertainty relative to a game with higher strategic uncertainty (Cason, Savikhin, and Sheremeta 2012).

Relevant measures for assessment of strategic uncertainty are the ex ante measure of complexity of the game and the ex post measure of volatility of behavior in the game. Using the measure of complexity, we posit that strategic uncertainty is greater in the contest than in the VCM. In the VCM, each subject forms beliefs about others' contributions and determines her probable outcome. In the contest, on the other hand, each subject must first form beliefs about others' bids and then form a belief about the probability that she will win, where this probability depends on her bid but also depends on other group members' bids. (8) While the equilibrium of the VCM is in dominant strategies, the equilibrium of the contest is not. Moreover, the payoff function is flatter (and concave) in the contest as compared to the VCM.

Bednar et al. (2012) and Cason, Savikhin, and Sheremeta (2012) also use a measurement of volatility of choices called "entropy" to describe the degree of strategic uncertainty. Similarly, we will be able to confirm the difference in strategic uncertainty between games ex post, measuring the degree of volatility in individual decision-making. Based on previous research, and the fact that the contest is a more complex game than the VCM, we expect subjects to apply strategies from the VCM to choices in the contest, causing behavioral spillover onto the contest.

Conjecture 1: Behavioral spillover caused by differences in strategic uncertainty will prompt subjects to apply strategies from the VCM to choices in the contest.

C. Path-Dependence

Path-dependence is the extent to which the outcomes of previous periods matter for the current period (Page 2006). For the purpose of this analysis, we define path-dependence as a within-game phenomenon where only past behavior and experience in the same game affect future behavior. Van Huyck, Battalio, and Beil (1990) use path-dependence to explain how decisions in future periods are influenced by subjects' shared experience within the same coordination game. Many games are path-dependent in the sense that current choices depend to some extent on previous choices of group members, but some games may be more path-dependent than others. Path-dependence is generally determined after data on behavior is obtained, yet the structure of the game can also inform the level of path-dependence ex ante.

We argue that the VCM is more path-dependent than the contest for several reasons. First, feedback in the VCM is less noisy (there is no probability involved), and individuals can react optimally to previous group members' choices without repeated exogenous shocks (e.g., winning the prize or not, as in the contest). Second, because the VCM does not involve a risk component (except strategic risk), individuals can more easily calculate their subjective best responses. While the VCM has a dominant strategy and conditioning one's behavior on the behavior of others is not required, the literature does document the existence of conditional cooperators, whose behavior depends heavily on behavior of group members (Fischbacher, Gachter, and Fehr 2001).

In addition to evaluating the structure of the game, evidence of path-dependent behavior can be obtained ex post through comparing individual behavior in period t with group behavior in period t - 1 (Falk, Fischbacher, and Gachter 2012). More path-dependent games should be less susceptible to influence from other games, because individuals rely heavily on actions of others in previous rounds of the same game while making decisions. On the other hand, less path-dependent games should be more susceptible to influence from other games, because individuals are less influenced by actions of others in the same game.

Conjecture 2: The contest, which is less path-dependent, is more likely to be susceptible to behavioral spillover as compared to the VCM, which is more path-dependent.

IV. RESULTS AND DISCUSSION

A. Overview

Table 2 reports the average contribution in the VCM and the average bid in the contest across all treatments. In contrast to the theoretical prediction of [b.sup.*] = 15, we find significant overbidding of about 120% in the Baseline Contest treatment (Wilcoxon signed-rank test, p < .05, n = 10). (9) This finding is consistent with previous experimental literature on contests, which document that on average subjects overbid relative to the theoretical predictions in the range from 20% to 200% (Morgan, Orzen, and Sefton 2012; Sheremeta 2011). (10) As a result of overbidding, subjects' payoffs are significantly lower than predicted.

The unique equilibrium prediction for contributions in the VCM is [c.sup.*] = 0. Relative to theoretical predictions, we find significant over-contribution in the VCM in the Baseline VCM treatment, which leads to more socially favorable outcomes (Wilcoxon signed-rank test, p < .05, n = 10). This finding is also consistent with previous experimental studies, which report that over-contribution is common in public goods environments due to altruism or social norms (Ledyard 1995). For example, Fehr and Gaechter (2000) report contribution levels at 40%-60% of the endowment during the experiment, with contributions falling to 27% in the final period.

RESULT 1. There is significant overbidding in the contest and significant over-contribution in the VCM relative to theoretical predictions.

Owing to learning and interaction between group members, behavior may change during the course of the 20 periods. Throughout this section, we examine decisions in all periods of the experiment as well as average bids and contributions in "early" and "later" periods. We use the average bid (contribution) in the first five and last five periods of the contest (VCM) when making comparisons between early and later periods; nevertheless choosing different subsets of early and later periods gives us very similar results.

Figure 1 displays the distribution of bids in the contest over the first and the last five periods of the experiment. Contrary to the unique pure strategy Nash equilibrium of 15, individual bids are distributed on the entire strategy space in all treatments. This variance in bids persists throughout all periods of the experiment. The high variance in individual bids is consistent with previous experimental findings on contests (Davis and Reilly 1998; Potters, De Vries, and Van Linden 1998; Sheremeta 2011).

Figure 2 displays the distribution of contributions in the VCM over the first and the last five periods of the experiment. In the first five periods of the experiment, individual contributions in the VCM are also distributed on the entire strategy space. However, in the last five periods of the experiment, individual contributions in the VCM are concentrated around the Nash equilibrium of 0. These observations are also consistent with previous experimental findings on VCMs (Fehr and Gaechter 2000; Fischbacher, Gachter, and Fehr 2001).

[FIGURE 1 OMITTED]

B. Comparison Between Simultaneous and Baseline Treatments

Figure 3 displays the time series of the average contribution and the average bid for the Baseline and Simultaneous treatments. In the Baseline VCM treatment, the average contribution in the VCM starts at 36.7 in the first five periods and decreases significantly to 12.6 in the last five periods (Wilcoxon signed-rank test, p < .05, n = 10). (11) Similarly, in the Simultaneous treatment, the average contribution starts at 35.6 in the first five periods and decreases significantly to 11.5 in the last five periods (Wilcoxon signed-rank test, p < .05, n = 10). The difference between the average contribution to the VCM in the Baseline and the Simultaneous treatment is not significant (Wilcoxon rank-sum test, p = .54, n = m = 10). This difference is also not significant for either the first five (Wilcoxon rank-sum test, p = .65, n = m = 10) or last five periods of the experiment (Wilcoxon rank-sum test, p = .76, n = m = 10).

[FIGURE 2 OMITTED]

RESULT 2. Simultaneous participation in both the VCM and the contest does not have a significant effect on contributions in the VCM.

Falk, Fischbacher, and Gachter (2012) use a design in which subjects play two public goods games simultaneously. They find that individuals are influenced in each game by the contributions of their own group members, but not by the contributions of the other group members. We find that even when playing two different games and with the same subjects, bids in the contest do not influence contributions to the public good. (12) Note that due in part to power limitations, we cannot say with certainty that the behavioral spillover from the contest to the VCM does not exist. (13) However, as we show next, even with the same power, we do find a significant spillover from the VCM to the contest, indicating that spillover effects exist.

In the Baseline Contest treatment, the average bid starts at 36.5 in the first five periods and decreases significantly to 33.7 in the last five periods (Wilcoxon signed-rank test, p = .06, n = 10). In the Simultaneous treatment, the average bid in the contest starts at 31.5 in the first five periods and decreases significantly to 24.4 in the last five periods (Wilcoxon signed-rank test, p < .05, n = 10). Overall, the declining bid trend in both treatments is consistent with previous research, documenting that overbidding decreases over time (Davis and Reilly 1998; Sheremeta 2011).

Figure 4 displays, by group, the average dissipation rate in the contest, defined as the sum of all bids divided by the value of the prize. Groups in the Baseline Contest treatment have greater dissipation rates than groups in the Simultaneous treatment. The difference between treatments appears mainly after subjects obtain some experience in playing the game(s). In the first five periods, the average bid in the Baseline treatment is higher, but it is not significantly different from the average bid in the Simultaneous treatment (Wilcoxon rank-sum test, p = .20, n = m = 10). However, the average bid in Baseline is significantly higher than the average bid in the Simultaneous treatment in the last five periods (Wilcoxon rank-sum test, p < .05, n = m = 10). This finding suggests that simultaneous participation in both the VCM and the contest reduces overbidding in the contest, although this behavioral spillover becomes more pronounced in later periods of the experiment. When averaging bids across all periods, we still find that bids are significantly higher in the Baseline treatment as compared to the Simultaneous treatment (Wilcoxon rank-sum test, p = .06, n = m = 10).

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

RESULT 3. Simultaneous participation in both the VCM and the contest reduces overbidding in the contest.

We can conclude from Results 2 and 3 that bid choices in the contest are influenced by contribution choices in the VCM, but that contribution choices in the VCM are not as affected by bid choices in the contest. These findings provide initial support for ex ante Conjectures 1 and 2, suggesting that strategic uncertainty and path-dependence are two of the driving forces of behavioral spillovers.

C. Behavioral Effects

As discussed in Section III, strategic uncertainty and path-dependence are two aspects of games that predict direction of behavioral spillover ex ante. The design of our experiment also allows us to provide an ex post analysis of strategic uncertainty and path-dependence in both the VCM and contest. Conjecture 1 predicts that behavioral spillover caused by differences in strategic uncertainty will prompt subjects to apply strategies from the VCM onto choices in the contest. Previous studies use a measure of entropy to evaluate the degree of volatility in individual decision-making and to determine the ex post amount of strategic uncertainty present in the game (Bednar et al. 2012; Cason, Savikhin, and Sheremeta 2012). However, in both studies of Bednar et al. (2012) and Cason, Savikhin, and Sheremeta (2012), the strategy space is very restricted (from 2 to 7 choices), and thus it is straightforward to measure the degree to which subjects arrive at a stable state (i.e., entropy state). In contrast, in our experiment, each of the four subjects in a group can choose any integer number between 0 and 80. Therefore, we use two alternative measures of the degree of volatility in individual decision-making. First, we compute the absolute difference between the decisions made in period t and period t - 1. Second, we calculate the number of stable states for each subject. We define a stable state as whenever a subject makes the same bid or contribution choice in period t as in period t - 1. We calculate both measures of volatility using the first five periods of game-play, as we want to observe the level of volatility before subjects become experienced. Based on both measures, we find that in the first five periods of the Simultaneous treatment, the average volatility of bids in the contest is significantly higher than the average volatility of contributions in the VCM. (14) These results suggest that in the Simultaneous treatment, the VCM game should have a stronger behavioral spillover effect onto the contest, which is predicted by Conjecture 1 and is in line with Results 2 and 3.

The prediction of Conjecture 2 is that the contest is less path-dependent than the VCM, and thus it is more likely to be susceptible to behavioral spillover from the VCM. To examine path-dependence, in Table 3 we report estimates of panel regressions conducted separately for each treatment. In these regressions, the dependent variable is either subject's bid in the contest (Regressions 1 and 3) or contribution in the VCM (Regressions 2 and 4). The independent variables are bid-lag, group-bid-lag (lagged average bid of other group members), contribution-lag, and group-contribution-lag (lagged average contribution of other group members). All regressions use a random effects error structure for the individual subjects to account for repeated measures, and a period trend to account for learning. Standard errors are clustered at the group level.

According to the estimation results in regression (1), the main determinant of bid in the Baseline Contest treatment is bid-lag, indicating that the individual subject's own previous bid influences her behavior in the contest. On the other hand, regression (2) shows that contribution in the Baseline VCM treatment is influenced by contribution-lag and group-contribution-lag, indicating that both individual subject's own previous bid, as well as group members' decisions, influence behavior in the VCM. These results provide additional support for our prediction that the VCM is more path-dependent (i.e., dependent on own and group previous behavior) than the contest.

Most importantly, by estimating regressions (3) and (4), we find that in the Simultaneous treatment, bid is not correlated with group-bid-lag, while contribution is significantly correlated with group-contribution-lag. Therefore, our ex post estimation results indicate that the VCM is more path-dependent than the contest. In line with Conjecture 2, the stronger path-dependence in the VCM causes the behavioral spillover from the VCM onto the contest.

Estimation results in Table 3 also indicate that contribution-lag negatively affects bid in the contest (regression 3) and bid-lag negatively affects contribution in the VCM (regression 4), although the latter finding is not statistically significant. (15) These results suggest that bids and contributions are negatively correlated. We further explore this correlation in the following subsection.

D. Correlation of Bids and Contributions

Because of the within-subjects design of the Simultaneous treatment, we can directly compare bids in the contest with contributions in the VCM for the same individual. Figure 5 displays individual contributions and bids for the Simultaneous treatment, averaged over Periods 1-5 and Periods 16-20. We use average choices in Periods 1-5 of the game in this analysis for several reasons. First, we want to observe behavior while subjects are not yet heavily influenced by interaction with group members. Second, we also want to allow for some learning of the payoff structure of the game. An average of choices in Periods 1-5 provides a compromise between these two considerations. We also compare our results for earlier Periods 1-5 to later Periods 16-20, when subjects have been maximally influenced by behavior of their group members in both games.

A Spearman's rank correlation test shows that individuals who contribute more to the VCM also bid less in the contest in the first five periods of the game, and this correlation is significant at the 10% level when bids are aggregated at the individual level across the five rounds (correlation -0.27, p < .10). The negative correlation between individual contributions and bids disappears over time. When analyzing the last five periods of the experiment, we do not find a significant correlation (correlation 0.13, p = .43). This result is not surprising, given that by the end of the experiment, subjects' decisions have already been heavily influenced by the decisions of others and therefore social preferences play a less important role in the later periods.

RESULT 4. Bids in the contest are negatively correlated with contributions to the VCM in early periods', suggesting that inherently more competitive subjects are less cooperative and vice versa.

To explain the negative correlation between bids and contributions, we consider two competing theories that are often employed to explain individual behavior in the public goods and contest experiments. Two common explanations for non-zero contributions to public goods are based on bounded rationality or mistakes (Andreoni 1995; Anderson, Goeree, and Holt 1998) and social preferences (Fehr and Schmidt 1999; Fischbacher, Gachter, and Fehr 2001; Falk, Fehr, and Fischbacher 2005). The same arguments are also often applied to explain behavior in contests (Herrmann and Orzen 2008; Mago, Savikhin, and Sheremeta 2012; Sheremeta 2011). The design of our Simultaneous treatment enables us to distinguish between these two competing theories, because they generate opposing predictions for the direction of correlation between bids and contributions.

Bounded rationality and mistakes are often cited as reasons why behavior is not in line with theory in many settings. Using a quantal response equilibrium (QRE) model, which accounts for errors made by individual subjects, Anderson, Goeree, and Holt (1998) show that depending on the magnitude of the decision error, mean contributions to the VCM lie between the Nash prediction ([c.sup.*] = 0) and half the endowment (c = 40), and higher decision errors correspond to higher contributions. Sheremeta (2011) shows that according to QRE, mean bids in the contest lie between the Nash equilibrium ([b.sup.*] = 15) and half the endowment (b = 40), and higher decision errors correspond to higher bids. Therefore, bounded rationality implies that subjects who make mistakes both contribute and bid more, which should result in a positive, rather than a negative, correlation between bids and contributions.

[FIGURE 5 OMITTED]

Social preferences are among other commonly cited reasons why subjects' behavior deviates from theoretical benchmarks. Intuitively, pro-social behavior implies higher contributions (Andreoni 1995; Fischbacher, Gachter, and Fehr 2001), while spite implies lower contributions to the VCM (Falk, Fehr, and Fischbacher 2005). On the other hand, prosociality implies lower bids and spite implies higher bids in the contest (Hehenkamp, Leininger, and Possajennikov 2004; Mago, Savikhin, and Sheremeta 2012). The main reason why social preferences work in the opposite direction in the VCM and the contest is that in the VCM individual contributions exert a positive externality on others, while in the contest individual bids exert a negative externality. (16)

We conclude, therefore, that the negative correlation between bids and contributions can be explained by social preferences but not by bounded rationality. This finding is also in line with related work on social preferences and sorting into competitive environments (Bartling et al. 2009; Dohmen and Falk 2011; Teyssier 2009). In contrast to previous studies, however, we did not explicitly elicit social preferences, but instead we measured cooperative individual behavior in the VCM and compared it to competitive individual behavior in the contest.

V. CONCLUSION

We study simultaneous decision-making in two contrasting environments: an environment that encourages competition (a lottery contest) and an environment that encourages cooperation (a public good game). We find that simultaneous participation in the public good game affects behavior in the contest, decreasing sub-optimal overbidding in the contest. However, contributions to the public good are not affected by simultaneous participation in the contest. The direction of behavioral spillover can be explained by differences in strategic uncertainty and path-dependence across the two games. Our design also allows us to simultaneously compare individual preferences for cooperation and competition. We find that in early periods of the experiment, there is a significant negative correlation between decisions made in competitive and cooperative environments, which can be justified by social preferences such as altruism or spite but not by bounded rationality theory.

Our findings provide clear evidence that the institutional context matters for some decision-making environments. Given that many activities in practice involve simultaneous decision-making in environments similar to contests and public goods, it is important to continue to study these competitive and cooperative environments in ensemble. Studies of other alternative environments in which there is competition (such as first and second price auctions, oligopolistic competition, and rank-order tournaments) and cooperation (such as trust games, weakest-link public goods, and common pool resources) are of great interest. Investigating behavioral spillover in different environments will allow for the development of a unifying theory of behavioral spillover. Finally, it is important to investigate how behavioral spillovers can be used to design more efficient economic systems. We leave these extensions for future research.

SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

APPENDIX S1: Instructions for the Simultaneous Treatment.

doi: 10.1111/j.1465-7295.2012.00474.x

ABBREVIATIONS

QRE: Quantal Response Equilibrium

VCM: Voluntary Contribution Mechanism

REFERENCES

Ahn, T.K., E. Ostrom, D. Schmidt, R. Shupp, and J. Walker. "Cooperation in PD Games: Fear, Greed. and History of Play." Public Choice, 106(1), 2001, 137-55.

Anderson, S. P., J. K. Goeree, and C. A. Holt. "A Theoretical Analysis of Altruism and Decision Error in Public Goods Games." Journal of Public Economics, 70, 1998, 297-323.

Andreoni, J. "Cooperation in Public Goods Experiments: Kindness or Confusion." American Economic Review, 85, 1995, 891-904.

Battling, B., E. Fehr, M. A. MarEchal, and D. Schunk. "Egalitarianism and Competitiveness." American Economic Review, 99(2), 2009, 93-98.

Bednar, J., Y. Chen, T. X. Liu, and S. Page. "Behavioral Spillovers and Cognitive Load in Multiple Games: An Experimental Study." Games and Economic Behavior, 74(1), 2012, 12-31.

Bernasconi, M., L. Corazzini, S. Kube, and M. Marechal. "Two Are Better Than One! Individuals' Contributions to "Unpacked" Public Goods." Economic Letters, 104, 2009, 31-33.

Biele, G., J. Rieskamp, and U. Czienskowski. "Explaining Cooperation in Groups: Testing Models of Reciprocity and Learning." Organizational Behavior and Human Decision Processes, 106, 2008, 89-105.

Blanco, M., D. Engelmann. and H. T. Normann. "A Within-Subject Analysis of Other-Regarding Preferences." Games and Economic Behavior, 72, 2011, 321-38.

Brandts, J., and D. J. Cooper. "It's What You Say, Not What You Pay: An Experimental Study of Manager-Employee Relationships in Overcoming Coordination Failure." Journal of the European Economic Association, 5, 2007, 1223-68.

Camerer, C. F. Behavioral Game Theory: Experiments on Strategic Interaction. Princeton, NJ: Princeton University Press, 2003.

Cason, T., A. Savikhin, and R. Sheremeta. "Behavioral Spillovers in Coordination Games." European Economic Review, 56, 2012, 233-45.

Cherry, T. L., and J. F. Shogren. "Rationality Crossovers." Journal of Economic Psychology, 28(2), 2007, 261-77.

Cherry, T. L., and D. L. Dickinson. "Voluntary Contributions with Multiple Public Goods," in Environmental Economics, Experimental Methods, edited by T. L. Cherry, S. Kroll, and J. F. Shogren. New York: Routledge, 2008, 184-93.

Cherry, T. L., T. D. Crocker, and J. F. Shogren. "Rationality Spillovers." Journal of Environmental Economics and Management, 45(1), 2003, 63-84.

Cooper, D. J., and J. H. Kagel. "Learning and Transfer in Signaling Games." Economic Theory, 34(3), 2008, 415-39.

Davis, D., and R. Reilly. "Do Many Cooks Always Spoil the Stew? An Experimental Analysis of Rent Seeking and the Role of a Strategic Buyer." Public Choice, 95, 1998, 89-115.

Devetag, G. "Precedent Transfer in Coordination Games: An Experiment." Economics Letters, 89(2), 2005, 227-32.

Dickinson, D. L., and R. J. Oxoby. "Cognitive Dissonance, Pessimism, and Behavioral Spillover Effects." Journal of Economic Psychology, 32(3), 2011, 295-306.

Dohmen, T., & A. Falk. "Performance Pay and Multidimensional Sorting--Productivity, Preferences and Gender." American Economic Review, 101, 2011, 556-90.

Falk, A., E. Fehr, and U. Fischbacher. "Driving Forces Behind Informal Sanctions." Econometrica, 73(6), 2005, 2017-30.

Falk, A., U. Fischbacher, and S. Gachter. Forthcoming. "Living in Two Neighborhoods--Social Interaction Effects in the Lab." Economic Inquiry, 2012. DOI: 10.1111/j.1465-7295.2010.00332.x.

Febr, E., and S. Gaechter. "Cooperation and Punishment in Public Goods Experiments." American Economic Review, 90, 2000, 980-94.

Fehr, E., & K. Schmidt. "A Theory of Fairness, Competition, and Cooperation." Quarterly Journal of Economics, 114, 1999, 817-68.

Fellner, G., and G. Lunser. "Cooperation in Local and Global Groups." Vienna University of Economics, Working Paper No. 122, 2008.

Fischbacher, U. "Z-tree: Zurich Toolbox for Ready-Made Economic Experiments." Experimental Economics, 10, 2007, 171-78.

Fischbacher, U., S. Gachter, and E. Fehr. "Are People Conditionally Cooperative? Evidence from a Public Goods Experiment." Economics Letters, 71, 2001, 397-404.

Groves, T., and J. Ledyard. "Optimal Allocation of Public Goods: A Solution to the Free Rider Problem." Eeonometrica, 45, 1977, 783-809.

Grund, C., & D. Sliwka. "Envy and Compassion in Tournaments." Journal of Economics and Management Strategy, 14, 2005, 187-207.

Hehenkamp, B., W. Leininger, and A. Possajennikov. "Evolutionary Equilibrium in Tullock Contests: Spite and Overdissipation." European Journal of Political Economy, 20(4), 2004, 1045-57.

Herrmann, B., and H. Orzen. "The Appearance of Homo Rivalis: Social Preferences and the Nature of Rent Seeking." University of Nottingham, Working Paper, 2008.

Huck, S., P. Jehiel, and T. Rutter. "Feedback Spillover and Analogy-Based Expectations: A Multi-Game Experiment." Games and Economic Behavior, 71(2), 2011, 351-65.

Kagel, J. H. "Cross-Game Learning: Experimental Evidence from First-Price and English Common Value Auctions." Economics Letters, 49(2), 1995, 163-70.

Knez, M., and C. Camerer. "Increasing Cooperation in Prisoner's Dilemmas by Establishing a Precedent of Efficiency in Coordination Games." Organizational Behavior and Human Decision Processes, 82(2), 2000, 194-216.

Ledyard, J. "Public Goods: A Survey of Experimental Research," in Handbook of Experimental Economics, edited by J. Kagel, and A. E. Roth. Princeton, NJ: Princeton University Press, 1995.

Mago, S. D., A. C. Savikhin, and R. M. Sheremeta. "Facing Your Opponents: Social Identification and Information Feedback in Contests." Chapman University, Working Paper, 2012.

Millner, E. L., and M. D. Pratt. "An Experimental Investigation of Efficient Rent-Seeking." Public Choice, 62, 1989, 139-51.

--. "Risk Aversion and Rent-Seeking: An Extension and Some Experimental Evidence." Public Choice, 69, 1991, 81-92.

Morgan, J., H. Orzen, and M. Sefton. Forthcoming. "Endogenous Entry in Contests." Economic Theory, 2012. DOI: 10.1007/s00199-010-0544-z.

Page, S. E. "Path Dependence." Quarterly Journal of Political Science, 1(1), 2006, 87-115.

Potters, J. C., C. G. De Vries, and F. Van Linden. "An Experimental Examination of Rational Rent Seeking." European Journal of Political Economy, 14, 1998, 783-800.

Samuelson, L. "Analogies, Adaptation, and Anomalies." Journal of Economic Theory, 97, 2001, 320-66.

Schotter, A. "Worker Trust, System Vulnerability, and the Performance of Work Groups," in Economics, Values and Organization, edited by A. Ben-Ner and L. G. Putterman. Cambridge: Cambridge University Press, 1998, 364-407.

Sheremeta, R. M. "Expenditures and Information Disclosure in Two-Stage Political Contests." Journal of Conflict Resolution, 54, 2010a, 771-98.

--. "Experimental Comparison of Multi-Stage and One-Stage Contests." Games and Economic Behavior, 68, 2010b, 731-47.

--. "Contest Design: An Experimental Investigation." Economic Inquiry, 49, 2011,573-90.

Sheremeta, R. M., and J. Zhang. "Can Groups Solve the Problem of Over-Bidding in Contests?" Social Choice and Welfare, 35, 2010, 175-97.

Teyssier, S. "Experimental Evidence on Inequity Aversion and Self-Selection between Incentive Contracts." Working Paper, 2009.

Tullock, G. "Efficient Rent Seeking," in Toward a Theory of the Rent-Seeking Society., edited by J. M. Buchanan, R. D. Tollison, and G. Tullock. College Station, TX: Texas A&M University Press, 1980, 97-112.

Van Huyck, J. B., R.C. Battalio, and R. O. Beil. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure." American Economic Review, 80(1), 1990, 234-48.

--. "Strategic Uncertainty, Equilibrium Selection, and Coordination Failure in Average Opinion Games." Quarterly Journal of Economics, 106, 1991, 885-910.

ANYA C. SAVIKHIN and ROMAN M. SHEREMETA *

* We thank two anonymous referees and an Advisory Editor for valuable suggestions, as well as Jack Barron, Tim Cason, David Dickinson, Justin Krieg, Casey Rowe, seminar participants at Purdue University, University of California, Irvine, and participants at the 2009 Economic Science Association conference for helpful comments. Any remaining errors are ours.

Savikhin: Department of Consumer Science, School of Human Ecology, University of Wisconsin-Madison, 1305 Linden Drive, Madison, W1 53706. Phone 765-409-0425, Fax 714-532-6081, E-mail anya@purdue.edu

Sheremeta: Argyros School of Business and Economics, Chapman University, One University Drive, Orange, CA 92866. Phone 765-418-7175, Fax 714-532-6081, E-mail sheremet@chapman.edu

(1.) Overbidding decreases when subjects gain experience (Davis and Reilly 1998; Sheremeta 2011), when groups make bids instead of individuals (Sheremeta and Zhang 2010), and when individual bidding space is constrained (Sheremeta 2011).

(2.) Contributions increase when subjects are allowed to punish, assign disapproval points, send signals, or communicate with other subjects prior to contributions in the VCM (Fehr and Gaechter 2000; Ledyard 1995).

(3.) Other existing studies consider simultaneous interaction in several public goods environments, either breaking a single public good into multiple parts or presenting multiple public goods (Biele, Rieskamp, and Czienskowski 2008; Bernasconi et al. 2009; Cherry and Dickinson 2008; Fellner and Lunser 2008).

(4.) Note that treatments with two simultaneous contests or two simultaneous public goods are also possible as baselines. We believe that our Baseline Contest and Baseline VCM treatments are more appropriate for several reasons. First, this design allows us to see if behavior in ensemble games is different from behavior in isolated games. Second, if two simultaneous contests or two simultaneous public goods were played as the baseline, subjects would learn the game more quickly in the baselines than in the Simultaneous treatment, and we would not be able to make a direct comparison between treatments. Finally, although subjects did earn double the amount in Simultaneous as in VCM and Contest baselines, we do not expect to see an endowment effect since only two periods were randomly selected at the end for payment.

(5.) We used categorical (and not ordinal) nomenclature to label each game, the colors blue and green (instead of, for example, 1 and 2 or A and B).

(6.) When the contest game was displayed on the left, subjects made a decision in the contest game first 92% of the time. When the VCM was displayed on the left, subjects made a decision in the VCM game first 93% of the time. This is unsurprising, given that over 95% of subjects in the experiment self-reported that they read and write from left to right horizontally in their native language, and that all instructions were in English, which reads from left to right. Despite differences in order of decision-making within each period, we do not find any difference between individual behavior in the two Simultaneous sessions; therefore, we pool the sessions.

(7.) Although we consider the impact of simultaneous game-play, spillovers of behavior or expectations are also present in settings with sequential game-play, as in as in Knez and Camerer (2000), Alan et al. (2001), Cherry, Crocker, and Shogren (2003), Devetag (2005), Cherry and Shogren (2007), Herrmann and Orzen (2008), Dickinson and Oxoby (2011) and Cason, Savikhin, and Sheremeta (2012).

(8.) Understanding probability can be difficult for subjects due to bounded rationality (Camerer 2003).

(9.) Unless otherwise stated, all nonparametric tests employ four subjects in a group across all periods as one independent observation.

(10.) Sheremeta (2010a, 2010b, 2011) and Sheremeta and Zheng (2010) cite noise and errors, probability judgment biases, and a non-monetary utility of winning as explanations for overbidding.

(11.) The rank-sum test uses as one independent observation the difference between the average contribution by four subjects in a group in the first five periods and the last five periods.

(12.) Note that in the Falk, Fischbacher, and Gachter (2012) and in our study, endowments are not shared between the two games; rather, subjects receive a set endowment for each game. This result may be most applicable in this setting, but whether this result holds when endowments are shared across simultaneous games could be considered in future work.

(13.) Using an average of contributions across 20 rounds, we must assume that each group is one independent observation and therefore there are only 10 independent observations per treatment. With only 10 independent observations, we have power of 80% to detect an effect size of 1.19 standard deviations using the Wilcoxon Mann-Whitney test.

(14.) The average absolute difference of bids is 17.4 and the absolute difference of contributions is 13.6. The estimated number of stable states for each subjects indicate that 29.4% of contributions to the VCM and only 18.1% of bids in the contest are qualified as stable (i.e., state of entropy). This difference is significant (Wilcoxon rank-sum test, p < .05, n = m = 10). Note also that the volatility of bids is also higher than the volatility of contributions in the last five periods of the experiment, although the difference is not significant. The average absolute difference of bids is 14.5 and the absolute difference of contributions is 9.1. Furthermore, 42.0% of contributions to the VCM and only 36.5% of bids in the contest are qualified as stable, although again this difference is not significant.

(15.) Both coefficients are significant when using the data only from the first five periods of the experiment.

(16.) Similar to pro-sociality and spite, one can make an argument that inequity aversion can explain the negative correlation between contributions in the VCM and bids in the contest. Fehr and Schmidt (1999), for example, show that subjects who dislike disadvantageous inequity (i.e., the case when subjects dislike having the lowest relative payoff) should make lower contributions in the VCM in order to avoid the circumstance where they are the highest contributors with the lowest payoffs. Similarly, Grund and Sliwka (2005) and Herrmann and Orzen (2008) show that disadvantageous inequity aversion should cause subjects to bid more in the lottery contest in order to avoid a circumstance where they do not win a prize and thus receive the lowest payoff. Conversely to disadvantageous inequity aversion, advantageous inequality aversion (i.e., the case when subjects dislike having the highest relative payoff) should increase VCM contributions and decrease contest bids. Therefore, both disadvantageous and advantageous inequity aversion imply negative correlation between bids and contributions. It is important to emphasize that although inequality aversion is a potential explanation of our findings, in a recent study, Blanco, Engelmann, and Normann (2011) showed that there is a low correlation of subjects' inequality aversion between different games.

TABLE 1
Summary of Treatments

 Number of
 Number of Number of Independent
Treatment Game Played Sessions Subjects Observations

Baseline contest Contest 2 40 10
Baseline VCM VCM 2 40 10
Simultaneous Contest & VCM 2 40 10

TABLE 2
Average Statistics

Game Played Variable Equilibrium Simultaneous Baseline
 Prediction Treatment Treatments

Contest Bid 15 26.8 (0.8) 33.5 (0.8)
 Payoff 85 73.2 (1.2) 66.5 (1.2)
VCM Contribution 0 22.4 (0.9) 23.9 (l.0)
 Payoff 80 93.4 (0.7) 94.3 (0.8)

Notes: Standard error of the mean in parentheses.

TABLE 3
Regression Models of Individual Subject Choices

Treatment Baseline

 (1) (2)
Regression Contest VCM
Subject's Choice bid contribution

bid-lag 0.535 ***
 (0.105)
group-bid-lag -0.123
 (0.099)
contribution-lag 0.562 ***
 (0.063)
group-contribution-lag 0.159 *
 (0.068)
period -0.097 -0.518 **
 (0.051) (0.187)
constant 20.869 *** 11.303 **
 (5.747) (4.154)
Observations 760 760
Number of subjects 40 40

Treatment Simultaneous

 (3) (4)
Regression Contest VCM
Subject's Choice bid contribution

bid-lag 0.406 *** -0.055
 (0.059) (0.034)
group-bid-lag -0.054 -0.059
 (0.065) (0.052)
contribution-lag -0.068 * 0.456 ***
 (0.033) (0.042)
group-contribution-lag -0.063 0.348 ***
 (0.063) (0.029)
period -0.575 *** -0.432 ***
 (0.128) (0.126)
constant 26.577 *** 10.967 **
 (3.981) (3.565)
Observations 760 760
Number of subjects 40 40

Notes: All regressions use a random effects error structure for the
individual subjects to account for repeated measures, and a period
trend to account for learning. Standard errors are clustered at the
group level. group bid-lag and group contribution-lag only include
the bids and contributions of all other group members, excluding the
individual under study.

* p < .10, ** p < .05, *** p < .01.