Nash Prediction Research Articles

Varying the intensity of competition in a multiple prize rent seeking experiment

We experimentally test a rent seeking model under five levels of competition. At one extreme, a subject’s probability of winning a prize is equal to her share of the total expenditures. At lower levels of competition, a subject’s probability of winning is affected more by her own expenditures than by the expenditures of others. Predicted expenditure levels are positively associated with higher levels of competition. Consistent with previous rent seeking experiments, we find that subjects spend significantly more than the Nash equilibrium prediction at all levels of competition. However, expenditure patterns generally follow the Nash prediction; expenditures decrease as the level of competition decreases. Our experimental design also includes a lottery choice experiment to control for subjects’ risk preference. We find that subjects who are more risk averse spend significantly less in the contest and this effect is particularly strong for female subjects.

Asymmetric Behavioral Effects of Informal Sanction and Reward on Cooperation in an Experimental Public Good Game

This study reports data from a laboratory experiment that investigates the effects of nonmonetary sanctions and rewards on cooperation in a standard public good game. We use performance based disapproval and approval ratings for nonmonetary sanction and reward, respectively. The treatments vary in terms of subjects' opportunities to assign (1) only the approval ratings to other group members, (2) only the disapproval ratings to other group members, and (3) either the approval or the disapproval ratings (but not both) to other group members, after they play a public good game. Since these ratings are costless, payoff irrelevant, and are assigned anonymously, the Nash prediction for all the games is still the zero individual contribution. The results show, however, that the contributions are significantly higher in all the treatments relative to the baseline treatment where no such rating exists. However, the approval ratings generate significantly lower contributions than that of the disapproval ratings. The treatment in which subjects could assign either the approval or the disapproval ratings produces the highest level of contributions. We conclude that the induced approval and disapproval ratings have asymmetric behavioral effects on cooperation. We discuss the implications that these findings may have for design of efficient institutions.

Mergers, Asymmetries and Collusion: Experimental Evidence

We analyse the impact of mergers in experimental Bertrand‐Edgeworth oligopolies. Treatment variables are the number of firms (two, three) and the distribution of industry capacity (symmetric, asymmetric). Consistent with a dynamic collusion model, we find that, even though they are more concentrated, asymmetric markets exhibit lower prices than symmetric markets with the same number of firms. Consistent with the static Nash prediction, duopolies charge higher prices than triopolies when we control for (a)symmetry. The overall impact of a merger (which comprises both fewer firms and an asymmetry) is anti‐competitive but the price increase is not significant.

Mergers, Asymmetries and Collusion: Experimental Evidence

We analyze the impact of mergers in experimental Bertrand-Edgeworth oligopolies. Treatment variables are the number of firms (two, three) and the distribution of industry capacity (symmetric, asymmetric). Consistent with a dynamic collusion model, we find that, even though they are more concentrated, asymmetric markets exhibit lower prices than symmetric markets with the same number of firms. Consistent with the static Nash prediction, duopolies charge higher prices than triopolies when we control for (a)symmetry. The overall impact of a merger (which comprises both fewer firms and an asymmetry) is anti-competitive but the price increase is not significant.

HOW MUCH COLLUSION? A META-ANALYSIS OF OLIGOPOLY EXPERIMENTS

Oligopoly has been among the first topics in experimental economics. Over half a century, some 150 papers have been published. Each individual paper was interested in demonstrating one effect, but in order to do so, experimenters had to specify many more parameters. Thus they have generated a huge body of evidence, untapped so far. This meta-analysis makes this evidence available. More than 100 of the papers lend themselves to calculating an index of collusion. The database behind this paper covers some 500 different settings. The experimental results may be normalized as a percentage of the span between the Walrasian and the Pareto outcomes. In the same way, results may be expressed as a percentage of the distance between the Nash and the Pareto outcomes. For each and every one of the parameters, these two indices make it possible to answer two questions: How far is the market outcome away from the competitive equilibrium? And how good is the Nash prediction? Most importantly, however, the meta-analysis sheds light on how features of the experimental setting interact with each other. Most main effects and many interaction effects are indeed statistically significant.

Strategic Errors and Audit Quality: An Experimental Investigation

We report experimental results for a simple bimatrix game between a manager and an auditor. We investigate whether the quality of audited financial statements improves if the relative proportion of perfectly honest auditors increases. We find that the quality of audited reports is higher if computerized auditors who always perform a high audit effort are present. This result is in direct contrast to the Nash prediction for our game. The Quantal Response Equilibrium, which explicitly takes into account boundedly rational behavior, supports our experimental data. Our main findings depend neither on framing nor the payoff matrix we use.

How Much Collusion? A Meta-Analysis on Oligopoly Experiments

Oligopoly has been among the first topics in the experimental economics. Over half a century, some 150 papers have been published. Each individual paper was interested in demonstrating one effect. But in order to do so, experimenters had to specify many more parameters. That way they have generated a huge body of evidence, untapped thus far. This meta-analysis makes this evidence available. More than 100 of the papers lend themselves to calculating an index of collusion. The data bank behind this paper covers some 500 different settings. The experimental results may be normalised as a percentage of the span between the Walrasian and the Pareto outcomes. The same way, results may be expressed as a percentage of the distance between the Nash and the Pareto outcomes. For each and every of the parameters, these two indices make it possible to answer two questions: how far is the market outcome away from the competitive equilibrium? And how good is the Nash prediction? Most importantly, however, the meta-analysis sheds light on how features of the experimental setting interact with each other. Most main effects and many interaction effects are indeed statistically significant.

Individual Decision Making in a Negative Externality Experiment

The experimental treatments analysed in this paper are simple in that there is a unique Nash equilibrium resulting in each player having a dominant strategy. However, the data show quite clearly that subjects do not always choose this strategy. In fact, when this dominant strategy is not a “focal” outcome it does not even describe the average decision adequately. It is shown that average individual decisions are best described by a decision error model based on a censored distribution as opposed to the truncated regression model which is typically used in similar studies. Moreover it is shown that in the treatments where the dominant strategy is not “focal” dynamics are important with average subject decisions initially corresponding to the “focal” outcome and then adjusting towards the Nash prediction. Overall, 66.7% of subjects are consistent with Payoff Maximization, 27.8% are consistent with an alternate preference maximization and 5.6% are random.

Cost Structures and Nash Play in Repeated Cournot Games

This paper reports an experiment designed to assess the effects of a rotation in the marginal cost curve on convergence in a repeated Cournot triopoly. Increasing the cost curve's slope both reduces the serially-undominated set to the Nash prediction, and increases the peakedness of earnings. We observe higher rates of Nash equilibrium play in the design with the steeper marginal cost schedule, but only when participants are also rematched after each decision. Examination of response patterns suggests that the treatment with a steeper marginal cost curve and with a re-matching of participants across periods induces the selection of Nash Consistent responses.

An experimental examination of double marginalization and vertical relationships

The presence of a vertical externality, and therefore an incentive to integrate or to impose vertical restraints, is investigated in 11 posted-offer experiments. Upstream markets are characterized by a single seller. When the downstream market consists of three firms, there is no evidence of a vertical externality, and behavior is consistent with the vertically integrated outcome. With a single firm downstream, a vertical externality is present and the Nash prediction is supported. An analysis of individual market behavior reveals that firms approximate their best response functions, with some indication that they improve over time.

The voluntary provision of a pure public good with diminishing marginal returns

In experiments investigating the voluntary provision of a pure public good, participants consistently allocate resources to this good when the Nash prediction is to allocate nothing. This paper explores the robustness of this result when the Nash prediction calls for a division of resources between the private and public goods. We consider how a change in individual resource endowments and supplemental earnings information affect allocations to the public good. Results indicate that, under both the high and low endowment conditions, groups continue to allocate more resources than the Nash prediction. However, providing participants with detailed instructions that describe the declining marginal benefit to the public good leads to a significant decrease in allocations to the public good.

A theoretical analysis of altruism and decision error in public goods games

We formalize an equilibrium model in which altruism and decision-error parameters determine the distribution of contributions for linear and quadratic public goods games. The equilibrium density is exponential for linear games, and normal for quadratic games. Our model implies: (i) contributions increase with the marginal value of the public good, (ii) total contributions increase with the number of participants, (iii) mean contributions lie between the Nash prediction and half the endowment. These predictions, which are not implied by a Nash analysis, are consistent with laboratory data. Maximum likelihood estimates of altruism and error parameters are significant and plausible.

Anonymity and the voluntary provision of public goods

Experimental research investigating the voluntary provision of a pure public good has shown that participants consistently allocate a portion of their resources to this good when the full-information noncooperative game theoretic (Nash) prediction is to allocate zero resources to this good. This paper considers whether the discrepancy between empirical results and the Nash prediction is due to a lack of anonymity. We report a sequence of public goods experiments in which participants do not know the identity of other group members and the experimenter cannot associate any participant's decisions with that person's identity. The results indicate that these procedures do not alter the tendency for token allocations to differ from the Nash prediction.

REWARDS, EXPERIENCE AND DECISION COSTS IN FIRST PRICE AUCTIONS

Consistent with a model of asymmetric risk aversion, subjects in first price auctions consistently bid above the risk neutral Nash prediction. It has been argued that this is due to low opportunity cost of deviating from the risk neutral bid. We increase opportunity cost (and payoff levels) by factors of 0, 1, 5, 10, and 20, from the normal levels generating payoffs up to $250 for risk neutral subjects and observe an insignificant increase in the slope of individual bid functions. The RMSE of bids declines significantly. This is consistent with a reward/decision cost model of bidding behavior.