Commitment versus Discretion in the Peasant-Dictator Game

Commitment versus Discretion in the Peasant-Dictator Game

John B. Van Huyck, Raymond C. Battalio, and Mary F. Walters

Revised January 1995

Research Report No. 2
TAMU Economics Laboratory
Department of Economics
Texas A&M University
College Station, TX 77843-4228

Abstract: We report an experiment designed to test the influence of commitment versus discretion in a simple bargaining game. Game theory predicts and the public policy literature emphasizes that the ability to make commitments promotes efficiency. We find that commitment does significantly increase efficiency in the experiment. Finally, we relate our findings to the extant literature on extensive form bargaining experiments by examining fairness and trust as explanations for some observed anomalies.

Key words: Commitment, Discretion, Subgame Perfection, Bargaining, Fairness, Trust, Human Behavior.

JEL classification: c720, c790, c920, e610.

Acknowledgments: We thank Donald Deere, Michelle Garfinkle, and Steve Wiggins for helpful comments and Eric Battalio for implementing the experimental design on the TAMU economics laboratory network. The National Science Foundation and the Texas Advanced Research Program provided financial support.

Introduction

The ability to bind ones future actions has long been recognized as an advantage when bargaining over a given surplus. A strategic analysis predicts that the party with the ability to make a commitment will receive all of the surplus. This outcome is often judged unfair. However, in many situations a strategic analysis also predicts that in order to create an efficient surplus one of the parties must have an ability to make commitments.

The public policy games literature emphasizes the role commitment plays in promoting efficiency. For example, Kydland and Prescott (1977) describe numerous areas of public policy in which public commitments promote economic efficiency, including patents, flood plain projects, and investment tax credits. Barro and Gordon (1983) emphasize the role commitments play in promoting efficient monetary policy. Other examples include debt repudiation and capital income taxation. [1]

For concreteness consider the following version of the capital income taxation problem: A peasant endowed with beans in the spring can either eat them or plant them in a field. If he plants them, he earns a gross rate of return greater than one. Efficiency requires that he plant the beans. However, the land is ruled by a dictator. If the peasant plants the beans, the dictator can tax his harvest in the fall. The dictator chooses the tax rate to maximize his tax revenue. [2] What tax rate does the dictator pick? How many beans does the peasant plant? How do the answers to these questions depend on whether the dictator can make a commitment?

We attempt to answer these questions by formalizing the peasant-dictator parable into a well defined game, solving the game for the predicted outcomes, and studying the accuracy of these predictions in the laboratory. We find that commitment does significantly increase efficiency as predicted by the public policy games literature. Finally, we relate our findings to the extant literature on extensive form bargaining experiments by examining fairness and trust as explanations for some observed anomalies.

Conclusion

Our experiment reveals both a statistically and economically significant increase in efficiency under commitment. This efficiency gain from commitment was inversely related to the rate of return on investment varying from a low of 49 percent to a high of 81 percent. Hence, the emphasis on commitment in the public policy games literature seems well placed.

Our results stand in marked contrast to the early sequential bargaining experiments. The usual reported finding was that the key strategic variables were uncorrelated with the data. Here we find that the strategic variables are highly correlated with the data. Nevertheless, our data exhibits some of the same anomalies emphasized in the sequential bargaining literature and both the strategic and cooperative bargaining models can be rejected at the usual levels of statistical significance. The data on individual behavior reveals that a small number of tax rate observations violate the abstraction assumption of money motivated behavior under discretion and an even smaller number of investment observations violate the abstraction assumption under commitment.

These violations made it profitable for the dictator to choose a tax rate less than that predicted by a strategic analysis of the commitment treatment. The empirically optimal deviation was decreasing in the endowment. So, the average peasant is not just responding to the absolute incentive to invest but also to the relative incentive to invest.

While many peasants did trust the dictator under discretion, this was not profitable on average. The theoretically optimal level of investment was the empirically optimal level. However, the pecuniary incentive to invest nothing was small when the endowment was small, which may explain why even experienced subjects exhibit this anomaly.

The fairness hypothesis, which implies that dictators don't exploit their bargaining power, and the trust hypothesis, which implies that peasants don't expect dictators to exploit their bargaining power, can both be rejected by the data. Given our limited ability, we conclude that a strategic analysis based on the abstraction assumptions of individual rationality, mutual consistency, and money motivated behavior provides the best predictions for the peasant-dictator game. Given the discovered anomalies, it should be possible to invent abstraction assumptions that lead to more accurate theories.

References

Robert J. Barro and David B. Gordon, "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy, 91(4), August 1983: 589-611.

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Footnotes

[1] See Persson and Tabellini (1990) for introduction and references to the public policy literature. See Veitch (1986) on repudiations and confiscations by the medieval state and Eichengreen (1989) on capital levies during the inter-war period. See Schelling (1960,[1980]) on the role commitment plays in bargaining.

[2] Both benevolent and proprietary dictators have an incentive to tax capital income. Consider a benevolent dictator seeking to minimize welfare reducing distortions introduced by taxes used to finance a given level of useful public expenditures. Taxing labor introduces a distortion that lowers work effort and, hence, welfare, while taxing accumulated capital, since it is already installed, does not introduce any distortions and, hence, does not lower welfare. The proprietary dictator assumption is used in the parable for simplicity.