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Game Theory for Playing Games: Sophistication in a Negative-Externality Experiment

I. INTRODUCTION A significant body of literature addresses the behavior of individuals in experimental games and how this behavior often deviates from theoretical predictions. Specifically, this literature raises a concern with the lack of observed behaviors supporting theoretical (Nash) predictions. For example, voluntary contribution experiments often yield significant deviations from the Nash predictions, and participants' behaviors typically respond to experimental treatments that have no effect on the Nash predictions (Holt and Laury, (2008); Laury and Holt, (2008)). Moreover, greater than Nash contributions continue even in relatively long treatments (50 rounds and more). This tendency to over-contribute has been attributed to reciprocal altruism and decision errors. c While these explanations may be correct, there may be reasons for these deviations which are supported by standard theory (e.g., Binmore 1999). We conjecture that some of the observed differences from theoretical predictions may be due to inexperience with the concepts of maximizing behavior and strategic interactions. Simply put, if individuals do not know what constitutes optimal decision making, it should not be surprising that optimal decision making is not observed. As a result, individuals may rely on simple rules or heuristics to make decisions even though these rules may be suboptimal. To test this conjecture, we conduct a series of moral hazard experiments with participants who vary in their familiarity with the concepts and tools of optimal and strategic decision making. Specifically, we compare the behaviors of a "sophisticated" subject pool with those of a more standard pool of participants (i.e., undergraduate university students). In identifying sophisticated participants, we chose individuals who (at a minimum) had taken an undergraduate game theory course. Our rationale was that these students should be familiar not only with the idea of marginal analysis but also with the concepts of the Nash equilibrium and the identification of dominant strategies in games. Thus, our sophisticated subject pool can be thought of as having been trained in "payoff maximization." (2) Our interest lies in how these individuals behave relative to a more standard pool of "unsophisticated" participants. As such, our analysis is akin to that which attempts to induce behavior which is consistent with theoretical predictions such as Plott and Zeiler (2005), Cherry, Crocker, and Shogren (2003), and Charness, Frechette, and Kagel (2004). In our environment, subjects choose decision numbers for which higher decision numbers correspond to higher individual payoffs and higher social costs, analogous to the emission of a pollutant that is costly to abate. Under the assumption that these decision numbers are private information, this is a classic moral hazard in groups problem similar to the worker effort problem in the labor literature (e.g., Holmstrom 1982) and the nonpoint source pollution in the environmental literature (e.g., Segerson 1988). We use two instruments based on the family of exogenous targeting instruments suggested by Segerson (1988). These instruments involve an exogenously chosen target for aggregate (i.e., group) decision numbers, analogous to the aggregate environmental level of a nonpoint source pollutant. The two instruments we use create incentives for individuals to choose optimal decisions by providing penalties (a tax) or rewards (a subsidy) for implementing aggregate decisions greater than or less than the exogenous target. (3) Our Tax/Sub sidy instrument involves a tax if the sum of individual decision numbers exceeds the target and a subsidy if the sum is below the target. Under this instrument, there is a unique, interior dominant strategy Nash equilibrium and a group (Pareto) optimal outcome. Our Tax instrument involves only the tax if the aggregate decision number of subjects in the group exceeds the target level. …