This paper experimentally investigates cooperative game theory from a normative perspective. Subjects designated as Decision Makers express their view on what is fair for others, by recommending a payoff allocation for three subjects (Recipients) whose substitutabilities and complementarities are captured by a characteristic function. We show that axioms and solution concepts from cooperative game theory provide valuable insights into the data. Axiomatic and regression analysis suggest that Decision Makers’ choices can be (noisily) described as a convex combination of the Shapley value and equal split solution. A mixture model analysis, examining the distribution of Just Deserts indices describing how far one goes in the direction of the Shapley value, reveals heterogeneity across characteristic functions. Aggregating opinions by averaging, however, shows that the societal view of what is fair remains remarkably consistent across problems.
Consumers purchase multiple types of goods and services, but may be able to examine only a limited number of markets for the best price. We propose a simple model which captures these features, conveying some new insights. A firm’s price can deflect or draw attention to its market, and consequently, limited attention introduces a new dimension of competition across markets. We fully characterize the resulting equilibrium, and show that the presence of partially attentive consumers improves consumer welfare as a whole. When consumers are less attentive, they are more likely to miss the best offer in each market; but the enhanced cross-market competition decreases average price paid, as leading firms try to stay under the consumers’ radar.
Theories of bounded rationality are typically characterized over an exhaustive data set. How does one tell whether observed choices are consistent with a theory if the data is incomplete? How can out-of-sample predictions be made? What can be identified about preferences? This paper aims to operationalize some leading bounded rationality theories when the available data is limited, as is the case in most practical settings. We also point out that the recent bounded rationality literature has overlooked a methodological pitfall that can lead to ‘false positives’ and ‘empty’ out-of-sample predictions when testing choice theories with limited data.
We study optimal contracting in team settings, featuring stylized aspects of production environments with complex tasks. Agents have many opportunities to shirk, task-level monitoring is needed to provide useful incentives, and because it is difficult to write individual performance into formal contracts, incentives are provided informally, using wasteful sanctions like guilt and shame, or slowed promotion. These features give rise to optimal contracts with “empty promises” and endogenous supervision structures. Agents optimally make more promises than they intend to keep, leading to the concentration of supervisory responsibility in the hands of one or two agents.
Savage (1954) provided a set of axioms on preferences over acts that were equivalent to the existence of an expected utility representation. We show that in addition to this representation, there is a continuum of other “expected utility” representations in which for any act, the probability distribution over states depends on the corresponding outcomes. We suggest that optimism and pessimism can be captured by the stake-dependent probabilities in these alternative representations; e.g., for a pessimist, the probability of every outcome except the worst is distorted down from the Savage probability. Extending the DM’s preferences to be defined on both subjective acts and objective lotteries, we show how one may distinguish optimists from pessimists and separate attitude towards uncertainty from curvature of the utility function over monetary prizes.
We propose a model of history-dependent risk attitude, allowing a decision maker’s risk attitude to be affected by his history of disappointments and elations. The decision maker recursively evaluates compound risks, classifying realizations as disappointing or elating using a threshold rule. We establish equivalence between the model and two cognitive biases: risk attitudes are reinforced by experiences (one is more risk averse after disappointment than after elation) and there is a primacy effect (early outcomes have the greatest impact on risk attitude). In dynamic asset pricing, the model yields volatile, path-dependent prices.
We study optimal contracting in a team setting with moral hazard, where teammates promise to complete socially efficient but costly tasks. Teammates must monitor each other to provide incentives, but each team member has limited capacity to allocate between monitoring and productive tasks. Players incur contractual punishments for unfulfilled promises that are discovered. We show that optimal contracts are generally “forgiving” and players optimally make “empty promises” that they don’t necessarily intend to fulfill. As uncertainty in task completion increases, players optimally make more empty promises but fewer total promises. A principal who hires a team of agents optimally implements a similar contract, with profit-sharing and employment-at-will. When agents differ in their productivity, the model suggests a “Dilbert principle” of supervision: less productive players optimally specialize in monitoring the more productive players’ promises.
This paper studies a class of multi-self decision-making models proposed in economics, psychology, and marketing. In this class, choices arise from the set-dependent aggregation of a collection of utility functions, where the aggregation procedure satisfies some simple properties. We propose a method for characterizing the extent of irrationality in a choice behavior, and use this measure to provide a lower bound on the set of choice behaviors that can be rationalized with n utility functions. Under an additional assumption (scale-invariance), we show that generically at most five “reasons” are needed for every “mistake.”