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We introduce a set-valued solution concept, M equilibrium, to capture empirical regularities from over half a century of game theory experiments. We show M equilibrium serves as a meta theory for various models that hitherto were considered unrelated. M equilibrium is empirically robust and, despite being set-valued, falsifiable. Results from a series of experiments that compare M equilibrium to leading behavioral game theory models demonstrate its virtues in predicting observed choices and stated beliefs. Data from experimental games with a unique pure-strategy Nash equilibrium and multiple M equilibria exhibit coordination problems that could not be anticipated through the lens of existing models. (JEL C72, C90, D83)

An important result in convex analysis is the duality between a closed convex set and its support function. We exploit this duality to develop a novel geometric approach to mechanism design. For a general class of social choice problems we characterize the feasible set, which is closed and convex, and its support function. We next provide a geometric interpretation of incentive compatibility and refine the support function to include incentive constraints using arguments from majorization theory. The optimal mechanism can subsequently be derived from the support function using Hotelling's lemma. We first assume that values are linear in types and types are independent, private, and one-dimensional. For this environment we provide a simple geometric proof that Bayesian and dominant strategy implementation are equivalent by showing that the feasible sets that remain after imposing either type of incentive constraints coincide. Furthermore, we derive the optimal mechanism for any social choice problem and any linear objective, including revenue and surplus maximization. As an illustration, we determine the optimal multi-unit auction for a class of value functions that exhibit decreasing marginal valuations. Other types of constraints, such as capacity constraints and budget balancedness, can be interpreted geometrically as well, which facilitates a unified approach to a range of social choice problems, including auctions, bargaining, and public goods provision. We discuss how our geometric approach extends to environments with value interdependencies, non-linear valuations, and correlated or multi-dimensional types. Specifically, we illustrate that with interdependent valuations the equivalence between Bayesian and dominant strategy implementation breaks down, and our approach naturally produces the second-best outcomes for both types of incentive constraints.

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private values. We provide a short and constructive proof that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents. We demonstrate the usefulness and applicability of our approach with several examples. Finally, we show that the equivalence between Bayesian and dominant strategy implementation breaks down when utilities are non-linear or when values are interdependent, multi-dimensional, or correlated.

This paper characterizes behavior with "noisy" decision making for models of political interaction characterized by simultaneous binary decisions. Applications include: voting participation games, candidate entry, the volunteer's dilemma, and collective action problems with a contribution threshold. A simple graphical device is used to derive comparative statics and other theoretical properties of a "quantal response" equilibrium, and the resulting predictions are compared with Nash equilibria that arise in the limiting case of no noise. Many anomalous data patterns in laboratory experiments based on these games can be explained in this manner.

Auctions are generally not efficient when the object's expected value depends on private and common value information. We report a series of first-price auction experiments to measure the degree of inefficiency that occurs with financially motivated bidders. While some subjects fall prey to the winner's curse, they weigh their private and common value information in roughly the same manner as rational bidders, with observed efficiencies close to predicted levels. Increased competition and reduced uncertainty about the common value positively affect revenues and efficiency. The public release of information about the common value also raises efficiency, although less than predicted.

This paper reports laboratory data for games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment in which behavior conforms nicely to predictions of the Nash equilibrium or relevant refinement. In each case, however, a change in the payoff structure produces a large inconsistency between theoretical predictions and observed behavior. These contradictions are generally consistent with simple intuition based on the interaction of payoff asymmetries and noisy introspection about others' decisions. (JEL C72, C92)

We describe the design and implementation of a combinatorial exchange for trading catch shares in New South Wales, Australia. The exchange ended a decades-long political debate by providing a market-based response to a major policy problem faced by fisheries worldwide: the reallocation of catch shares in cap-and-trade programs designed to prevent overfishing. The exchange was conducted over the Internet to lower participation costs and allowed for all-or-nothing orders to avoid fragmented share portfolios. A subsidy was distributed endogenously to facilitate the transfer of shares from inactive to active fishers. Finally, prices were linear and anonymous to ensure that sellers of identical packages received the same payments. These features were crucial to mitigate economic distortions from introducing catch shares and to gain broad acceptance of the program. However, they led to computationally challenging allocation and pricing problems. The exchange operated from May to July 2017 and effectively reallocated shares from inactive fishers to those who needed them most: 86% of active fishers' bids were matched and their share deficits were reduced by 95% in high-priority share classes. Similar reallocation problems arise in fisheries with catch-share systems worldwide as well as in other cap-and-trade systems for resource rights, e.g., water and pollution rights. The implemented exchange illustrates how computational optimization and market design can provide policy tools, able to solve complex policy problems considered intractable only a few years ago.