Implementation theory assumes that participants' choices are rational, in the sense of being consistent with the maximization of a context-independent preference. The paper investigates implementation under complete information when individuals' choices need not be rational. (JEL D11, D60, D83, R31)

A vibrant literature incorporates elements of bounded rationality into choice theory. We survey this work, discussing five central ways in which the literature has modeled departures from the rational choice procedure. We discuss the variety of purposes axiomatic choice characterizations serve for these positive theories, delve into experimental tests, synthesize the welfare debate, and assess important future directions. (JEL D11, D44, D60, D83, D91)

Our concern is the extension of the theory of the Shapley value to problems involving externalities. Using the standard axiom systems behind the Shapley value leads to the identification of bounds on players' payoffs around an “externality-free” value. The approach determines the direction and maximum size of Pigouvian-like transfers among players, transfers based on the specific nature of externalities that are compatible with basic normative principles. Examples are provided to illustrate the approach and to draw comparisons with previous literature.

We propose relaxing the first-order conditions in optimization to approximate rational consumer choice. We assess the magnitude of departures with a new, axiomatically founded measure that admits multiple interpretations. Standard inequality tests of rationality for any given reference class of preferences can be conveniently repurposed to measure goodness-of-fit with that class. Another advantage of our approach is that it is applicable in any context where the first-order approach is meaningful (e.g., convex budget sets arising from progressive taxation). We apply these ideas to shed new light on existing portfolio-choice data.

Following Kamenica and Gentzkow, this paper studies persuasion as an information design problem. We investigate how mistakes in probabilistic inference impact optimal persuasion. The concavification method is shown to extend naturally to a large class of belief updating rules, which we identify and characterize. This class comprises many non-Bayesian models discussed in the literature. We apply this new technique to gain insight into the revelation principle, the ranking of updating rules, when persuasion is beneficial to the sender, and when it is detrimental to the receiver. Our key result also extends to shed light on the question of robust persuasion.

Non-equilibrium models of choice (e.g. level-k reasoning) have significantly different, sometimes more accurate, predictions in games than does Nash equilibrium. When it comes to the maximal set of functions that are implementable in mechanism design, however, they turn out to have similar implications. Focusing on single-valued rules, we discuss the role and implications of different behavioural anchors (arbitrary level-0 play), and prove a level-k revelation principle. If a function is level-k implementable given any level-0 play, it must obey a slight weakening of standard strict incentive constraints. Further, the same condition is also sufficient for level-k implementability, although the role of specific level-0 anchors is more controversial for the sufficiency argument. Nonetheless, our results provide tight characterizations of level-k implementable functions under a variety of level-0 play, including truthful, uniform, and atomless anchors.

We study bargaining over contingent contracts in problems where private information becomes public or verifiable when the time comes to implement the agreement. We suggest a simple, two-stage game that incorporates important aspects of bargaining. We characterize equilibria in which parties always reach agreement, and study their limits as bargaining frictions vanish. Under mild regularity conditions, we show all interim-efficient limits belong to Myerson’s (1984) axiomatic solution. Furthermore, all limits must be interim efficient if equilibrium beliefs satisfy no-signaling-what-you-don’ t-know. Results extend to other bargaining protocols. (JEL C78, D82, D83, D86)

Consumers purchase multiple types of goods but may be able to examine only a limited number of markets for the best price. We propose a simple model that captures these features, conveying new insights. A firm’s price can deflect or draw attention to its market, and consequently, limited attention introduces a new dimension of cross-market competition. We characterize the equilibrium and show that having partially attentive consumers improves consumer welfare. With less attention, consumers are more likely to miss the best offers; but enhanced cross-market competition decreases average price paid, as leading firms try to stay under the consumers’ radar.

A key feature of arbitration is the possibility for conflicting parties to participate in the selection of the arbitrator, the individual who will rule the case. We analyze this problem of the selection of arbitrators from the perspective of implementation theory. In particular, theoretical analyses document problems with veto-rank—a simultaneous procedure commonly used in practice—and develop a new sequential procedure—shortlisting—with better properties. Experimental results are consistent with the theoretical predictions, highlighting both the disadvantages associated with the veto-rank procedure and the advantages associated with the shortlisting procedure. (JEL D71, D72)