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We develop a tool akin to the revelation principle for dynamic mechanism-selection games in which the designer can only commit to short-term mechanisms. We identify a canonical class of mechanisms rich enough to replicate the outcomes of any equilibrium in a mechanism-selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. Our result simplifies the search for the designer-optimal outcome by reducing the agent’s behavior to a series of participation, truth telling, and Bayes’ plausibility constraints the mechanisms must satisfy.

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.

The communication revelation principle (RP) of mechanism design states that any outcome that can be implemented using any communication system can also be implemented by an incentive-compatible direct mechanism. In multistage games, we showthat in general the communication RP fails for the solution concept of sequential equilibrium (SE). However, it holds in important classes of games, including singleagent games, games with pure adverse selection, games with pure moral hazard, and a class of social learning games. For general multistage games, we establish that an outcome is implementable in SE if and only if it is implementable in a canonical Nash equilibrium in which players never take codominated actions. We also prove that the communication RP holds for the more permissive solution concept of conditional probability perfect Bayesian equilibrium.

This paper generalizes the concept of Bayes correlated equilibrium (Bergemann and Morris, 2016) to multi-stage games. We apply our characterization results to a number of illustrative examples and applications.

This paper generalizes the concept of Bayes' correlated equilibrium Bergemann and Morris (2016) to multistage games. We apply our characterization results to a number of illustrative examples and applications.

We introduce two novel matching mechanisms, Reverse Top Trading Cycles (RTTC) and Reverse Deferred Acceptance (RDA), with the purpose of challenging the idea that the theoretical property of strategy-proofness induces high rates of truth-telling in economic experiments. RTTC and RDA are identical to the celebrated Top Trading Cycles (TTC) and Deferred Acceptance (DA) mechanisms, respectively, in all their theoretical properties except that their dominant-strategy equilibrium is to report one’s preferences in the order opposite to the way they were induced. With the focal truth-telling strategy being out of equilibrium, we are able to perform a clear measurement of how much of the truth-telling reported for strategy-proof mechanisms is compatible with rational behaviour and how much of it is caused by confused decision-makers following a default, focal strategy without understanding the structure of the game. In a school-allocation setting, we find that roughly half of the observed truth-telling under TTC and DA is the result of naïve (non-strategic) behaviour. Only 14–31% of the participants choose actions in RTTC and RDA that are compatible with rational behaviour. Furthermore, by looking at the responses of those seemingly rational participants in control tasks, it becomes clear that most lack a basic understanding of the incentives of the game. We argue that the use of a default option, confusion and other behavioural biases account for the vast majority of truthful play in both TTC and DA in laboratory experiments.

We report on an experiment exploring whether and how subjects may learn to use a correlation device to coordinate on a correlated equilibrium of the Battle of the Sexes game which Pareto dominates the mixed-strategy Nash equilibrium of that game. We consider a direct correlation device with messages phrased in terms of players' actions as well as an indirect device with a priori meaningless messages. According to the revelation principle, it does not matter whether the correlation device is direct or indirect so long as it implements a correlated equilibrium. However, we find that subjects had an easier time coordinating on the efficient correlated equilibrium with a direct rather than an indirect device. Nevertheless, subjects were able to learn to use the indirect device to better coordinate their play. We further find that, when paired with a fixed partner, subjects utilized history-contingent strategies (e.g., \"alternation\") as a coordinating device and were more likely to ignore the correlation device in this setting; the fixed-matching protocol can thus serve as a substitute for a correlation device in achieving an efficient coordination outcome.

Game theory is an important analytical tool for measuring problems caused by behaviors that deviate from contractual ethics. However, the PPP literature still does little to explore this research topic. This paper analyzes and improves the equilibrium conditions of a renegotiation model of PPPs by introducing the asymmetry of information in the contract. To achieve this goal, the Mechanism Design Theory is used to demonstrate how the correct tracking of the investor directly influences the payoffs of the renegotiation. The study concludes that the lack of incentive constraints in the bidding document, as an ex ante condition, does not provide sufficient information on investor management capability. In this way, this information is only revealed in the renegotiation phase. Consequently, this contract failure results in high political costs to the government due to excessive subsidies.

This paper extends the revelation principle to environments in which the mechanism designer cannot fully commit to the outcome induced by the mechanism. We show that he may optimally use a direct mechanism under which truthful revelation is an optimal strategy for the agent. In contrast with the conventional revelation principle, however, the agent may not use this strategy with probability one. Our results apply to contracting problems between a principal and a single agent. By reducing such problems to well-defined programming problems they provide a basic tool for studying imperfect commitment.

We consider a class of mechanism games in which there are multiple principals and three or more agents. For a mechanism game in this class, a sort of folk theorem holds: there is a threshold value for each of the principals such that an allocation is achieved at a pure-strategy sequential equilibrium of the game if and only if (i) it is incentive compatible and (ii) it attains an expected utility for each principal that is greater than or equal to the threshold value for the principal.