Session 7: Dynamic Games, Contracts, and Markets

This paper develops a model to explore how favor exchange influences wealth dynamics. We identify a key obstacle to wealth accumulation: wealth crowds out favor exchange. Therefore, households must choose between growing their wealth and accessing favor exchange. We show that low-wealth households rely on favor exchange at the cost of having tightly limited long-term wealth. As a result, initial wealth disparities persist and can even grow worse. We then explore how communities and policymakers can overcome this obstacle. Using simulations, we show that community benefits and place-based policies can stimulate both saving and favor exchange, and in some cases, can even transform favor exchange into a force that accelerates wealth accumulation.

We study dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent’s value for an object is supermodular in her type and the quality of the object, and her payoff is quasilinear in her waiting cost. We identify the welfare-maximizing mechanism in the class of direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. When the social planner can design the information disclosed to the agents about the objects, this mechanism can be implemented by a first-come first-served wait-list with deferrals. The optimal disclosure policy pools adjacent object types. Moreover, the hazard rate of the distribution of the agents' types determines the structure of the optimal disclosure policy, when the agents' utility function is separable.  A single-peaked (single-dipped)  hazard rate leads to the optimality of a lower censorship (upper censorship) policy.

This paper re-visits the canonical random search and matching model with Nash bargaining. By introducing pair-specific production shocks, our framework generates meeting-contingent match outcomes that are random. We provide a robust characterization of probabilistic matching patterns for any non-stationary environment, generalizing results by Shimer and Smith (2000). We nd that, although their prediction of single-peaked preferences over meetings is robust, search frictions upset positive assortative matching across well-assorted pairs. As a second contribution, we show that the non-stationary random search matching model is a mean eld game, and admits a representation as a system of forward-backward stochastic differential equations. This representation affords a novel existence and uniqueness result, casting doubt on the robustness of multiple self-fulfilling equilibrium paths frequently reported in the literature.

I develop a model in which a long-lived seller concurrently negotiates with multiple long-lived buyers over two periods. Within this framework, I consider two protocols: a public negotiation process and a confidential negotiation process. In the confidential negotiation process, buyers competitively engage in “price experimentation”: they sacrifice initial profits so that they can enjoy informational advantages over competitors later. Due to this channel, the seller benefits from (1) maintaining confidentiality over past offers and (2) reducing the number of buyers in the confidential negotiation process, even without any entry cost.

We study settings in which, prior to playing an incomplete information game, players observe many draws of private signals about the state from some information structure. Signals are i.i.d. across draws, but may display arbitrary correlation across players. For each information structure, we define a simple learning efficiency index, which only considers the statistical distance between the worst-informed player's marginal signal distributions in different states. We show, first, that this index characterizes the speed of common learning (Cripps, Ely, Mailath, and Samuelson, 2008): In particular, the speed at which players achieve approximate common knowledge of the state coincides with the slowest player's speed of individual learning, and does not depend on the correlation across players' signals. Second, we build on this characterization to provide a ranking over information structures: We show that, with sufficiently many signal draws, information structures with a higher learning efficiency index lead to better equilibrium outcomes, robustly for a rich class of games and objective functions. We discuss implications of our results for constrained information design in games and for the question when information structures are complements vs. substitutes.

 

This paper develops a theory for the expected cost of optimally acquired information when information can be acquired sequentially and there is no explicit cost of delay. We study the “reduced-form” Indirect Cost functions for information generated by sequential minimization of a “primitive” Direct Cost function. The class of Indirect Costs is characterized by a recursive condition called Sequential Learning-Proofness. This condition is inconsistent with Prior Invariance: Indirect Costs must depend on the decision-maker’s prior beliefs. 

We show that Sequential Learning-Proofness provides partial optimality foundations for the Uniformly Posterior Separable (UPS) cost functions used in the rational inattention literature: a cost function is UPS if and only if it is an Indirect Cost that (i) satisfies a mild regularity condition or, equivalently, (ii) is generated (only) by Direct Costs for which the op timal sequential strategy involves observing only Gaussian diffusion signals. We characterize the unique UPS cost function that is generated by a Prior-Invariant Direct Cost; it exists only when there are exactly two states. 

We also propose two specific UPS cost functions based on additional optimality principles. We introduce and characterize Total Information as the unique Indirect Cost that is Process Invariant when information can be decomposed both sequentially and “simultaneously”: it is uniquely invariant to the “merging” and “splitting” of experiments. Under regularity conditions, Mutual Information is the unique Indirect Cost that is Compression-Invariant when as pects of the state space can be “freely ignored”: it is uniquely invariant to the “merging” and “splitting” of states. We argue that Total Information and Mutual Information represent the normatively ideal costs of, respectively, “producing” and “processing” information. 

We derive an optimal dynamic contest for environments where the principal monitors effort through a coarse, binary performance measure and chooses prize-allocation and termination rules together with a real-time feedback policy. The optimal contest takes a stark cyclical form: contestants are kept fully apprised of their own successes, and at the end of each fixed-length cycle, if at least one agent has succeeded, the contest ends and the prize is shared equally among all successful agents regardless of when they succeeded; otherwise, the designer informs all contestants that nobody has yet succeeded and the contest resets.

A regulator faces a stream of agents each engaged in crime with stochastic returns. The regulator designs an amnesty program, committing to a time path of penalty reductions for criminals who self-report before they are detected. In an optimal time path, the intertemporal variation in the returns from crime can generate intertemporal variation in the generosity of amnesty. I construct an optimal time path and show that it exhibits amnesty cycles. Amnesty becomes increasingly generous over time until it hits a bound, at which point the cycle resets. Agents engaged in high return crime self-report at the end of each cycle, while agents engaged in low return crime self-report always. I discuss applications to desertion in war, tax evasion, and illegal gun ownership.

We identify a new dynamic agency problem: that of incentivising the prompt disclosure of productive information. To study it, we introduce a general model in which a technological breakthrough occurs at an uncertain time and is privately observed by an agent, and a principal must incentivise disclosure via her control of the agent’s utility. We uncover a deadline structure of optimal mechanisms: they have a simple deadline form in an important special case, and a graduated deadline structure in general. We apply our results to the design of unemployment insurance schemes.