Session 7: Dynamic Games, Contracts, and Markets
- Simon Board, University of California, Los Angeles
- Gonzalo Cisternas, Massachusetts Institute of Technology
- Mira Frick, Yale University
- George Georgiadis, Northwestern University
- Andrzej Skrzypacz, Stanford GSB
- Takuo Sugaya, Stanford GSB
The idea of this session is to bring together microeconomic theorists working on dynamic games and contracts with more applied theorists working in macro, finance, organizational economics, and other fields. First, this is a venue to discuss the latest questions and techniques facing researchers working in dynamic games and contracts. Second, we wish to foster interdisciplinary discussion between scholars working on parallel topics in different disciplines, in particular, helping raise awareness among theorists of the open questions in other fields.
This is a continuation of successful SITE annual sessions 2013-2020. In previous years, we attracted people from economics, finance, operations research, political economy, and other related fields, ranging from Ph.D. students to senior professors. We hope to have a similar number of attendees this year as in the past. Specific topics likely to be covered include repeated and stochastic games, dynamic optimal contracts, dynamic market pricing, reputation, search, and learning and experimentation.
In This Session
Wednesday, August 18, 2021
Wealth Dynamics in Communities
This paper develops a model to explore how favor exchange in communities influences wealth dynamics. We identify a key obstacle to wealth accumulation: wealth crowds out favor exchange. Therefore, low-wealth households are forced to choose between growing their wealth and accessing favor exchange within their communities. The outcome is that some communities are left behind, with wealth disparities that persist and sometimes even grow worse. Using numerical simulations, we show that place-based policies encourage both favor exchange and wealth accumulation and so have the potential to especially benet such communities.
Optimal Dynamic Allocation: Simplicity through Information Design
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 analyze direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. We identify the welfare-maximizing mechanism and show that it can be implemented by a first-come first-served wait-list with deferrals when the
marketmaker can design the information disclosed to agents about the objects. The optimal disclosure policy pools adjacent object types.
Probabilistic Assortative Matching under Nash Bargaining
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.
Thursday, August 19, 2021
Price Experimentation in Confidential Negotiations
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.
Large-Sample Rankings of Information Structures in Games
The Cost of Optimally Acquired Information
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.
Friday, August 20, 2021
Optimal Feedback in Contests
We derive optimal contests for environments where output takes the form of breakthroughs and the principal has an informational advantage over the contestants. Whether or not the principal is able to provide real-time feedback to contestants, the optimal prize allocation is egalitarian: all agents who have succeeded in a pre-specified time interval share the prize equally. When providing feedback is feasible, the optimal contest takes a stark cyclical form: contestants are fully apprised of their own success, and at the end of each fixed-length cycle, they are informed about peer success as well.
Dynamic Amnesty Programs
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.
Screening for Breakthroughs
We identify a new and pervasive dynamic agency problem: that of incentivising the prompt disclosure of productive information. To study it, we introduce a 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 striking 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.