Theoretical Economics September 2018 is now online
TABLE OF CONTENTS, Volume 13, Number 3 (September 2018)
Full Issue
Title: Rationing rules and stable coalition structures
Pages: 933-950
Authors: Oihane Gallo, Elena Inarra
Abstract: This paper introduces a model of coalition formation with claims.
It assumes that agents have claims over the outputs they could produce by forming coalitions. Outputs, insufficient to meet the claims and are rationed by a rule whose proposals of division induce each agent to rank the coalitions in which she can participate. As a result, a hedonic game of coalition formation emerges. Using resource monotonicity and consistency, we characterize the continuous rationing rules that induce hedonic games that admit core-stability.
Keywords: Coalition formation, hedonic games, core-stability, rationing rules
JEL classification: C71, D63, D74
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Title: Efficient chip strategies in repeated games
Pages: 951-978
Authors: Wojciech Olszewski, Mikhail Safronov
Abstract: We study a class of chip strategies in repeated games of incomplete information. This class generalizes the strategies studied by Möbius (2001) in the context of a favor-exchange model and the strategies studied in our companion paper Olszewski and Safronov (2017).
In two-player games, if players have private values and their types evolve according to independent Markov chains, then under very mild conditions on the stage game, the efficient outcome can be approximated by chip-strategy equilibria when the discount factor tends to 1.
We extend this result (assuming stronger conditions) to stage games with any number of players. Chip strategies can be viewed as a positive model of repeated interactions, and the insights from our analysis seem applicable in similar contexts, not covered by the present analysis.
Keywords: Repeated games
JEL classification: C73
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Title: Pareto efficiency and identity
Pages: 979-1008
Authors: Christopher Phelan, Aldo Rustichini
Abstract: This paper examines the set of Pareto efficient allocations in a finite period Mirrlees (1971, 1976) economy; each period represents a lifetime for an agent who cares about the utility of his descendants. In making Pareto comparisons, we use an interim concept of efficiency, and consider an individual as indexed not only by his date of birth but also by the history of events up to his birth, including his own type. That is, we assume the child of a high skilled parent is a different person than the child of a low skilled parent, even if both children have the same skill level. Our contributions are characterization of these efficient allocations and their implementation.
We completely characterize the set of efficient allocations under full information.
We show that for efficient allocations, implicit inheritance taxes from the perspective of the parent’s type, can be either progressive or regressive. Further, imposing no taxes of any kind, coupled with each agent owning his own production, results in a Pareto efficient allocation.
Under private information, we completely characterize the set of Pareto efficient allocations for the two-period economy where skill types take on two values, and again show that implicit inheritance taxes can be either progressive or regressive, again relative to the parent’s type. For more general multi-period economies with private information, we show that the reciprocal Euler condition of Rogerson (1985) and Golosov, Kocherlakota, and Tsyvinski (2003) holds as a necessary condition, but as an inequality and that the expected value of implicit inheritance tax rates conditional on a parent’s history are weakly negative. Finally, we derive conditions such that given private information, no taxes of any kind, coupled with each agent owning his own production, results in a Pareto efficient allocation.
Keywords: Pareto Efficiency, taxation, bequests, laissez-faire
JEL classification: H2
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Title: Strategy-proof tie-breaking in matching with priorities
Pages: 1009-1042
Authors: Lars Ehlers, Alexander Westkamp
Abstract: A set of indivisible objects is allocated among agents with strict preferences. Each object has a weak priority ranking of the agents. A collection of priority rankings, a priority structure, is solvable if there is a strategy-proof mechanism that is constrained efficient, i.e. that always produces a stable matching that is not Pareto-dominated by another stable matching. We characterize all solvable priority structures satisfying the following two restrictions:
(A) Either there are no ties, or there is at least one four-way tie.
(B) For any two agents i and j, if there is an object that assigns higher priority to i than j, there is also an object that assigns higher priority to j than i.
We show that there are at most three types of solvable priority structures:
The strict type, the house allocation with existing tenants (HET) type, where, for each object, there is at most one agent who has strictly higher priority than another agent, and the task allocation with unqualified agents
(TAU) type, where, for each object, there is at most one agent who has strictly lower priority than another agent. Out of these three, only HET priority structures are shown to admit a strongly group strategy-proof and constrained efficient mechanism.
Keywords: Weak priorities, stability, constrained efficiency, strategy-proofness
JEL classification: C78, D61, D78, I20
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Title: Transitivity of preferences: when does it matter?
Pages: 1043-1076
Authors: Laurens Cherchye, Thomas Demuynck, Bram De Rock
Abstract: We define necessary and sufficient conditions on prices and incomes under which quantity choices can violate SARP (Strong Axiom of Revealed Preference) but not WARP (Weak Axiom of Revealed Preference). As SARP extends WARP by additionally imposing transitivity on the revealed preference relation, this effectively defines the conditions under which transitivity adds bite to the empirical analysis. For finite datasets, our characterization takes the form of a triangular condition that must hold for all three-element subsets of normalized prices, and which is easy to verify in practice. For infinite datasets, we formally establish an intuitive connection between our characterization and the concept of Hicksian aggregation. We demonstrate the practical use of our conditions through two empirical illustrations.
Keywords: Revealed preferences, warp, sarp, transitive preferences, testable implications, Hicksian aggregation
JEL classification: C14, D01, D11, D12
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Title: Competition and networks of collaboration
Pages: 1077-1110
Authors: Nikita Roketskiy
Abstract: I develop a model of collaboration between tournament participants in which agents collaborate in pairs, and an endogenous structure of collaboration is represented by a weighted network. The agents are forward-looking and capable of coordination; they value collaboration with others and higher tournament rankings. I use von Neumann-Morgenstern stable sets as a solution. I find stable networks in which agents collaborate only within exclusive groups. Both an absence of intergroup collaboration and excessive intragroup collaboration lead to inefficiency. I provide a necessary and sufficient condition for the stability of efficient outcomes in winner-takes-all tournaments. I show that the use of transfers does not repair efficiency.
Keywords: Network, collaboration, farsighted agent, stable set, tournament
JEL classification: D85, C71
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Title: Modes of persuasion toward unanimous consent
Pages: 1111-1150
Authors: Arjada Bardhi, Yingni Guo
Abstract: A fully committed sender seeks to sway a collective adoption decision through designing experiments. Voters have correlated payoff states and heterogeneous thresholds of doubt. We characterize the sender-optimal policy under unanimity rule for two persuasion modes. Under general persuasion, evidence presented to each voter depends on all voters' states.
The sender makes the most demanding voters indifferent between decisions, while the more lenient voters strictly benefit from persuasion. Under individual persuasion, evidence presented to each voter depends only on her state. The sender designates a subgroup of rubber-stampers, another of fully informed voters, and a third of partially informed voters. The most demanding voters are strategically accorded high-quality information.
Keywords: Information design, collective decision-making, unanimity rule, information guard
JEL classification: D71, D82, D83, G28, K20, O32
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Title: A complete characterization of equilibria in an intrinsic common agency screening game
Pages: 1151-1190
Authors: David Martimort, Aggey Semenov, Lars A. Stole
Abstract: We characterize the complete set of equilibrium allocations to an intrinsic common agency screening game as the set of solutions to self-generating optimization programs. We provide a complete characterization of equilibrium outcomes for regular environments by relying on techniques developed elsewhere for aggregate games and for the mechanism design delegation literature. The set of equilibria include those with non-differentiable payoffs and discontinuous choices, as well as equilibria that are smooth and continuous in types. We identify one equilibrium, the maximal equilibrium, which is the unique solution to a self-generating optimization program with the largest (or ``maximal'') domain, and the only equilibrium that is supported with bi-conjugate (i.e., least-concave) tariffs. The maximal equilibrium exhibits a n-fold distortion caused by each of the n principal's non-cooperative behavior in over-harvesting the agent's information rent. Furthermore, in any equilibrium, over any interval of types in which there is full separation, the agent's equilibrium action corresponds to the allocation in the maximal equilibrium. Under reasonable conditions, the maximal equilibrium maximizes the agent's information rent within the class of equilibrium allocations. When the principals'
most-preferred equilibrium allocation differs from the maximal equilibrium, we demonstrate that the agent's choice function exhibits an interval of bunching over the worst agent types, and elsewhere corresponds with the maximal allocation. The optimal region of bunching trades off the principals' desire to constrain inefficient n-fold marginalizations of the agent's rent against the inefficiency of pooling agent types.
Keywords: Intrinsic common agency, aggregate games, mechanism design for delegated decision-making, duality, equilibrium selection
JEL classification: D82, D86
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Title: Efficient cooperation by exchanging favors
Pages: 1191-1232
Authors: Wojciech Olszewski, Mikhail Safronov
Abstract: We study chip-strategy equilibria in two-player repeated games.
Intuitively, in these equilibria players exchange favors by taking individually suboptimal actions if these actions create a "gain" for the opponent larger than the player's "loss" from taking them. In exchange, the player who provides a favor implicitly obtains from the opponent a chip that entitles the player to receiving this kind of favor at some future date.
Players are initially endowed with a number of chips, and a player who runs out of chips is no longer entitled to receive any favors until she provides a favor to the opponent, in which case she receives one chip back.
We show that such simple chip strategies approximate efficient outcomes in a class of repeated games with incomplete information, when discounting vanishes. This class includes many important applications, studied in numerous previous papers, such as the discrete-time favor exchange model of Möbius (2001), repeated auctions, and the repeated Spulber's duopoly of Athey and Bagwell (2001), among others. We also show the limitation of chip strategies. For example, if players have more than two types, then such simple chip strategies may not approximate efficient outcomes even in symmetric games.
Keywords: Repeated games, efficiency, chip strategies
JEL classification: C73, D43, D44, D61
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Title: Optimal adaptive testing: informativeness and incentives
Pages: 1233-1274
Authors: Rahul Deb, Colin Stewart
Abstract: We introduce a learning framework in which a principal seeks to determine the ability of a strategic agent. The principal assigns a test consisting of a finite sequence of tasks. The test is adaptive: each task that is assigned can depend on the agent's past performance. The probability of success on a task is jointly determined by the agent's privately known ability and an unobserved effort level that he chooses to maximize the probability of passing the test. We identify a simple monotonicity condition under which the principal always employs the most (statistically) informative task in the optimal adaptive test. Conversely, whenever the condition is violated, we show that there are cases in which the principal strictly prefers to use less informative tasks.
Keywords: Adaptive testing, dynamic learning, ratcheting, testing experts
JEL classification: D82, D83, C44
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Title: On mechanisms eliciting ordinal preferences
Pages: 1275-1318
Authors: Gabriel Carroll
Abstract: When is a mechanism designer justified in only asking for ordinal information about preferences? Simple examples show that, even if the planner's goal (expressed by a social choice correspondence, or SCC) depends only on ordinal information, eliciting cardinal information may help with incentives. However, if agents may be uncertain about their own cardinal preferences, then a strong robustness requirement can justify the focus on ordinal mechanisms. Specifically, when agents' preferences over pure outcomes are strict, if a planner is able to implement an SCC (in ex-post
equilibrium) using a mechanism that is robust to interdependence of arbitrary form in cardinal preferences, then there must exist such a mechanism that elicits only ordinal preferences. The strictness assumption can be dropped if we further allow the possibility of non-expected-utility preferences.
Keywords: Cardinal extension, ex-post implementation, interdependence, ordinal mechanism, robust mechanism design
JEL classification: D81, D82
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Title: The optimal degree of monetary-discretion in a New Keynesian model with private information
Pages: 1319-1368
Authors: Yuichiro Waki, Richard Dennis, Ippei Fujiwara
Abstract: This paper considers the optimal degree of monetary-discretion when the central bank conducts policy based on its private information about the state of the economy and is unable to commit. Society seeks to maximize social welfare by imposing restrictions on the central bank's actions over time, and the central bank takes these restrictions and the New Keynesian Phillips curve as constraints. By solving a dynamic mechanism design problem we find that it is optimal to grant "constrained discretion" to the central bank by imposing both upper and lower bounds on permissible inflation, and that these bounds should be set in a history-dependent way. The optimal degree of discretion varies over time with the severity of the time-inconsistency problem, and, although no discretion is optimal when the time-inconsistency problem is very severe, it is a transient phenomenon and some discretion is granted eventually.
Keywords: Rules versus discretion, monetary policy, New Keynesian model, private information, delegation, mechanism design, inflation targeting
JEL classification: D82, E52, E58
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Title: A tractable model of monetary exchange with ex-post heterogeneity
Pages: 1369-1424
Authors: Guillaume Rocheteau, Pierre-Olivier Weill, Russell Wong
Abstract: We construct a continuous-time, New-Monetarist economy that displays an endogenous, non-degenerate distribution of money holdings.
Properties of equilibria are obtained analytically and equilibria are solved in closed form in a variety of cases. Lump-sum transfers financed with money creation are welfare-enhancing when labor productivity is low whereas regressive transfers approach first best when labor productivity is high and agents are not too impatient. We introduce illiquid government bonds and draw implications for liquidity-trap equilibria. We also study transitional dynamics under quadratic preferences and the velocity of money under heterogeneous preference shocks.
Keywords: Money, inflation, risk sharing, liquidity traps
JEL classification: E40,E50
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Title: A general solution method for moral hazard problems
Pages: 1425-1481
Authors: Rongzhu Ke, Christopher Thomas Ryan
Abstract: Principal-agent models are pervasive in theoretical and applied economics, but their analysis has largely been limited to the ``first-order approach'' (FOA) where incentive compatibility is replaced by a first-order condition. This paper presents a new approach to solving a wide class of principal-agent problems that satisfy the monotone likelihood ratio property but may fail to meet the requirements of the FOA. Our approach solves the problem via tackling a max-min-max formulation over agent actions, alternate best responses by the agent, and contracts.
Keywords: Principal agent, moral hazard, solution method
JEL classification: D82, D86
