Maciej H. Kotowski

Trading Networks and Equilibrium Intermediation

We consider a network of intermediaries facilitating exchange between buyers and a seller. Intermediary traders face a private trading cost, a network characterizes the set of feasible transactions, and an auction mechanism sets prices. We examine stable and equilibrium networks. Stable networks, which are robust to agents’ collusive actions, exist when cost uncertainty is acute and multiple, independent trading relationships are valuable. A free-entry process governs the formation of equilibrium networks. Such networks feature too few intermediaries relative to the optimal market organization and they exhibit an asymmetric structure amplifying the shocks experienced by key intermediaries. Welfare and empirical implications of stable and equilibrium networks are investigated.

Audits as Signals

A broad array of law enforcement strategies, from income tax to bank regulation, involve self-reporting by regulated agents and auditing of some fraction of the reports by the regulating bureau. Standard models of self-reporting strategies assume that although bureaus only have estimates of the of an agent’s type, agents know the ability of bureaus to detect their misreports. We relax this assumption, and posit that agents only have an estimate of the auditing capabilities of bureaus. Enriching the model to allow two-sided private information changes the behavior of bureaus. A bureau that is weak at auditing, may wish to mimic a bureau that is strong. Strong bureaus may be able to signal their capabilities, but at a cost. We explore the pooling, separating, and semi-separating equilibria that result, and the policy implications. Important possible outcomes are that a cap on penalties increases compliance, audit hit rates are not informative of the quality of bureau behavior, and by mimicking strong bureaus even weak bureaus can induce compliance.

On the continuous equilibria of affiliated-value, all-pay auctions with private budget constraints☆

We consider all-pay auctions in the presence of interdependent, affiliated valuations and private budget constraints. For the sealed-bid, all-pay auction we characterize a symmetric equilibrium in continuous strategies for the case of N bidders. Budget constraints encourage more aggressive bidding among participants with large endowments and intermediate valuations. We extend our results to the war of attrition where we show that budget constraints lead to a uniform amplification of equilibrium bids among bidders with sufficient endowments. An example shows that with both interdependent valuations and private budget constraints, a revenue ranking between the two auction formats is generally not possible. Equilibria with discontinuous bidding strategies are discussed.

Bribing in First-Price Auctions: Corrigendum

We clarify the sufficient condition for a trivial equilibrium to exist in the model of Rachmilevitch (2013). Rachmilevitch (2013), henceforth R13, studies the following game. Two ex ante identical players are about to participate in an independent-private-value first-price, sealed bid auction for one indivisible object. After the risk-neutral players learn their valuations but prior to the actual auction, player 1 can offer a take-it-or-leave-it (TIOLI) bribe to his opponent in exchange for the opponent dropping out of the contest. If the offer is accepted, player 1 is the only bidder and obtains the item for free; otherwise, both players compete non-cooperatively in the auction as usual. This is called the first-price TIOLI game.1 R13 shows that under the restriction to continuous and monotonic bribing strategies for player 1, any equilibrium of this game must be trivial—the equilibrium bribing function employed by player 1, if it is continuous and non-decreasing, must be identically zero. In this note, we clarify the sufficient conditions under which a trivial equilibrium exists. These are less stringent than originally proposed.

MULTIPERIOD MATCHING: MULTIPERIOD MATCHING

We examine a dynamic, two‐sided, one‐to‐one matching market where agents on both sides interact over a period of time. We define and identify sufficient conditions for the existence of a dynamically stable matching, which may require revisions to initial assignments. A generalization of the deferred acceptance algorithm can identify dynamically stable outcomes in a large class of economies, including cases with intertemporal preference complementarities. We relate our analysis to market unraveling and to common market design applications, including the medical residency match.

Rules and Standards When Compliance Costs Are Private Information

A regulator, seeking to maximize net benefits, must choose between rules and standards and then set a level of care. The regulated agents have private information about their compliance costs. Rules are set ex ante, so agents know the required level of care. Standards are established after agents have taken initial actions, in anticipation of the regulating bureau’s directive. Those actions allow the bureau to make inferences about agents’ costs and thus set more appropriate requirements. Standards, however, expose agents to adjustment costs when they misjudge the required level of care before it is set. Nuanced trade-offs emerge. Standards are relatively more attractive when adjustment costs are low and compliance costs are more uncertain. If some agents are large relative to the market, those agents will choose their actions strategically to influence the ultimate standard. Rules, in contrast, are immune to strategic posturing. We discuss applications to financial regulation.

On the Continuous Equilibria of Affiliated-Value, All-Pay Auctions with Private Budget Constraints, Third Version

We consider all-pay auctions in the presence of interdependent, affiliated valuations and private budget constraints. For the sealed-bid, all-pay auction we characterize a symmetric equilibrium in continuous strategies for the case of N bidders. Budget constraints encourage more aggressive bidding among participants with large endowments and intermediate valuations. We extend our results to the war of attrition where we show that budget constraints lead to a uniform amplification of equilibrium bids among bidders with sufficient endowments. An example shows that with both interdependent valuations and private budget constraints, a revenue ranking between the two auction formats is generally not possible. Equilibria with discontinuous bidding strategies are discussed.

Liquidity Risk in Sequential Trading Networks

This paper develops a model of intermediated exchange with budget-constrained traders who are embedded in a trading network. An experimental investigation confirms the theorys baseline predictions. Traders adopt monotone strategies with higher-budget intermediaries offering to pay more for tradable assets. Traders closer to the final consumer in the network experience systematically greater payoffs due to lessened strategic uncertainty. While private budget constraints inject uncertainty into the trading environment, they also serve as a behavioral speed-bump, preventing traders from experiencing excessive losses due to overbidding.

Endowments, Exclusion, and Exchange

We propose a new cooperative solution for discrete exchange economies and resource allocation problems, the exclusion core. The exclusion core is neither weaker nor stronger than the (strong) core and it rests upon a foundational idea in the legal understanding of property, the right to exclude others. By reinterpreting endowments as a distribution of exclusion rights, we can extend our analysis to economies with qualified property rights and social hierarchies. The exclusion core characterizes a generalized top trading cycle algorithm in a large class of economies, including those featuring private and public ownership.

Signaling with Audits: Mimicry, Wasteful Expenditures, and Non-Compliance in a Model of Tax Enforcement

The audit policy of a tax authority can signal its audit effectiveness. We model this process and show that in limited circumstances an ineffective authority can masquerade as being effective. We show that high maximal penalties imply underreporting of income.