This is my personal webpage, updated on 01/06/2019. I am currently a Professor of Economics at NYU AD (on leave from Yeshiva University).

**Scientific service**: Co-Editor, Journal of Mathematical Economics; Associate Editor, Math. Soc. Sciences and Annals of Finance; Co-organizer, the Cowles Foundation Conference on General Equilibrium and Its Applications, Yale University.

**Old business**: Chair, the 2013 NBER/NSF/CEME seminar on general equilibrium and mathematical economics, Columbia Business School, New York City co-sponsored by Yeshiva University. The Cowles GE conference started before 2006, and the NBER/NSF/CEME conference was 6 years ago already...Time flies! THIS PAGE IS UNDER CONSTRUCTION

**Recently published papers:**

- “
*Designing competitive markets in large moral hazard economies**with nonexclusive contracts*”, with P. Siconolfi,__Economic Theory__, 2016, vol. 62, 325-360. We design competitive markets in large insurance economies with moral hazard, under the additional constraint that contracts may not be exclusive. In particular, we consider the situation where contracts are verifiable and enforceable within a local market, but globally, i.e., across markets, they are not. Agents can buy (or sell) insurance contracts in multiple markets subject to a (global) budget constraint. Because of local exclusivity, at equilibrium firms make zero profits. Equilibria are indeterminate and the 'best safe' contract is always an equilibrium, whereas incentive efficient contracts may not be an equilibrium with nonexclusivity. However, with*a Wilsonian or a forward induction refinement, we show that equilibrium is always 'third best' efficient*.

- “
*Incentive efficient price systems in large insurance economies with adverse selectio*n”, with P. Siconolfi,__International Economic Review__, 2016, vol. 57, 1027-1056. Motivated by Prescott and Townsend's (1984) original question on the decentralization of incentive efficient allocations through Walrasian markets, and using Gale's (1992) insight that such markets should not price individual trades in isolation, we study a Walrasian market for*mechanisms*in large insurance economies. The price system here is a substitute for rationing, typically used in matching models -directed search- to clear markets. Guided by the game-theoretic literature and our own study of refinement notions in this setup (see our JME below), we adapt C. Wilson's (1977) notion of 'anticipatory equilibrium' to this competitive market setup, and use it to define a competitive equilibrium in these matching markets -a 'no-price-cut' equilibrium (see also Makowski and Ostroy's notion of 'no surplus equilibrium'). We show that under standard, mild 'sorting' conditions, shared by, e.g., the directed search literature, our equilibrium exists and is incentive efficient. We also provide a way to compute an equilibrium via the solution to a programming problem. We provide examples of other classical adverse selection setups where our competitive market equilibrium works well. - "Uniqueness of competitive equilibrium with solvency constraints under gross substitution", with G. Bloise,
__Journal of Mathematical Economics__, 2015, vol. 61, 287-295. Under a gross substitution assumption, we prove existence and uniqueness of competitive equilibrium for an infi nite-horizon exchange economy with limited commitment and complete financial markets. Risk-sharing is limited as only a part of the private endowment can be used as collateral to secure debt. The unique equilibrium is Markovian with respect to a minimal state space consisting of exogenous shocks and Negishi's welfare weights. We represent equilibrium dynamics via a monotone operator acting on entire wealth distribution functions. We construct a fixed point of this operator generating a lower and an upper orbit and proving coincidence of accumulation points. The paper*de facto*offers a proof of existence for the Gottardi and Kubler, REStud 2015, model.

- “
*Group stability in matching with interdependent values*”, with A. Chakraborty, M. Ostrovsky,__Review of Economic Design__, 2015, vol. 19, 3-24. In the two-sided many-to-one matching markets with interdependent valuations and one-sided incomplete information, pairwise stability (see Chakraborty et al. (2010)) does not imply group stability: mechanisms that are stable with respect to deviations by pairs of agents may be vulnerable to deviations by groups. We formalize a notion of group stability in these settings. We construct a "modified serial dictatorship" mechanism that implements group stable matchings. We show that any nonvacuous notion of group stability with interdependent values makes necessary the restrictions on within-coalition communication and on counterproposals embedded in our notion. We finally examine efficiency properties of modified serial dictatorship: aside from pure common value or affiliated environments where private values enter in specific ways, modified serial dictatorship fares better than simple serial dictatorship.

- “
*Refinemenents and incentive efficiency in Walrasian models of insurance economies*”, with P. Siconolfi,__Journal of Mathematical Economics__, 2014, vol. 50, 208-218. We consider models of large insurance economies where markets price mechanisms -an extension of Gale's (1992) idea of Walrasian markets with adverse selection, applied to one-sided incomplete information economies. We show that commonly used refinement notions for the equilibrium set based on stability or forward induction generally do not suffice to guarantee that the equilibrium allocation is incentive efficient. As a by-product of the analysis, we prove existence of forward induction equilibria in the 2-states-2-types version of these economies -a novel result in itself, given the more general setup of the model when compared with standard game-theoretic analyses of the problem.

- “
*Recursive equilibria in stochastic OLG economies: Incomplete markets*”, with P. Siconolfi,__Journal of Mathematical Economics__, 2012, vol. 48, 322-337. Here we show that our previous result on generic existence of recursive equilibrium can be given more economic substance: financial markets can be incomplete, there could be production, long-lived assets in positive net supply, idiosyncratic risks, and so on. The result still holds provided there is enough intra-cohort household heterogeneity, and also given that financial assets connect savings in all histories and transition probabilities are different across (the exogenous) states --two generic conditions. The paper proves and uses a cascading version of the transversality theorem for families of functions, substantially generalizing the standard submersion condition applied to a map.

**Slightly older papers**:

- “
*Two-sided matching with interdependent values*”, with A. Chakraborty and M. Ostrovsky,__Journal of Economic Theory__, 2010, vol. 145, 85-105. When values are interdependent, assignment problems cannot be transparent lest the assignment mechanism be pairwise unstable -where the notion of stability must take into account the information revealed to agents after the assignment outcome takes place. If the mechanism only reveals the individual outcome privately to each agent, then a simple serial dictatorship mechanism is pairwise stable provided there's homogeneity of preferences on one side of the matching market. The paper explicitly uses the notion of anticipated renegotiation in constructing nonexistence examples. Applications include school-student problems, as well as 'task delegation' problems by an expert.

- “
*Recursive equilibria in stochastic OLG economies*”, with P. Siconolfi,__Econometrica__,*2010*, vol. 78, 309–347. A majority of macro and asset pricing models discussing the impact of the demographic structure on economic and financial variables -social security, unemployment distribution, stock market returns, and so on- uses a simplified notion of equilibrium known as 'recursive', a time-homogeneous Markov equilibrium for stationary economies where the state space is naturally given by the exogenous current shocks to the economy -TFP, individual productivity, marital status, liquidity- and by the current asset distribution. See, e.g., Ljungqvist and Sargent (2002). While approximate recursive equilibria can be at times used to simulate dynamic economies, their interpretation is doubtful when engaging in welfare comparisons or comparative statics exercises -e.g., what happens if we reform social security? Given the computational and epistemological appeal of the exact recursive equilibrium, we provide a proof of its existence in OLG economies with complete financial markets. The result holds provided there is enough intra-cohort household heterogeneity.

**Working papers:**

**Competitive equilibrium with private information** The profession is by now used to studying asymmetric information issues almost entirely in game-theoretic terms, often within the mechanism design problem (even with multiple principals and multiple agents). However, when competition is brought into the picture this hides** **an important point. Firms offering even exclusive contracts, or more generally menus of contracts, cannot prevent agents to liberally trade these contracts *before* entering a bilateral, exclusive, relation with a firm. To put it differently, monitoring trades in contracts is different than monitoring trade within a contract. The former may not be feasible (in occupational choice problems, a firm hiring a worker may force exclusivity clauses at the present job, but cannot monitor the worker's previous or future employment choices; tickets to sports events can be traded before the event takes place, but outside a venue's control, and is referred to 'scalping'; there are web platforms now that allow for these tickets to be exchanged). Mechanisms are the natural 'commodities' in markets where there is asymmetric information.
For example, in an insurance market, contracts are offered with
multiple options for quoted premium and coverage, together with the
possibility of financing their payments. We call these objects
'mechanisms'.

What trading system can be used to trade these mechanisms, while delivering constrained efficient outcomes and minimizing monitoring of individual trades or knowledge of the type distribution in the population? A Walrasian *market for mechanisms*, where the agents' only constraint is their budget, is the simplest way to guarantee anonymity and universality of trade.

To design a market for mechanisms, we follow the *Hylland and Zeckhauser* (1979) and *Prescott and Townsend* (1984) insights. Each mechanism is a commodity, with an associated Debreuvian price expressed in units of account: this price can be thought of as a ticket price to enter a mechanism.** **Only one mechanism can be entered, in the end. Thus, trade in tickets can occur, but tickets in multiple venues can only be purchased as lotteries over
tickets.** ** Formally, this means subjecting every agent's
choice to a budget constraint in lotteries. Lotteries are an agent's
consumption set. Firms offer seats or tickets at mechanisms selling tickets (or ticket lotteries).

In a competitive market, intermediaries buy and sell these lottery bundles making their prices linear in quantities, i.e., in lotteries. An agent has trading opportunities which do not appear in the standard game-theoretic formulation of this problem. For example, via a lottery an agent can buy a contract by selling another one. The income effect induced by lotteries -simply, via the budget constraint- can in principle** **affect equilibrium behavior and compromise the well-functioning of markets. For example, when there is adverse selection, ticket trading provides low-risk types ways to access actuarially favorable contracts, distorting the market away from efficiency.** **Will these markets perform efficiently?

In general, the answer is no, as there are a lot of (rational expectations, or Nash) equilibria. Standard equilibrium conditions do not pin down beliefs at inactive mechanisms. Thus, equilibrium prices may still leave surplus or profits on the table, which firms do not extract because of 'wrong beliefs'. In "Refinements and Incentive Efficiency..." we discuss why, under adverse selection, standard game-theoretic notions of refinements do not generally lead to efficient outcomes in these markets -unless trade is restricted to feasible (balanced) mechanisms (but should it be?). Forward induction is used in the related 'directed search' interpretation of these markets (where centralized rationing, instead of prices, clears markets), but no claim of efficiency is made (see Guerrieri et al. 2010). If equilibrium prices are instead subject to a 'no surplus' condition motivated by previous work by Makowski-Ostroy-Wilson, which we label 'no-price-cuts', efficiency is attained: see "Incentive Efficient Price Systems...".

In the first paper below, we extend the approach developed in "Incentive Efficient Price Systems..." to markets with multiple (standard) commodities, as in Akerlof's lemons market, but moving away from the Akerlovian view that identifies agents prior to trade into 'buyers' and 'sellers'. We show that the endogenous character of demand and supply may induce the need for cross-subsidies at the constrained efficient outcome even when the number of high types is low, an impossible effect in insurance economies. Akerlof's markets are constrained inefficient while our 'no-price-cuts' equilibria achieve this efficiency.

- “
*An incentive efficient market for mechanisms in large Akerlof economies*”, with P. Siconolfi, mimeo Dec 2018. [Warning: I am leaving an older version online as it contains supplemental material (proofs) for the most recent, and expanded, version of the paper, which can be found here.] We design a Walrasian market in large multiple-good economies with adverse selection, where goods differ in quality depending on their original owner, quality is 'vertical', and any individual -privately informed or not- may want to consume goods of different qualities. These economies are genuinely different than an insurance economy, because at least two are the physical goods that markets need to clear --e.g., 'money' and 'cars' in Akerlof's 'lemons' market-- and because there is a quantity vs. quality trade-off. We embed these economies into the framework we developed for insurance economies (see the IER paper) to decentralize incentive efficient allocations. Under standard, mild sorting assumptions we prove existence of an 'no-price-cuts' equilibrium. We compute one such equilibrium using a notion of 'generalized best-for-high-quality Walrasian incentive compatible' allocation, finding a fixed point in the space of 'input prices'. We also characterize such allocation and show that it may dominate the highest-price Akerlof equilibrium, and*it may entail subsidies from high quality to low quality goods owners even when there are lots of 'lemons' in the market*. Our design applies, e.g., to financial asset trading with counterparty risk.

What about the moral hazard case? Prescott and Townsend (1984) had already showed that the market we described above almost does the job: one needs to add quantity (that is, incentive) constraints even at the ex-ante stage, and then standard equilibria are constrained efficient. Under forward induction, we show in the paper below that our market design bypasses this 'quantity constraint' drawback (present also in Jerez (2003, 2005) or Rustichini and Siconolfi (2012)). The paper also offers a general framework to embed various types of manipulations -stemming from superior information either on the consumers' side or the firms' side. It thus offers a constrained efficient market even in the presence of some behavioral biases -though it will typically not protect consumers according to the most myopic paternalistic view.

- "Constrained efficient markets for manipulation economies", with P. Siconolfi, mimeo November 2016 (formerly circulated with the title 'Designing constrained efficient markets under moral hazard or hidden information"). We design a competitive market for exclusive contracts in large economies of observable types where trades are subject to manipulations. We do not impose quantity restrictions --incentive constraints--on the consumption or production sets. We establish existence and constrained optimality of equilibrium. Efficiency losses may be derived from restricting agents to trading incentive compatible contracts. Our design can accommodate manipulations stemming from private information as well as from behavioral biases --e.g., time inconsistency and false beliefs. We discuss the size and complexity of the commodity set.

"Designing competitive markets..." above finally studies these markets for mechanisms under moral hazard, but with in addition partial nonexclusivity ex-post. While classic insurance is still the primary reference example of allocation problems tackled by our analysis, it is clear that again securities trading represents another application dealt with by the model, where the uncertainty affected by moral hazard is counterparty risk.

**Dynamic competitive equilibrium** I have been working recently on models with limited commitment, the other big market friction. Here is where I stand.

- "Asset shortages, liquidity and speculative bubbles", with G. Bloise, mimeo 2018. A vast literature explains credit volume collapses via deterioration of agency problems or the arrival of bad news that either lower the payoff of collateral or make lower payoffs more likely. Collateral is, though, often posted or ultimately backed by durables or long-term assets. For such assets, future payoffs reflect both 'dividends' (pledgeable resources) and resale value. Agency problems or bad news negatively affect the amount of pledgeable resources in the economy. Will they affect also the value of collateral, and would this reduce credit volume to zero when dividends vanish? We show that, provided autarky is constrained inefficient, although
pledgeable resources may vanish, collateral does not lose its value in the limit: credit markets keep working and trading volumes remain significant. In the
limit, a bubble appears as in Hellwig and Lorenzoni (2009). Our result applies to economies with incomplete markets, or to
collateral equilibria where asset-specific margin requirements may bind,
so that the payoff valuation functional is only sublinear. Thus, when there are some minimal gains from trade at autarky, vanishing pledgeable resources do not lead to credit crashes. Deterioration of agency problems or the arrival of bad news are not sufficient to create credit market crashes. Instead, we draw attention to endowment dispersion and gains from trade as a fundamental
reason for credit markets to function even with vanishing collateral resources. Similar conclusions hold when some debt is unsecured and sustained by a reputational debt-enforcement mechanism: the weakening
of a severe enough enforcement mechanism does not lead to credit collapse if there are gains from trade at
autarky. Moreover, when unsecured debt is sustained by weak enforcement and the economy suffers a declining supply of outside assets to secure debt, again a bubble forms. The bubble-like behavior of asset prices in their
roll-over debt equilibrium is not drastically different than the
behavior displayed in a market where debt is secured by little
collateral. Our result extends similar conclusions obtained by
*Fahri and Tirole*(2012) in the context of an OLG economy. Our theory of bubble formation does not require abrupt changes in the equilibrium or other discontinuities for bubbles to arise. Our result also shows how studies of liquidity-constrained markets via approximation using no-trade equilibrium (see, e.g., Werning, 2015) can be misleading.