ABSTRACTS. Computing time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty

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1 ABSTRACTS Łukasz Balbus Wrocław University of Technology Kevin Reffett Arizona State University Łukasz Woźny Computing time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty We study the question of existence and computation of time-consistent Markov policies of quasi-hyperbolic consumers under a stochastic transition technology and borrowing constraints. Under standard assumptions on preferences, as well as a mild geometric condition on a transition probabilities, we prove existence of the greatest and the least time-consistent policies, and provide conditions for (Lipschitz) continuous and monotone equilibria. We show how our methods extend the results in Harris and Laibson (2001). We present a simple approximation scheme for extremal equilibrium, and provide some monotone equilibrium comparative statics results in the model's deep parameters. Aristotelis Boukouras Georg-August University Goettingen Kostas Koufopoulos University of Warwick Information Aggregation and Adverse Selection We consider a general economy, where agents have private information about their types. Types can be multi-dimensional and potentially interdependent. We show that, if the interim distribution of types is common knowledge (the exact number of agents for each type is known), then a mechanism exists, which is consistent with truthful revelation of private information and which implements first-best allocations of resources as the unique Bayes- Nash equilibrium. Our result requires weak restrictions on preferences (Local Non-Common Indifference Property) and on the Pareto correspondence (Anonymity) and it is robust to small perturbations regarding the knowledge of the interim distribution. Our paper is useful in understanding the power of information aggregation in alleviating incentive constraints and is particularly pertinent to games with large populations, in which case the interim distribution of types converges to a unique distribution.

2 Robert Golański Properties of matching algorithm in college admission problem with variable capacity quotas The standard matching college admission models analyzed in the literature assume that in a two-sided, many-to-one, matching problem colleges set fixed admission quotas, which are then filled based on preferences of students. This paper analyzes a related problem, in which the quotas set by colleges are not fixed and predetermined, but instead are themselves determined based on the students' preferences. The properties of matching algorithms under such setup are studied. We show that stability and monotonicity properties need not be satisfied by the standard matching rules. Strategic behavior of students is analyzed - by revealing their preferences strategically, students can influence quotas assigned to particular colleges and be in effect admitted to a college which is more preferred by them than one that they would be admitted to if they sincerely revealed their true preferences. We analyze the effects of such strategic behavior and the extent to which such manipulability is possible Grzegorz Grabek National Bank of Poland Skewness in DSGE Models

3 Aleksander Jakimowicz University of Warmia and Mazury in Olsztyn Polish Academy of Sciences, Institute of Economics Sources of Complexity in R. M. Goodwin Business Cycle Model Goodwin s model, which was formulated in 1951, still attracts economists attention. The model possesses numerous interesting properties that have been discovered only recently due to the development of the chaos theory and the complexity theory. The first numerical explorations of the model were conducted in the early fifties of the twentieth century by Strotz, McAnulty and Naines (1953). They discovered coexistence of attractors and, nowadays well-known, two properties of chaotic systems: the sensitive dependence on the initial conditions and the sensitive dependence on parameters. The occurrence of periodic and chaotic attractors is dependent on the value of parameters in a system. In case of certain parametric values there occur fractal basin boundaries which results in enormous system sensitivity to external noise. If periodic attractors are placed in the neighborhood of the fractal basin boundaries, then even a low external noise can move the trajectory into the region in which the basins structure is tangled. This leads to a kind of movement that resembles a chaotic movement on a strange attractor. In the Goodwin s model, apart from typical chaotic behavior, there exists yet another kind of complex movements transient chaotic behavior which is caused by the occurrence of invariant chaotic sets that are not attracting. Such sets are represented by chaotic saddles. Some of the latest observation methods of trajectories lying on invariant chaotic sets that are not attracting are straddle methods. The article provides examples of the basin boundary straddle trajectory and the saddle straddle trajectory. These cases were studied by Lorenz and Nusse (2002). I supplement the results they acquired with calculations of capacity dimension and correlation dimension.

4 Michał Karpowicz Warsaw University of Technology On the Nash Equilibrium Design Problem: the case of price-anticipating agents The following special case of the Nash equilibrium design problem is addressed: how to implement a solution to the constrained optimization problem in a Nash equilibrium point of the game in which agents solving decomposed subproblems anticipate values of Lagrange multipliers. The key result to be presented gives conditions for Nash-implementation of a regular and isolated optimum for the class of continuously differentiable optimization problems with equality constraints. The result also provides a description of the Nash equilibrium design procedure that can be applied in multi-agent environments to reduce adverse effects of the expected price-anticipating strategies. As a case study the analysis of the mechanism (or game) design costs will be presented for the class of linear-quadratic problems. In particular, the hierarchical mechanism design game played between the mechanism designer and agents capable of anticipating values of Lagrange multipliers will be investigated. Fundamental properties of the developed mechanisms, namely, incentive compatibility, individual rationality and budget balancing conditions, will be illustrated in the considered setting, as well. Kostas Koufopoulos University of Warwick Endogenous Commitment and Nash Equilibria in Competitive Markets with Adverse Selection In this paper, we provide a unified framework for analyzing competitive markets with adverse selection. The key feature of our model is that whether the firms (uninformed) are committed to the contracts they offer or not is determined endogenously. Due to endogenous commitment, our model always has a unique Bayes-Nash equilibrium without using any refinement to restrict beliefs off-the-equilibrium path. We show that both the non-existence problem in the two-stage screening games and the multiplicity of equilibria in the three-stage screening and the signalling games are due to exogenous full commitment (non-existence) and exogenous lack of commitment (multiplicity).

5 Michał Lewandowski Gambles with prices and operational measure of riskiness. In this paper I analyze operational measure of riskiness defined by Foster and Hart (2007). I give simple intuition behind their main result. Then I extend the concept of riskiness measure in two respects - I define a generalized riskiness measure based on decreasing absolute risk aversion utility function. I derive necessary and sufficient conditions for existence of such measure for DARA and CRRA class of utility functions. In addition, I show the way how to compare riskiness of gambles with negative expectation or with nonnegative outcomes only. To this end I use properties of buying and selling price for a lottery and their relations to riskiness measure. In particular, I show how buying and selling price for a lottery concepts may be used complementary to the concept of riskiness measure. Agnieszka Lipieta, Andrzej Malawski Cracow University of Economics Machanisms of Schumpeterian Evolution The paper extends the research program of modeling the Schumpeterian vision of innovative development in the Arrow - Debreu theory of general equilibrium. The core of this set - up is based on modeling of the two fundamental forms of economic life distinguished by Schumpeter, namely the circular flow and economic development by specific extensions of the production system being a part of the Debreu private ownership economy, so that the analysis includes static as well as dynamic forms. In this context the paper aims at studying the mechanisms of Schumpeterian evolution in the conceptual apparatus of the modern theory of economic mechanisms. To this purpose two mechanisms of Schumpeterian innovative evolution are studied. First, price mechanism corresponding to the circular flow, and second, qualitative mechanism based on innovations. Wojciech Olszewski, Diego Klabjan, Asher Wolinsky Northwestern University Attributes An agent makes the decision whether to acquire an object. Before making this decision, she can discover, at some cost, some attributes of the object (such as beauty, intelligence or personality of a potential spouse). We aim to characterize the optimal set of attributes to be discovered; and if the agent is allowed to discover attributes sequentially, the ordering in which the attributes should be discovered. We also study a dynamic matching model in the style of Burdett and Coles, QJE 1997, and show the existence of non-monotonic steady states. In such steady states, agents reject objects when they discover a higher value of an attribute and accept objects with lower values of the attribute, because of the lower values give better signals regarding other attributes. This happens even when the attributes are independent random variables.

6 Tymon Słoczyński Population Average Gender Effects In this paper I develop a consistent estimator of the population average treatment effect (PATE) which is based on a nonstandard version of the Oaxaca-Blinder decomposition. What follows, I extend the recent literature which has utilized the treatment effects framework to reinterpret this technique, and propose an alternative solution to the reference group choice problem that is inherent therein. Moreover, I use the new estimator of this paper and its semiparametric extension to decompose gender wage differentials with the Current Population Survey (CPS) data, while providing separate estimates of the average gender effect on men, women, and the whole population. Tomasz Strzalecki Harvard University Temporal Resolution of Uncertinity and Recursive Models of Ambiguity Aversion Models of ambiguity aversion have recently found many applications in dynamic settings. This paper shows that there is a strong interdependence between ambiguity aversion and the preferences for the timing of the resolution of uncertainty, as defined by the classic work of Kreps and Porteus (1978): the modeling choices that are being made in the domain of ambiguity aversion influence the set of modeling choices available in the domain of timing attitudes. The main result of the paper is that the only model of ambiguity aversion that exhibits indifference to timing is the maxmin expected utility of Gilboa and Schmeidler (1989). This paper also examines the structure of the timing nonindifference implied by the other commonly used models of ambiguity aversion. The interdependence of ambiguity and timing that this paper identifies is of interest both conceptually and practically - especially for economists using these models in applications.

7 Zbigniew Świtalski University of Zielona Góra Price Equilibria in a Gale-Shapley Market Model We define price equilibria (competitive market equilibria) in some kind of market model based on Gale-Shapley model of college admissions. We show that equilibria allocations in our model are exactly the stable matchings in the sense of Gale and Shapley, i.e. we show that a matching u is stable if and only if it is a competitive equilibrium allocation. The result is analogous to a result for the simplest version of Shapley-Shubik model (called the assignment game ) which can be very roughly formulated as follows: The assignment u is optimal if and only if it is a competitive equilibrium allocation ). The main difference between our model and the SS model is that in our model the buyers preferences are independent on prices (and in the SS models they depend on prices and hence the definition of equilibrium is quite different).