Iterative monotone comparative statics, 2023
(joint with Lukasz Balbus and Wojciech Olszewski and Kevin Reffett)

We propose a novel approach to equilibrium comparative statics in economic environments where complementarities play a critical role, including environments in which the existing methods for obtaining monotone comparative statics appear inadequate. Our approach is dynamic and, methodologically, in the spirit of the celebrated ''correspondence principle'', a concept first presented in the work of Samuelson (1947). It applies even to: (a) environments with a continuum of equilibria (b) environments in which all equilibria are unstable; and (c) chaotic environments, in which adaptive learning sequences may not converge. Finally, our propositions extend several previously existing results.

On journal rankings and researchers' abilities, 2023 (joint with Wojciech Charemza and Michal Lewandowski)

Over the last few years, ranking lists of academic journals have become one of the key indicators for evaluating individual researchers, departments and universities. How to optimally design such rankings? What can we learn from commonly used journal ranking lists? To answer these questions, we propose a simple model of optimal rewards for publication in academic journals. Based on a principal-agent model with researchers' hidden abilities, we characterize the second-best journal reward system, where all available journals are assigned to one of several categories or ranks. We provide a tractable example that has a closed-form solution and allows numerical applications. Finally, we show how to calibrate the distribution of researchers' ability levels from the observed journal ranking schemes.

A Tarski-Kantorovich theorem for correspondences, 2023
(joint with Lukasz Balbus and Wojciech Olszewski and Kevin Reffett)

For a strong set order increasing (resp., strongly increasing) upper order hemicontinuous correspondence mapping a complete lattice A into itself (resp., a sigma-complete lattice into itself), we provide conditions for tight fixed-point bounds for sufficiently large iterations starting from any initial point in A. Our results, hence, prove a generalization of the Tarski-Kantorovich principle. We provide an application of our results to a class of social learning models on networks.

Dynastic preferences, recursive utility and time consistency, 2023
(joint with Lukasz Balbus and Kevin Reffett)

We consider a class of infinite horizon, stochastic, non-stationary dynastic consumption-savings models with a general forms of recursive, time-varying altruistic preferences including direct and indirect pure altruism as well as paternalistic altruism. It is well-known such models lead to time-inconsistent dynastic preferences. Within this class of economies, we propose a novel set-iterative procedure for characterizing all Markov perfect time-consistent solutions in the space of increasing investments. Our approach involves both: value functions and policy iterations. We prove existence of Markov Perfect equilibria in stationary, periodic and also non-stationary strategies. We provide numerous applications to altruistic growth models, behavioral discounting models and collective household models and also discuss the role of various certainty equivalence operators.

On collective intertemporal choice, time-consistent decision rules and altruism, 2021 (joint with Lukasz Balbus and Jean-Pierre Drugeon)

We consider a dynamic decision problem of a collective-household with heterogeneous discount factors. We prove existence a time-consistent decision rule in Markovian policies. In fact, decision rules we consider are characterized by monotone and Lipschitz continuous investments policies. We provide sufficient conditions for the validity of the (generalized) first-order approach. Finally, we propose a novel method to approximate the constructed decision rule by a sequence of equilibria of bequest games with paternalistic altruism.

Efficiency in rewarding academic journal publications. The case of Poland, 2021 (joint with Wojciech Charemza and Michal Lewandowski)

We consider the efficiency of a mechanism for incentivising publication in academic journals where a research supervisory body awards points for papers that appear in quality publications. Building on the principal-agent literature with hidden types, we assume that such a body wants to maximise the expected prestige of academic disciplines. It sets up a reward system so that researchers who are aiming to maximise their own rewards also maximise the objective function of the research supervisory body, through their submission decisions. The model is calibrated to the reward scheme introduced within the Polish higher education reform in 2018, for which a series of policy recommendations is given.

Interim correlated rationalizability in large games, 2020
(joint with Lukasz Balbus, Michael Greinecker and Kevin Reffett)

In this paper we provide general theoretical foundations for modeling strategic uncertainty in large distributional Bayesian games of with general type spaces in terms of a version of interim correlated rationalizability. We then focus on the case that payoff functions are supermodular in actions as in much literature on global games. This allows us to identify extremal interim correlated rationalizable solutions with extremal interim Bayes-Nash equilibria. No order structure on types is used.

Supermodular comparative statics, 2019
(joint with Pawel Dziewulski)

An important set of questions in economics concern how changes in the model’s exogenous parameters (income, wealth, productivity, distortions, information, etc.) impact individual choices and market outcomes. In this paper, we develop a theory of supermodular comparative statics that addresses this set of issues. Specifically, we show ordinal and cardinal conditions one should impose on the optimization problem so that its solution is a supermodular function or a supermodular correspondence. We illustrate application to industrial organization, diversity and performance, supermodular stochastic orders and extensive form games with strategic complements.

Repeated moral hazard with costly self-control, 2017

In this paper I solve for the optimal dynamic contract when an agent exhibits costly self control, demonstrating that reduction of agent’s temptations can provide incentives. Intrinsic motivation is most powerful when temptations are high. Then, the moral hazard problem can be mitigated. The optimal contract calls for a lower bonus deferral than for agents with no temptations. Under limited commitment, presence of self-control also reduces agent’s willingness to break or renegotiate the contract, and can make the optimal contract spot implementable. Impact of self-control on the cost of implementation as well as on willingness to save is ambiguous.

An experiment on temptation and attitude towards paternalism, 2017
(joint with Michal Krawczyk)

In this project we investigate experimentally the link between self-control and attitude towards paternalism in the context of food choice. We invite our subjects for a free lunch: a beef burger or a turkey. We verify in a pre-test that the beef burger is considered (much) more tasty and tempting, while the turkey is seen as healthier. In the experiment proper, we observe what menus subjects assign to one another – i.e. whether they let them choose or paternalistically assign the healthy option. We also record how they react to such choices made for them by another subject. Finally, we give them an opportunity to restrict future choices for themselves (a commitment device useful in case of self-control problems). There is a strong link between these three tendencies, suggesting a common thread underlying the use of commitment devices and paternalistic behavior as well as approval thereof in environments involving temptations. We discuss policy implications of our findings.

Some others

Lecture notes on Microeconomics, ISBN: 978-83-65416-11-7, Agencja Reklamowa TOP, 2016 [pdf].

Wodzeni na ekonomiczne pokuszenie, Obserwator finansowy, 2015 [link].

Niespójnosc czasowa decyzji, czyli o zeglowaniu, przestawianiu budzika i rzucaniu palenia
[wspólautor M. Jakubczyk], Gazeta SGH, nr 252, [pdf].

Wynagrodzenia polskich menedzerów: wysokie, ale malo motywujace
[wspólautor: A. Kunysz], Harward Business Review, nr 63, 2008, [Link].

Komplementarnosc dóbr i zachowan w ekonomii
[wspólautor M. Jakubczyk, M. Knauff], Gazeta SGH, nr 226, 2006, [pdf].

Drazliwy temat
[wspólautor K. Latuszynski], Personel i Zarzadzanie, nr 5 (194), 2006, [pdf].