Equilibria in dynamic games with recursive payoffs and behavioral discounting, 2020
(joint with Lukasz Balbus and Kevin Reffett)

At least since Ramsey (1928) or Koopmans (1960) the question of discounting in assessing values of future utility streams has played an important role in work in many fields in economics. In particular, discounting affects intertemporal tradeoffs and makes an explicit account of the distant future and therefore encompasses motives related to sustainability, transmission to offsprings and altruism. Many of the analyzed models of preferences over time are normative, i.e. they assume the objective is given by the separable, exponentially discounted utility. Another source of normative representations of preferences over time is proposed by social sciences and include concepts such as ‘‘just savings’’ or ‘‘sustainable development’’. On the contrary, behavioral models try to accommodate behavior that is consistent with empirical or experimental observations (see e.g. models of hyperbolic or quasi-hyperbolic discounting). With a notable exception of exponential discounting, both normative and behavioral models typically lead to time-consistency problems. The question of design and computation of optimal among time consistent plans has received a great attention in economic literature. This also includes important from behavioral (and numerical) perspective short memory decision rules, like Markov ones. In this paper we prove existence of Markov Stationary Equilibrium in a wide class of dynamic models with generalized discounting involving both behavioral and normative applications. In particular we show existence of MSE (and related time-consistent solution) in a deterministic model of consumption-saving with beta-delta discounting and its generalized, semi-hyperbolic versions. We also show existence of MSE (and its approximation) in a model of collective choice for agents with different discount factors.


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.


Distributional equilibria in dynamic supermodular games with a measure space of players and no aggregate risk, 2019
(joint with Lukasz Balbus, Pawel Dziewulski and Kevin Reffett)

In this one we study a class of discounted infinite horizon stochastic games with strategic complementarities with a continuum of players. In order to analyse transition of private signals to aggregate distributions, we develop a dynamic law of large numbers, that implies a.o. no aggregate uncertainty. We define a suitable equilibrium concept, namely: Markov Stationary Equilibrium and prove its existence under a new set of assumptions, via constructive methods. Our construction allows to overcome some problems in characterizing beliefs and dynamic complementarities in a class of games recently studied by Mensch (2018). In addition, we provide constructive monotone comparative dynamics results for ordered perturbations of the space of games (extending those of Acemoglu, Jensen (2014) and Light, Weintraub (2019) from steady states or invariant measures to dynamic equilibria). For this end, we use our new fixed point comparative statics theorem, suitable for comparing equilibrium objects in spaces of distributions or measurable functions. Finally, we discuss the relation of our result to the literature on equilibria in oblivious strategies of e.g. Weintraub, Benkard, Van Roy (2008), Adlakha, Johari, Weintraub (2015) and recent works on large but finite dynamic games (Kalai, Shmaya 2018) providing approximation of our large game by its small counterparts. We provide numerous examples including social dissonance models, dynamic global games, keeping up with the Joneses or OLG economies with intergenerational interactions.


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].