Quasi-hyperbolic discounting

We proposed a set of tools for studying Markov stationary equilibria (time consistent policies) in a class of quasi-hyperbolic discounting consumption saving models. Our results involve conditions for equilibrium existence, its comparative statics, computability and uniqueness. Most notably in JET 2022 we proved a general equilibrium existence for deterministic and stochastic consumption-saving and growth models.

Large games

Here we studied large games in their distributional and individualistic versions. Most of the papers focused on supermodular versions of these games. In the 2025 working paper we show how to model aggregate, strategic uncertainty in large Bayesian games w/o common priors. We also proved BNE existence and constructed a universal type spaces for this class of games.

  • Interim correlated rationalizability in large games, 2025 (with L.Balbus, M.Greinecker and K.Reffett).
  • Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk, Theoretical Economics, 2022, (with L.Balbus, P.Dziewulski and K.Reffett), [PDF].
  • A qualitative theory of large games with strategic complementarities, Economic Theory, 2019, (with L.Balbus, P.Dziewulski and K.Reffett), [PDF].
  • Monotone equilibria in nonatomic supermodular games. A comment, Games and Economic Behavior, 2015, (with L.Balbus and K.Reffett), [PDF].
  • Differential information in large games with strategic complementarities, Economic Theory, 2015, (with L.Balbus, P.Dziewulski and K.Reffett), [PDF].

Stochastic games

Over the years we analyzed an open question of existence of Markov stationary equilibria in N-player stochastic games. We contributed by showing some new equilibrium existence conditions and most notably showed how to compute them in some cases. We also proposed a short-memory version of a celebrated APS procedure.

  • Stochastic Games of Risk-Sensitive Players with Quasi-Hyperbolic Discounting, Automatica, 2026 (with A.Jaskiewicz and A.S.Nowak), [PDF].
  • A strategic dynamic programming method for studying short-memory equilibria of stochastic games with uncountable number of states, Dynamic Games and Applications, 2016, (with L.Balbus), [PDF].
  • A constructive study of Markov equilibria in stochastic games with strategic complementarities, Journal of Economic Theory, 2014, (with L.Balbus, and K.Reffett), [PDF].
  • Markov stationary equilibria in stochastic supermodular games with imperfect private and public information, Dynamic Games and Applications, 2013, (with L.Balbus, and K.Reffett), [PDF].

Bequest games and altruism

Here another set of results for studying equilibria in games of intergenerational altruism. These are games between parents and kinds over bequests. In the 2024 working paper we advocate a new class of non-stationary Markov equilibria to characterize time consistent solutions in very general class of such games. Look also there for periodic equilibria to understand some computability or indeterminacy problems reported for this class of games. This set of papers also involve one of my only few experiments correlating temptations and paternalism.

Fixed points and comparative statics

In these papers we proposed a new, iterative method for conducting equilibrium comparative statics in monotone environments. It is order theory based only and not restricted to extremal equilibria. Look up whenever your traditional comparative static methods are too restrictive.

Indifference prices and preferences over prospects

This is our new research agenda on measuring uncertainty. It involves studying loss aversion and identifying reference points via indifference prices over prospects. Puzzled by WTA-WTP disparity? We show its not a behavioral phenomenon but a nice measure of uncertainty aversion.

Recursive competitive equilibrium

Having my macro class with Ed Prescott I couldn't resist to write these papers on consequences / limits of recursive competitive equilibria.

  • Lipschitz recursive equilibrium with a minimal state space and heterogeneous agents, Journal of Mathematical Economics, 2019, (with R.Raad), [PDF].
  • Comparing recursive equilibrium in economies with dynamic complementarities and indeterminacy, Economic Theory, 2018, (with M.Datta and K.Reffett), [PDF].

Journal rankings

These two papers were a by-product of having to live in a world of academic incentives in Poland.

Costly self control

How a principal can use agents' temptations for its own benefit? It is possible to price commitment assets on a market? I answer these and other relate questions below.