arXiv subjects

Michael Greinecker

Publications and source records attributed to Michael Greinecker.

8 recordsLinked to original sources

arXiv2026

The Set of Correlated Equilibrium Payoffs for a Fixed Information Structure Need Not Be Closed

Aumann (1974) showed that an atomless public randomization device makes the feasible- and equilibrium-payoff sets of a game with a fixed information structure convex, and asked whether they are closed. We show that, in every case the question leaves open, they need not be. One information structure drives all the examples: two sequences of fair signs whose coordinate correlations increase to a ceiling $\rho<1$ that no pair of separately measurable square-integrable rules attains. For every $0<\rho<1$ it yields a three-player game with a public randomization device whose equilibrium-payoff set is exactly the open interval $\{(0,0,t):-\rho<t<\rho\}$; a two-player game with a public randomization device whose equilibrium-payoff set is convex, full dimensional, and not closed; and, without any public device, nonclosed feasible- and equilibrium-payoff sets, the latter along equilibria with unique best replies modulo null events whose payoffs approach a vector that is not even feasible. With distinct but mutually absolutely continuous subjective priors, even the feasible-payoff set can fail to be closed in the presence of an objective public randomization device, together with every $\varepsilon$-equilibrium payoff set and the set of induced law tuples. Our construction also allows us to resolve a conjecture of Stinchcombe (2011). The main results and the lemmas supporting them are formalized in the Lean proof assistant; an appendix records the exact coverage of each statement, including the clauses for which only a paper proof is given.

econ.TH↗

arXiv2026

Many-to-many stable matching in large economies

We study stability notions for networked many-to-many matching markets with individually insignificant agents in distributional form. Outcomes are formulated as joint distributions over characteristics of agents and contract choices. Characteristics can lie in an arbitrary Polish space. We provide a mechanical method for transferring existence results for finite matching models to large matching models for many stability notions. In particular, we show that tree-stable and pairwise-stable outcomes exist.

econ.TH↗

arXiv2026

The Core in a Distributional Economy

An economy, large or small, has traditionally been defined in terms of an explicit set of agents and an assignment of characteristics to each agent. But when individual agents are negligible, most economically relevant properties of an economy can be defined in terms of the distribution of characteristics alone. Agents need not be specified. It has been frequently asserted that the distributional description of an economy is too sparse for core analysis. Notions of coalitions and blocking require the individualistic description of agents. This paper shows that this is not so. The presence of blocking coalitions can be directly identified in terms of distributions alone. Indeed, we give a purely distributional proof of the classical core-equivalence theorem that delivers the core-equivalence theorem for individualistic economies as a corollary. Our methods have applications outside of general equilibrium theory. They apply to large matching markets and to analogs of the Shapley-value for atomless economies.

econ.TH↗

arXiv2026

Sequential Equilibria in a Class of Infinite Extensive Form Games

Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a class of infinite extensive form games in which information behaves continuously as a function of past actions and define a natural notion of sequential equilibrium for this class. Sequential equilibria exist in this class and refine Nash equilibria. In standard finite extensive-form games, our definition selects the same strategy profiles as the traditional notion of sequential equilibrium.

econ.TH↗

arXiv2025

Strict Comparisons of Infinite Utility Streams

There exists a preference relation on infinite utility streams that does not discriminate between different periods, satisfies the Pareto criterion, and so that almost all pairs of utility streams are strictly comparable. Such a preference relation provides a counterexample to a claim in [Zame, William R. ``Can intergenerational equity be operationalized?'' Theoretical Economics 2.2 (2007): 187-202.]

econ.TH↗

arXiv2025

Interim correlated rationalizability in large games

We provide general theoretical foundations for modeling strategic uncertainty in large distributional Bayesian games with general type spaces, using a version of interim correlated rationalizability. We then focus on the case in which payoff functions are supermodular in actions, as is common in the literature on global games. This structure allows us to identify extremal interim correlated rationalizable solutions with extremal interim Bayes-Nash equilibria. Notably, no order structure on types is assumed. We illustrate our framework and results using the large versions of the electronic mail game and a global game.

econ.TH↗

arXiv2023

Robust equilibria in cheap-talk games with fairly transparent motives

For cheap-talk games with a binary state space in which the sender has state-independent preferences, we characterize equilibria that are robust to introducing slight state-dependence on the side of the sender. Not all equilibria are robust, but the sender-optimum is always achieved at some robust equilibrium.

econ.TH↗

arXiv2022

Limit Orders and Knightian Uncertainty

A range of empirical puzzles in finance has been explained as a consequence of traders being averse to ambiguity. Ambiguity averse traders can behave in financial portfolio problems in ways that cannot be rationalized as maximizing subjective expected utility. However, this paper shows that when traders have access to limit orders, all investment behavior of an ambiguity-averse decision-maker is observationally equivalent to the behavior of a subjective expected utility maximizer with the same risk preferences; ambiguity aversion has no additional explanatory power.

econ.TH↗